{"id":2290,"date":"2023-05-03T04:47:26","date_gmt":"2023-05-03T04:47:26","guid":{"rendered":"https:\/\/vartmaaninstitutesirsa.com\/?page_id=2290"},"modified":"2024-03-08T03:01:21","modified_gmt":"2024-03-08T03:01:21","slug":"chapter-15-wave-motion","status":"publish","type":"page","link":"https:\/\/vartmaaninstitutesirsa.com\/index.php\/chapter-15-wave-motion\/","title":{"rendered":"Chapter 15\u00a0 Wave motion"},"content":{"rendered":"<h1><strong>Chapter 15\u00a0 Wave motion\u00a0<\/strong><\/h1>\n<p>Transverse and longitudinal waves, speed of wave motion, displacement relation for a progressive wave, principle of superposition of waves, reflection of waves, standing waves in strings and organ pipes, fundamental mode and harmonics, Beats, Doppler effect.<\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><strong><u><span style=\"font-family: 'Times New Roman';\">Unit-10(B): Waves<\/span><\/u><\/strong><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><strong><u><span style=\"font-family: 'Times New Roman';\">21 Waves Motion:<\/span><\/u><\/strong><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><em><span style=\"font-family: 'Times New Roman';\">It is a disturbance which travels through a medium due to vibrations of the particles of the medium about their mean position. The disturbance is handed from one particle to the next particle.<\/span><\/em><\/p>\n<p style=\"margin-top: 5pt; margin-left: 18pt; margin-bottom: 5pt; text-indent: -18pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: Wingdings;\">\uf0d8<\/span><span style=\"width: 5.29pt; font: 7pt 'Times New Roman'; display: inline-block;\">\u00a0\u00a0\u00a0\u00a0<\/span><span style=\"font-family: 'Times New Roman';\">In a wave motion both information and energy is transferred in form of signal from one place to another place.<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-left: 18pt; margin-bottom: 5pt; text-indent: -18pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: Wingdings;\">\uf0d8<\/span><span style=\"width: 5.29pt; font: 7pt 'Times New Roman'; display: inline-block;\">\u00a0\u00a0\u00a0\u00a0<\/span><span style=\"font-family: 'Times New Roman';\">For example when a stone is dropped in pond of water then a circular pattern of alternating crest and trough is formed due to vibration of particles of water. These particle transfers energy from one layers to another layer and when a piece of paper is placed on water surface then it does not moves, show that during wave motion the particle of the medium does not moves.\u00a0<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><strong><u><span style=\"font-family: 'Times New Roman';\">Characteristics of Wave Motion:<\/span><\/u><\/strong><\/p>\n<ul>\n<li><span style=\"width: 38.9pt; font: 7pt 'Times New Roman'; display: inline-block;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>In wave motion disturbance moves in a medium due to vibration of the particle of the medium.<\/li>\n<li><span style=\"width: 34.45pt; font: 7pt 'Times New Roman'; display: inline-block;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>The energy is transferred during wave motion.<\/li>\n<li><span style=\"width: 30.01pt; font: 7pt 'Times New Roman'; display: inline-block;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>There is a little phase difference between vibrations of the particle.<\/li>\n<li><span style=\"width: 31.8pt; font: 7pt 'Times New Roman'; display: inline-block;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>The velocity of wave motion is different from velocity of vibrations of the particles.<\/li>\n<li><span style=\"width: 36.24pt; font: 7pt 'Times New Roman'; display: inline-block;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>The velocity of particles is maximum at mean position and zero at extreme positions. While wave velocity remains constant in medium.<\/li>\n<li><span style=\"width: 31.8pt; font: 7pt 'Times New Roman'; display: inline-block;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>There should be elasticity, properties of inertia and minimum friction for propagation of a wave.<\/li>\n<\/ul>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><strong><u><span style=\"font-family: 'Times New Roman';\">22 Types of Wave<\/span><\/u><\/strong><strong><em><u><span style=\"font-family: 'Times New Roman';\">:<\/span><\/u><\/em><\/strong><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Waves are mainly of three types:<\/span><\/p>\n<ul>\n<li><span style=\"width: 38.9pt; font: 7pt 'Times New Roman'; display: inline-block;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><u>Mechanical Wave:<\/u><\/li>\n<\/ul>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><em><span style=\"font-family: 'Times New Roman';\">The wave which requires a material medium for propagation is called M.W.<\/span><\/em><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">e.g: Water waves, sound waves, seismic waves (waves produced during earth quake).<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-left: 36pt; margin-bottom: 5pt; text-indent: -18pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: Wingdings;\">\uf0d8<\/span><span style=\"width: 5.29pt; font: 7pt 'Times New Roman'; display: inline-block;\">\u00a0\u00a0\u00a0\u00a0<\/span><em><span style=\"font-family: 'Times New Roman';\">The propagation of M.W. depends upon elastic properties of medium so also called elastic waves.\u00a0<\/span><\/em><\/p>\n<ul>\n<li><span style=\"width: 34.45pt; font: 7pt 'Times New Roman'; display: inline-block;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><u>Electromagnetic Waves:<\/u><\/li>\n<\/ul>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><em><span style=\"font-family: 'Times New Roman';\">The waves which travel in from of oscillating electric and magnetic field and do not require any material medium for their propagation is called E.M.<\/span><\/em><span style=\"font-family: 'Times New Roman';\">\u00a0waves e.g: Visible and ultraviolet lights, radio waves, micro waves, infrared waves,\u00a0<\/span><img decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"12\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0rays and\u00a0<\/span><img decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"12\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0rays.<\/span><\/p>\n<ul>\n<li style=\"line-height: 150%; font-size: 16pt;\"><strong><u><span style=\"font-family: 'Times New Roman';\">Matter Waves:<\/span><\/u><\/strong><\/li>\n<\/ul>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><em><span style=\"font-family: 'Times New Roman';\">The waves associated with material particles, when they are in motion are called matter waves.<\/span><\/em><span style=\"font-family: 'Times New Roman';\">\u00a0These waves have significance in microscopic particles.<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">e.g: Electron microscope uses matter wave associated with fat moving<\/span><img decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"29\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">.<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><strong><u><span style=\"font-family: 'Times New Roman';\">23 Spring Model for Propagation of a Wave through an Elastic Medium:<\/span><\/u><\/strong><\/p>\n<p><span style=\"width: 17.34pt; font: 7pt 'Times New Roman'; display: inline-block;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><u>Propagation of Sound Waves through Air:<\/u><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">If we suppose a small region of air as spring, connected with other small regions or spring. When sound waves moves through air then it compresses or expand a small region. When there is compression in one region then there is rarefaction in other region. Thus compression and rarefaction moves from one region to another region which causes the propagation of wave in a medium.<\/span><\/p>\n<p><span style=\"width: 16.45pt; font: 7pt 'Times New Roman'; display: inline-block;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><u>Propagation of Sound Waves in Solids:<\/u><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">In solids, we can assume that each atom is connected with other neighboring atom with a elastic spring. When sound wave propagates through solid then atoms displaces from their equilibrium produced by this force travel to next atom and so on. In this way a wave propagate in solids.<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><strong><u><span style=\"font-family: 'Times New Roman';\">24 Transverse Waves:<\/span><\/u><\/strong><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><em><span style=\"font-family: 'Times New Roman';\">The wave in which the particle of the medium vibrates perpendicular to the propagation of waves is called transverse waves<\/span><\/em><span style=\"font-family: 'Times New Roman';\">.<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Suppose a string whose one end is fixed and when a jerk is given to the other end held in hand, then a crest or trough is forms in string which moves toward other fixed end of the string.\u00a0<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Each part of the string vibrate up and down while wave along the string so the wave in the string are transverse in nature.<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">The point of maximum displacement in upward direction are called crest and the points of maximum displacement in downward direction are called trough. One crest and one trough together from a wave.<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><strong><u><span style=\"font-family: 'Times New Roman';\">25 Longitudinal Waves:<\/span><\/u><\/strong><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><em><span style=\"font-family: 'Times New Roman';\">The waves in which the particle of medium vibrates along the propagation of waves are called longitudinal waves for example<\/span><\/em><span style=\"font-family: 'Times New Roman';\">.<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Suppose if we push or pull a piston in a small hollow cylinder filled with some air then sound wave travel in from of alternating Compressions and rarefactions. The oscillations of particle are parallel to propagation of wave. Thus sound waves are longitudinal waves.<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-left: 36pt; margin-bottom: 5pt; text-indent: -18pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: Wingdings;\">\uf0d8<\/span><span style=\"width: 5.29pt; font: 7pt 'Times New Roman'; display: inline-block;\">\u00a0\u00a0\u00a0\u00a0<\/span><em><span style=\"font-family: 'Times New Roman';\">A transverses wave can be produced in solids or string and not in fluids as it moves in from of crest and trough.<\/span><\/em><\/p>\n<p style=\"margin-top: 5pt; margin-left: 36pt; margin-bottom: 5pt; text-indent: -18pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: Wingdings;\">\uf0d8<\/span><span style=\"width: 5.29pt; font: 7pt 'Times New Roman'; display: inline-block;\">\u00a0\u00a0\u00a0\u00a0<\/span><em><span style=\"font-family: 'Times New Roman';\">But due to surface tension, the free surface of liquid maintains its level so transverse waves can be formed on liquid surface.<\/span><\/em><\/p>\n<p style=\"margin-top: 5pt; margin-left: 36pt; margin-bottom: 5pt; text-indent: -18pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: Wingdings;\">\uf0d8<\/span><span style=\"width: 5.29pt; font: 7pt 'Times New Roman'; display: inline-block;\">\u00a0\u00a0\u00a0\u00a0<\/span><em><span style=\"font-family: 'Times New Roman';\">Longitudinal waves can be propagating in all three mediums solid, liquid and gas.<\/span><\/em><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><strong><u><span style=\"font-family: 'Times New Roman';\">26 Some Definitions in Connection with Wave Motion:<\/span><\/u><\/strong><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><img loading=\"lazy\" decoding=\"async\" style=\"float: left;\" 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YRVxv69++vhoJpBEP\/lEnBiBEj1P\/kspJnOVZ2ZvhCsCfPspgwYUKizYtyCJ4+YtmAohUgh\/uE+CHiasXZeq5ntv2OzO8UgYe+\/ea+ReOQ5s13cOJG7MsImVdnEterp\/egSb2aqNPoa4wcPhh1alRH\/ZZd4Xnv2TYgIq46fCFo9MJe5H9p4TwvXD9rWQc7ZswYPTV1wUr6iy++UGXQpk0bZembmNBYjSb0\/H+9evUSA6d4IuJqxdl6rqO71kalpt9DWTuYwvFTm+r4tFk\/hD3jVWFenUlcTeG+qFEyF\/pNWa2OH7gfQo70r2DQTOsmCfYQcTXDrYhoSUpxpWl1UsMXkcOhdJ1ozyTcmfn5559Vj5UuJGn6nhTwpXznnXfUHCwfQOH5cSZxfXjdDWvXrMHCP+Zj3JjRmD5nPrbtP4G4LrpzJnEN97uNsnmyYuLfBxHgdRdTRg5A6+4\/4IHvs1dLMK\/OJK63z25H1szv4JDHQ3V868xWZM2QEeuOXlXHsZHqxZXzcPQ4wl4Ml3wkVy+Gc4HMA1338WFILZw4cULNsbJxcebMGT01aVhjrkwprpx\/FScTz48ziWug921UM\/dQvuo4FL4+j\/HXpJ\/weprXMHHZfv2K2HEmcXXdtQiZcxTCDnN++nRsgfwffISD52\/pZ2OHeXUmcV04uisKV2qKgAgTgv0eonODz\/Ht2D9gPnwmqV5c+YXZaypcuHCyuiVkj61o0aLKCxE3dE4NcN2wi4uLalRMmjRJT006+NJZ5l\/btWsnw8PPiVOJ6\/2LKJgjMxbu0ipgvzvnkSfja5iQCsX1l171UaFhb4SbX4fI4If4uHA29J2yRj8bO8yr04hrRADqueRBt6EzMW\/SSJQoUgSzV+8zC2vc6olULa78hxwapKDxx0luuPSElqy0VOZcrLNDQWXDhkufkuv70skEvTdxXS0rbiHuOJO4Hvh7IrLlc8FtX873m7Bq6gAU\/l9t3PWN3TrWgrOIa0TgPVQokA1jF+9Rx6aQR6hkFtd+qVBc753fjWyZc2DvxbsICvBFv5ZV8GGtbto8dBxIteLKXgqHgdlroTN9R4A9Ob4QnPu15+vSWaA1Nue56YD\/5MmTemrywIeZZU4Xi0FBmnWk8GycR1wj0a95ZXzZ\/idcdD2FSSMHomufwXGyCLXgLOLqtm85MmfLD9c7mhV9hP9dlM2bCT3HLVHHz4J5dRZxXTahNwqUbwA\/3Ypr4vdNUPiTVs806rKQasWVBf3aa68hY8aM6sdwFFjQ7EVxOZA9n5UpHTZs6FqSDZt+\/fol+3AsRYJ+o9mLnjZtmp4qPAtnEdfgRx4o+k5mzF1\/CNvXLcUnZQqj40+zzP3XuOMs4np6z3pMnLPUKiARwZj36wiMmTIfAXFQFebVKcQ1MghNKhZAtzGL9ARgdPc6KPxpa8R1LUOqFFcaMbVo0UJV7rRUdST4IDRt2lTljZsGOCN0wM+h+Lx58z7zB08qjh8\/rhpb2bJlU9bjwrNxFnE9snY6suYugxvemjXs5P7NUKBSizj3UIgzzbn+F5hXZxBXn2snUKJwUey5cFdPAeYO7YwCJSrD9VbcOj2pUlxplcreYc6cOePtED4xYSVFv7rMHx8uZ4JOHEqXLq16iaw0HQU2uLp166YaNV26dNFThdhwDnE14cfWVVC93ZCoZTcTv2+Mgs8x\/EdEXDWYV2cZFo7585siI8zPfNzX4Kc6cWUl2rJlS1WJcvNzR4TDpJwHZh6dzbEEfQfze9GJAx96R+Lu3buq58oebGpcb\/y8OIO4hnlfwwfvZsLsjSf0FA7\/1cZ7pWrCl+aycUTEVYN5dRZx\/a+kOnHlQ0\/H8FzbGBAQoKc6HnwQ6Lz+3XffVdvUOQM0FmK503iID5MjwmkCij8rSyF2nEFcA73uYd26TfAJsvZIrl04joWLlsLzbtxtHkRcNZhXEVeNVCWu7BHSvR6HJLlDiiPDvHbs2FFV9MOGDdNTUzZjx45V34ebIyS3EZM9aETGBg3nhDkPK9jHWeZcEwIRVw3mVcRVI1WJK3dB4Vxm9uzZ1Z6qjg43bqb3IuaXhZOS4UvCrd44anDx4kU91TFhw4uNgC+\/\/FJPEYwQcbUi4qrBvIq4aqQqcR0wYICqNAcPHqynODbs3bVt21bledSoUXpqymTgwIHqe3BzeEfttVqgp658+fIphx58gAVjRFytiLhqMK8irhqpRlx5Yw73ZciQQT2IKYWzZ88qA5uUPPdKhxEsd84h88FPCfABZWOA618dvTGQXIi4WhFx1WBeRVw1Uo24zpo1S1WWXN+akrCsyeU8cUpc90phsnjC4t+UAo2v6MiD5X7w4EE9VbBFxNVKShNXTov5+fnpR9Hh7xrbfta0qrfnrpR5FXHVSBXiyk3IS5Ysqda2HjhwQE9NOZw6dUrlPVeuXCluc28+\/Jzn5nZ6fClTEnPnzlWNgq+++kp6rwbEJq7r1q1TFSMDKxWj+L59+3D06FHDc7ZxbgNJ8WCcFQp3UmKcz5aIa\/zE9fvvv1fL4ozgZz788EP96Gm4i5i9BifzGpu4stFl+V3t\/d78TqynGafv70WLFhlex+eC92ScYsxGF+PPK670dUCNMILr8mOzz+E5XmNEbOLKvNAGiGLKZX+XLl1ScX4fjlYyznD69GnDOK\/n54zOMc4y4P9JdHFla5fWn3zYWNApDea5cePGqqJnDzylQEGiQwbmm3OuKQ32XvPkyaOWDlEEhOjEJq6Ms8JPrHDt2jVVEaUkcaVQbNmyBXfu3FHBNs4KkdbpRuds4+yh8Z6M83o6xGGcZUJBstRvjiquFISYv2VCBj4Xzyuu3333nV1f7nyWy5cvrx9Fh\/flen17BpqxiSvzaZT\/hAq8P\/9PoosrC4GOIwoUKIAaNWpEBe6hGhMue7G9hoEPjC10sN+jR49o19SsWVO9VLZw6ISuDG2vYy+ILTNbbt26hYYNG0a7rl69eqplY4EvEhsIdHJge12jRo2e8jLFxgT\/j+113FotZuuML73tNQz09RuTX3\/99anrmGYLy5gCantN9erVlWN+WglbWn8c5qaRlu11LDvm2RZezwrL9rratWs\/tecrX9i6detGu45lxzK1heJYq1ataNfRUUfMzdlZWdtew9ECNg5iLh\/iM0FrYttrhwwZEu0axkePHh3tGn5m5syZ+hVWYj5PvI6tfFs4jNe+ffto1\/F33r8\/+rZoLDvuC8zz9OGcWDsOpTRx5agP31E+g0ZQxOxt1s93kUN39oiLuNKtptF3ScjAuomIuIq48v8kyZwrx+0pdLbhl19+0c9a4VrMmNexUGxhpdK\/f\/9o1\/Dl2rx5s36FBns+fNFjXsfhC1vY8qTg2F7XqlUr9TBa4A9JEWFFX6RIkajr+LmY4srhIv4f2\/vxgY+54wsrb9trGIYOHaqftUJPVjGvi+ngnvkbPnx41HmKEUWV+bW1zuZ1FBLbezGvHNaxhQ8C1\/naXse5Z1batnAYhOm211FQWKa2cOed5s2bR7uOlssxh9m5l67tNQxZs2ZVm6rbem3666+\/nrqOQhpTXLmtXszrFixYoF+hwetoyR7zOtthPkIrZqOyi1np0\/CtTJkyquzpalLEVYP5omgw30ZUqlRJLX8zgnVAp06d9KOn4e9gKQsRVxFXkmrE1Rlgj5dDlNzYPSws7j4ukwNWUhZH+Cndw9TkyZOVULEhYyuejgrzaBHXbdu26akJj4irFRFXDRFXK4klrp6XPXDk4H4cPnYSnp7G14i4Pif8MTkMSAtWViKOisXCmZX7iBEj9NSUC3uM3FSfDjD4oDo6HGJn2XPTfXvGFglBQovr7n\/W4rseXTFs+DB0+LopatdrgF9\/W2F4rYircXBGcT24ewsG9umOwcOGo2v7r1GzTj0MmbgAngbXOq24el7G3\/MnoWXzJvim9wCM\/2UM6lWvgHc\/+ARn3C4\/db2Iazzg\/Bp7r0WLFrVbSSQ3NM5I6WtzYzJu3DglWKxgHbn3yrxxrpt55RKWxCShxNXjwmn0bl0P9Vt3x+7Dx+Fx2RPubhcw5acuGDV\/o+FnUou4Xr50HkvmT0efvgPw08C+aNywIVq1745Dpy4YXu9M4urpcR4je7VC1fptsHnPEVzyuIzL7m5YNPlH9Bnzu+FnnFFcL186h97Nv0KNlt\/i1PmLUeme7q4YOHAILhv0XkVc4wF\/0C+++EJVnvYeiOSE+aNxFnvXzrSjDx9OziHTHSVfXkeF86+WxldiTx0khLh6up9H+zrl8UXr73HJLKq2504fOYjj56yViW1IDeJ6cOvf+MIsCkPGz8axE2eUUdWJw7tQ96s6OOrqbvgZZxFXz8vuGNC2FsrWaIvzl6L3zC6dPox9x12jpVmC04mrpweGdWuIwuXrwzVGOTDweY2ZxiDiGk+4Jo4VaP78+RPNWCW+cDkAjX9y586tnOA7E4MGDVKNGlpUO2LvlcPxtKhmHufMmaOnJh4JIa5\/jP8Ob2QrjP1nLxmetxecXVz\/3bEKhXLlxPSl\/zx1bsf27bgcI80SnEVcN\/0+DukyZMeGA2cNz9sLziauR7ctRaZ0r2Pait2G5+0FEdd4woqdy1dYic6bN09PTX7YU2Kvmr1Wo+UmKR1aIGfMmFH1YGNaIzsCbHTRH3JSNbr+q7iy11q1RA7UaPeD4fnYglOL6+WLqOOSF1+2G2hXRO0FpxBXT3e0+Lw4ytTsYDivGltwLnH1xJjeTZA+54c442F03n4Qcf0PcN0re6\/sITrKvrRcxsLKvVixYnY9nqR0WCmxUfPjjz\/qKY4BDZcsc61cdpYU\/Fdxdf13Pd586UX0\/3Wx4fnYgjOL68E1s\/Dyi2nwx9bjhudjC84grpfOHUa+N19Cq4GTDM\/HFpxKXNnI+Kw43itXO16NDP4fEdd4YhkCnDp1qp6SfLCnxIeQgs+Hylmhz9U333wTb7\/9tvK44yhs3bpVjRhwrtVSwSY2\/1VcT+9ZgjQvvIh+vy4yPB9bcGZxHf9dM7zwZkGcNJhje1ZwBnG9cHIXcqR5AV8PSO3i6oE21UvjrbwVcF56rkkLHSPQaxMrevrUTE74orJy5\/IPe5WXs9CrVy\/VqHGUTew5HM9yZ\/nTIXhS8V\/F1d31CIpmT4dC5evB1SO6MdOzgjOL65AONfFixsI4lUrFldaxnxbJhneKVMRRVw\/Da+wFpxJXc1g2dRBefvElNOkxHBej3hFP7N2z2+4aVwYR1wTgm2++URU9K\/zkMrKhuz364OXmAvQO5ezwweUWepx7jelmMTmgM3c+A6wE7Ln2Swz+q7gybPxrMt57+03kKlgc9Rs2RtPGDdC1Z28sWrvH8HpLcGZxXfJrX\/Pv+RJ+mvG34fnYglPMuZrD7g1\/onCurMiSqyDq1m+Ipk0bo1O3XpizeJ3h9ZbgbOLK9a3zfx2CyhXKImuWbPi02peo3bAlfluyJtahYhHXBIA7zWTKlEmtK2WFlhxYNkKn20FHXgOakPCF5HdmRZKc0CKbBkyc6965c6eemjQkhLgyXHK7iK0bVmLxijU4c+483D2e3WNzZnH19LiA7o0+x6uvvIaqteqjbbv2aNmyDfoN\/hlnL8ZeNs4irgzul9yw+5\/1+GvxCpw664pL7s\/uxTqduOrB0yyyLLvLMZar2QsirgkEfSRzSJCO6RPTI48RfGC5nVyWLFnMP\/xlPdX54dwrvzN7sHx4kwM2ZOiTmCIfc2OBpCChxDU+wZnFlYHrPI8d3o\/f5szCui07cfLUaVz2fHbF6kziGp\/grOL6vEHENYGgtTD9DdOYKCnn3DjXZ9lMwGiHIWeHFsP87typJimHYy3QYYRl1yG+UEmNiKuVhBbX+AYRVxFXBhHXBIQvNI2bOPeZVMZNrMg4HFm8eHG7W3U5M7QWps9hClxS7\/fK8uaON2xQxdyhKKkQcbUi4qoh4mpFxNVJ4JAg96xlT4qVAH\/4xIRbvXGvUxoxcR\/M1MrEiRPVkDz3X7VXaSc0\/G27deumfmtOBSTXDkkirlZEXDVEXK2IuDoRfHkpeOzBrlmzRk9NeFiZc0PypBJyR4YbmLPnzh58YjvKt8D9YPkbv\/fee6qRk1yIuFoRcdUQcbUi4upksDDp25c70tDRd2Lw66+\/quFIemJ61g+WGmBlyjKn1S6XJSUm3FSeBmQciqbjiORExNWKiKuGiKsVEVcng8PDPXr0UL1K\/vAJ7Rpx3759ameYN954QxnUCJrD\/ObNm6sy79q1a6JZ7bLCzpEjh+ol00I8uRFxtSLiqiHiakXE1QmhX19WFKzsufbUXmXyvLDiYeXOOcYZM2boqQKhM4mcOXOqHiwrlISGYkU\/0ix7R9mVR8TVioirhoirldjE9dSpU2pkkXnls8LnjnGWEf3GM87w77\/\/Gsb5P\/k5o3OMsz7i\/xFxTQS4DrNgwYKqMu7du\/d\/FlgPDw\/ky5dPCTbvl9TraVMCnHPlXChFli96QsGKzNKooSFTchkwxSQ2cd2+fbvaOYiB54zitLDmxvpG52zjdI7B8mScFcfZs2eV8xQR16eDo4vrtm3bDH9j2ziFhwJjOd60aVNU3Pa6HTt2qHsyzmfpzJkz6rmgwDi6uHLJJOtUxvfs2aNGARmnDQU\/Z7mO5WkUP3LkiPKGZ3TONi7imkiw4uJSEUulHBQUpJ95PlhRWIS1VatWDreHrKPAl6179+6qnFhR\/9flSbwf92WlowoOBbPH+l8bSQlJbOK6atWqqHP2XnxWDqwkjM7ZxtlooXAwzgr12LFjKp7SxJWBgsalcgy2cZYDp1yMztnGWSnznoxz\/p2NDcZZPhQhC44qrnTVaTln7\/em0PC7Mc7vxl2ejK7jvXhPxnft2qXKgnERV2tcxDURYQuQFsQUWC7bYOs5rnDocfXq1WpjAAoGl\/o4yvZ2joqPj4964VhejRo1gr+\/v37m+eBLxoYMRZVz3OPHj3e40QIRVytxFVd735F78bKSNTpnG7cVFNvyY\/nYTkeIuIq4Moi4JjJ80cuUKaMqfC7f4AbrXEISG5wPaNeunVrHynlEPoDx7fmmNtiAKVWqlGrQfPXVV8+1NR2vHTduHLJnz65+L86zcijNEeZYYyLiakXEVYN5FXHVEHFNJXCJCCuHtGnTqkq\/UKFCGDx4sPph+YByApwPCR8yWr5yz1KLGPMhTg73fikZGla4uLioMqRrSlYy9ip19nY5Z8SXnMP4\/Ax7qxzK53ySoyLiakXEVYN5FXHVEHFNRVAg+RBWr15diSwrcQauWeW6ScsxA4eCOcfnSBuCpzRYMTRu3FiVLwPFlg2aWbNmqd4ptwlkRWWxAma5s1HDxg3F1hF7q7aIuFoRcdVgXkVcNURcUyEUWRo7ca1kzZo1lY9a9mQrVKignNDzx01sZwipBc6TLlq0CCVLllSWxLYNGAaKKtcMV65cGWPHjlWVZEpBxNWKiKsG8yriqiHiKjgF7OU5ckePy2fYG508eTIGDRqEESNGqEqKy5r44KdERFytiLhqMK8irhoirkKKx\/feZbSuVw3dhs2GYw+kRmf48OGYOnWqfpTyEHG1IuKqwbyKuGqIuApqPSbn+VIipohg\/D5jMtaZX6a6jdshJCLlyKuIq4irJS7iao2LuIq4Og30avLBBx\/oR0\/DZTkWzy+ORkSQF54Eaus\/Z02fjtBIxxFXDgWzsrZnaS3iKuJqiYu4WuMiriKuToM9ceXDSEf03H3F0S1XYQrH+AkT4GgdV86ztmnTRlVGMUU2ruK6fPIgVPmiptrmr1zposhbuCTqmuN1an2JUuVrwSsseb60iKsVEVcN5lXEVUPE1QkxhQdg5i8jlOGMUdiw76x+pUZMcb106RI6duyoluPwIXB4YTWz+bfhqNNxmEPOufLl4RaAFEdWAJbyjIu4RgY9wpRp8xAUFmE+CEHHL8ugzY+ztHOhvpgwZbaKJwcirlZEXDWYVxFXDRFXJ8T90DoM+XUBLph\/9P0b\/kSWt7Ji4eb96iH4fdxALNkT\/WGwiCuHf+kb1+JAImPGjOqhTM7ASuNZXDq0Bvnz5kXPkfP0lKfh2lKj+ydVoON9lulrr72GJk2aKOfkw4YNe6a4msJDEBCkiYH3zdPImy0r1h7R9+k1RcLPP\/ncUYq4WhFx1WBeRVw1RFydEHfXswgM04Yg184YiLwf1YJ3qHZ8\/+p53PONvqsKxZVehPr374\/06dNHW4eZ3IE7oMSG9y1XlC2SH8u2bMbMP6yOy2PSt29fw\/snR6ADDxqQsYJ7njnX7X+MxLtFP8OjYMfwliXiakXEVYN5FXHVEHF1ZiJD0PrzD9Bx2Hw9wRjbYWE+KG3btlU9LHoO2rx5Mw4cOJBsIbaNAsKCnqB5lQ8xaPoaBN8+gj\/Xn9LPPA1fQqP7J0WgINC3M30009cwXyQODT+XQZMpDF1rl0XzfnEX48RGxNWKiKsG8yriqiHi6sR4XT2KXFmyYtPJ63qKMUYGTXwQW7Rogbp168Z7Z5fExBQZhnE9G6JmhyGgPc\/DE+uw7KD2Pe\/dueswc6+0su7SpYtyOcktxWznr59HXP3uuCJ\/tiz4+8AlPSX5EXG1IuKqwbyKuGqIuDoxm+YMxnslq+PJM4YRjcTVAodl+eA51lIcEzb+NhzFytfFo8AIleK27U807zkEi36bhpU7T6q05IauD1mx8sU3Mgp7HnHdvWgschSqhPv693UERFytiLhqMK8irhoirs6KKQztvyiBNj8925o0NnG14EgWwwEPLqNjm1Y4c+OJnmKu6B97oEHNGug39jeEO8haV5ZZbOUWZ3E1haNn\/XJo3GeinuAYiLhaEXHVYF5FXDVEXJ0U3xsn8V6WLFh\/7KqeYp\/AwEDl8zal40gNgLgQV3EN97+Ljs0b4Z\/jjuXUX8TVioirBvMq4qoh4uqkbF0wHLlKVIsaNhUcj+cyaHJARFytiLhqMK8irhoirk6Kn\/dj3H\/kpR8Jjggrcr5gKRURVysirhrMq4irhoirIAjxQsTVioirBvMq4qoh4ioIQrwQcbUi4qrBvIq4aoi4CoIQL0RcrYi4ajCvIq4aIq6CIMQLEVcrIq4azKuIq4aIqyAI8ULE1YqIqwbzKuKqIeIqCEK8EHG1IuKqwbyKuGqIuAqCEC+4+XtwcLAKFNZ79+6p+JMnT3DixImoc\/SpbBRn5XLt2jXDc7ZxiqmXl5eKc69hVp6M+\/j4PFVhbtq0Cf369dOPonP79m3UqFFDuaU0onHjxrh8+bJ+FB0K5oABA\/Sjp6Hg+Pr6qnzRZej9+\/ej8sgN8xlnsPcdKRIsD6Nz9sqClaal\/Ph\/KOgW6FCFjQxW1kZMnDhRfScj+JmWLVvqR0\/Tu3dvnDlzRj+KDst\/\/PjxUfk9fvy48gDHuLe3t9rIwnJu+\/bthnFufUnBYjwoKEg1qIyuo8BbyoKNIjYwGOfvwP9ry9y5c\/Ho0SP9KDo\/\/\/yzagwawTxPnz5dP3qaOXPm2BUt\/h62Is\/8WvLOxhTzw7ibm1vUb8\/\/t3\/\/\/qjr7JURvyuffaNztnFL44vxZ7mwFXEVBMEu7E3Y65kSVtb2YAVkz8vXf7lvchEWFmb3+7CBwcaREfwMP2uP2O7Le9prvBDbz9mLxySu18UX\/q6x5Tk5ScoyEnEVBEEQhARGxFUQBEEQEhgRV0EQBEFIYFKVuIaFhjrMpt+CIAgpgdBAP5w964qQsNj3sRaiEy9xTYxJ8ETFFIkdy6fB5cMPsWjHKT1REATBcaHF87MsUhObUL+H6Na4Ot7O8jbmbXacujMlaNBziyut+LiOiXuWphTuXz6BBUtWYtOKeRgw6jc9NWXCF87f318\/EgTBWWnQoIFaYpKcnDq8G\/d8gnDHdRemLtqhpyYvXJo2cOBAZXHuyDy3uPKLlShRwu4aJ0fEx9tHDQeH+dzBvIWrtcQUSuvWrbFlyxb9SBAEZ6V27drKGYIRXHualMtdHnoex8rtx\/SjxIc9U665NYJrpytWrBjr8iZHIEHFlQuh6dXDUXngfhjzVuzWjxyXO3fuYOvWrYYPT6tWrbB582b9SBAcl5uuh9CsXk1MW+oYPZ6UhpG4st4dM2aMXYcViYMJq+eMwcajnvpx0kBnIT\/88INycmJLqhFXtjDoQeXrr79WHlcctaseGvAILaqXxe87jD2hOBoU0CpVqmDNmjXRHiIRV+FZ0NWdPU9CSUWw733MmjIJCxfMQrMug+EopjCO6JzCHrbiSq9Fo0ePxnvvvafc8SXlnOP5fSvwbvZcOOLxRE9JOnbu3Il33nlHTUXeunVLpTm9uNIFFN1FtW3bFunSpUOjRo2U6zAWQFKGuAxPmyJCMKZXMxQpXgZbT2s\/kBFG90\/OQDdhr732GipUqKB8vvJhEnEVnsU333yjfKAmJ37eDxEQYm5om4Ixdepch7DSp+cg+juOzTOUI0Fxtbg\/zJkzJ1544QWULl0ao0aNUr3XhAr01WyPR1dPo3zJD9CuYze4P45ebvyc0f0SOlSrVk1990yZMqkOHBuPTiuuhQoVQvPmzZEhQwb1pRkYz5gxY5KHhg0b6jmzRyTWzxuOj6o0wZrFc3HyprEhFluCRvdP7vDSSy+p8n3llVeUs+xy5cqJuAqx0rlzZ0Nx5agSfcYmpbiEBdzDpNkL9aPEh+8xfQQbGf3RCDN\/\/vzJboEbVyiuxYoVw4svvhhVzyZGoHgZEeJ3H82rlcNPs1Zj2fyZeBgavYlkEb2kDvny5VP1oFOKa5EiRZSz6ezZs0d94axZs6rWVVKH2Bxikwv7VqJ4CRec8HyATYvm4HqAff+fRvdPzsDhkJdfflmV7+uvv44mTZoogRVxFWIjprhSVGl12q5dO7sGMomBKTIMswZ3RN8Jy\/WUpIGjaiwD7ppiu6ohJYorbS9mz56NAgUKKJEtU6YMpkyZgmnTpiVYsHWGb8EUHoyfuzVBw64jERweiQUzpiM4xvADP2d0v4QO3ByCdWCOHDnUpgB8lp1+zpVDl4MGDUKWLFnUg8DtjPz8\/JI0xDaH8uj6GVQoVQyLd5xWx4tmTsYjc6M9IsQft+8\/PZxsdP\/kCrQGnDRpEtKnT4\/69esrQzE2AGRYWHgWFnGl03fuZsLRHTaEOX+VdJiwe\/kU5DY3Eict36+nJR3cRcfFxUUNo3KLPW4ikBLF1dIY4i49U6dORcGCBdVfe5sEJAyRWDN7MMp+3hT3\/FhW4RgzbBSCIk245XYSnnd9tcuSABpuvf\/++xg6dKj6TUmqsha+efMm+vbti+7duzvMfEao\/wO0rOaCQVNX6PM9Joz7tiUG\/zLd3PoZjRtPglWqI0IR5R6ErBS5rRKPLYi4Cs+C4jpy5Ei1J2qaNGlUqz9btmyoXLlyggeKlhHXTm5H8WIlsWjJQqw\/GH1P19WrVxveK6FD0aJFo0bWypYtq+YIOaSYEsXVApenUFy5r6ttvZCQuO5ZgaLFXHDyil7Hm8LxbZPPUP6Tz\/Ddz3MRkTj\/9inYQ2VPlVvs2ZIql+LQZJr7TjoCx3aswA9jZiE43PoknNy+DM2\/bovtR931FMeES3EsPdWYiLgKz4LiSiM4TiVYxIVz95y3T+gQEBCg\/1crfg+u4LMyxTB77WG47l+HA+fv6Gc0Zs6caXivhA6WKRXL9+dG3Llz504x4konEtw\/1AjOKSfWyoyLpw7j7OXoy19ueZzFxn92wj80aey+Wfdx9M4IpxVXtlTpHSMlmbQ7E+JEQngWlmFhevNi\/NVXX1WGMRwi5kbSCRliDk9GhvqhS52K6PbzAtXDObR+IU5e9+YZPHygbYLN3pfRvRIycHPwjh07KmGlhTCHxFPasDCXU6WUvCYlXJbUo0cP5\/PQJCQvnp6edlt0gkAs4mqBzwyNmerWrZu4rjNNEZg6qA0+b\/YdAnQn76unDcVPk37DonkzsPds0qy9Za9n4sSJ+Pjjj5VBkGUEKKWJq5CyEXEVBCcjprgSCgx7cytWrEi04bSbZ\/egeavOuPHEaqF79cQ\/+PyTTzB63hpEJsFcHb8np1Q4dRLTPaCIq5CUiLgKgpMxZMgQbN++XT+KDodxLT25pCJxLVufxt5woYirkJSIuAqCk0HxcPT5qOSAIs81o1I2QlIg4ioIgiAICYyIqyAIgiAkMCKugiAIgpDAiLgKgiAIQgIj4ioIgiAICYyIqyAIgiAkMCKugiAIgpDAiLgKgiAIQgIj4ioIgiAICYyIqyAIgiAkMCKugiAIgpDAiLgKgiAIQgIj4ioIgiAICYyIqyAIgiAkMCKugiAIgpDAiLgKgpAkBAcH6zH7xOUaQUgJiLgKgpDoXL16FbVq1cK9e\/f0FE1IAwMD9SONNm3aYNOmTfqRc3HV9TDa1K+KbiPm6ynxJ+DJbYz7oQeq1O2IoEg9UXAoRFwNCAsLw4QJExAQEKCnGBMaGopJkybB399fTxEEISZ8PypVqoSVK1fixIkTqFixInLmzIkiRYogd+7c+N\/\/\/ofly5era2\/duoWiRYvC1dVVHRsRGeKLeZPH4NvvB8H9jo+emnj43ffEqDGT4Btq0lPiiSkC3zYsh2Z9J6vDEztWYcGqnSoeH7b+NgT5XOohIEJPEBwKEdcYmEwm9OrVC4MGDUJEhPWp9fDwQPv27XHo0CE9Rbt28uTJaNKkSazDWZGhAebK4hzOnTMK5+EXHKZfKQjOx9y5c1GtWjWEh4er92To0KF44YUXlNhevnwZlStXRtq0aZXwEjZYGzZsiMhIO10yUyQ8jm5BlgyZsevcbT0x8bh5YiPKlPsUHo+199QUGYHIeOmsCf2aVogS13kju6Fxr1Hm1Pix648RIq4OjIhrDPbs2aNa1DGHqzZu3IiXXnoJ9erVi\/bSs\/dapUoVLFy4UE95Gp\/z\/6DMJ7UxeMhQ\/NirHdK8nBbt+gzEsCFD0LD6x1i010O\/UhCcCwpq+fLlsWTJEj0FmD59uhLX7du3q+MpU6ao41WrVqnj+\/fvI2PGjLh586Y6NuLR5aPI\/laWJBFXiqKloR34yA2ffFQBF5+Eq+PnI7q4msz1SGT8VFoh4urYiLjGgPNCbDnHpFmzZsiTJw\/eeustXLlyRU\/VWLNmDUqWLKkqEiPuHN+CPe5eKu7vvhfp07yJfde040fuB7Hx8GUVFwRng3Otb7\/9Ntzd3fUUq7iuX79ezcHynStYsCAeP36sXwGULl0av\/\/+u370NLGKq7ln63n2kFm0J2PKtDm4\/tBXJQf5eWP7+mVY9c8+XLl4EtOnTsbcP\/9GQKimTkG+j7Dk97mYOnUKNu85ikM7Npj\/HsNl12OYM3s+ngSF4dKRlXjjlfQYM+tP\/L1lL0KD\/HFg+3osXrtD9UD9fR5h44q\/sOPIeXVP4vPoFpYsMN93yiR8VjqPEteQAF\/s3bIayzfvRURoIE4d2oE5C1fh7q1r+HPudEycPBN3fLTRsJAgPxzfvw2TJk7EpKmzceuxNg1lV1zN3\/\/uNTfMm2u+9ol2j\/AgL+w9dFLFybFda3HG84H53v44sX971L1vPvJDgPk7rFn2J\/Yev6RfbcLRXRtwzM1c1uZ7X794FFMmTcT0uQvhYy4TwRgRVxs4x5ohQwZcvHhRT9GgmH744YdYsGCB6r1yPtYWVhDZsmVTw7zPIqa4WogMD4Ovry8iIiPg5+uDwOAQlR4aEgRvb294+\/hGDUWFh4bAx4\/zwSb4m6\/19vZBhMnaAg7091Of8fXzV0PXgQF+CA6xvgQhwYEIDtUaAvy\/vNbH13ytSuHLHAD\/wGBEhIWoc+Hmf8yhMB8fcz7Mx4HBofqVQJieP7+AID3laYIC\/RFk85mQ4OCo\/xUZEQZ\/\/bP8H74+PvAy3y9Iz6\/J\/DL7m8slNNxagwQG+CMsXBs9CAsN1v9\/9JEGwTHgNErevHnNz451btQirvnz51fvDd+pX375JdqIUMuWLfHDDz\/oR08Tm7juWTYFn9dvj30HDmLm8B7Ilqc0Lt0PwoMbHmhZrRTylfoYvy9bi+XzxyNzutcwbc2\/iAzxRouqZTFk+mIc2rMZpd7Pig4Dx8P1ogdWzxmG9G\/mxNm7fti9egbSv5oB89bsxPFz7vB5cBO9m1VFyRodEG5+qG95uqJm2TzoOFwzWrpyfCsatWyHnfv\/xb8Hd+CzEu8pcX1y5yq6NqqMjxr0QpDPfYz7rhVey5wbE2YtwPZNf6N47sxoqvdw3Y5uw8KVG7B393bUdCmEut3GgCVlX1zDcXzPWhTK\/hbG\/KXN6R5YOh5Zi1ZDID8Y4Y+qZUvD7WEQLh3fgb\/+Xq\/uXet\/hVG7yyjcunoBzauWhkvtrgg1Xx\/ufx9fVKqIs7fNDYKV09GsywDs2b0DdSsURtfRf6r7C08j4mrD\/v37Vc+UBk22jBo1Cv3791eVeK5cuVCmTBmEhGjiR3i9i4sLFi9erKfYx0hcIwK9MX1ET6TLkAltv+mBskVy4uOm\/XBkyzJ8\/\/13aN2yCbJnegsTl+9B0OMbGNCxPl7P\/D76DR6K7m3qIe2raTHy983qXluXTka1GrUwcMAAVPysFg4c2I2Pi72HRr0nKEEzRQSiQ51PsergZXjddEWXTm3QtnVL5M6ZE39sOY7bHqfR8LNSeP8DF\/Tq3NZckbyCOesPYmDHRmjStiu+\/aYVvu47Ud3r4qHNaN+6FVo2rotc+UrgiMd9lQdbrl34F1+4FEDNziO1BFMIGlQohRO3NWOxPUvGoaX5fuEBdzF4UD9zfjqgYqlCKFOtFbyDw81lsBj5s72JYfO3qOtD\/O6iajkXuN7xx+VTO9H269Zo3aIhcryTFwcvPVDXCI7D2rVrVa\/UdlTHIq4rVqzA6dOn0bx5cyWwc+bM0a8AunXrpgTWHvbENTLEB9VK5MKcjdr8LZ\/3akWzoPcEzWBqbLd6+LLTSL1xF45mFfKiy5g\/cf\/ifrydJSdOXH1iTjdhaPvqqNNzjLrqvts2ZDKLq+vDUPjeOoSMaTPj9ENrHfHnyE5wqdvd3MDVjvs2\/1gTV1MY2lcvYRbvo9oJ832jzbkOa6\/ElR87sGQCMhX9AiH6Pab3b4EStTpFNagjIyLMDe0Q\/DWqG0rX6IQwc3rsw8ImTO7TBMW\/MIt+RDiG9G6DvDkyYeXha7hyYBma9B6nl4H13ovGdEep6h3UvS\/sXWquC3PgwKX7OLfzL7QZMBlhAQ9Qudj7GDR2BpYsXoQ2tSrgi45D9LsIMRFxtYFzPmxN21YEQUFBKFCgAFq1aoUhQ4agWLFieOWVV6IZNhEaZbD1\/Szs9VzvnNuFrFnex9mbPrh8bAf+3mF5IYkJv\/Ssj8otB6ijY6umIl2eTxCsvx2ju9ZG6a86m1vOEWhcLida9p+EMPNbefLgHjw2v3mbfxuKTO+VwtXHwXjgfhDVGnRAYIhZZGtXxMIdHL4yYUKPevik9UB1v9k\/toJLg57q5Vu2YBpO7V2P9OkzY9WhC+ZLw7Fjxx4Ee11DRXNvnq1ZRAah0f8KYMCU1erzMTm8YiLSZSuG2wGRuH9mI9KnTYu+k1aaz0Tgm7qfYr+HdTiQ3HXdhSyZcuK4qugiMb5XIxSq1FhVIqe3zEXTbych1P8uPileFCdu+ZvzFIGWnxdEj3HLtBsIDsOWLVuUuNoa\/MWccz1\/\/jxefvllNTxsoVOnTujQoYN+9DTG4mpC4JNryJ\/xNSz450xUWtfaZdBy4Ax1FF1cI9HmMz43i829M\/PzZG6Ejpi\/GSH+D1GnfDHMXHtEXRUXca3YqE+UEFrENTLwJj54NxPmbbVYPsddXOcNbosy5p4j73l4w19o3LgpevQZiBY1K8ZRXM35vrgTmd\/Mii27tmPYlMWY0q8Zan3zM0b1bIn97o\/UNUc2LdLvPQAtv6oUJa6mMD80KJcPPcctxOAuLXD48kP43D6HnBlex8gZS3DB\/Yoa3bIZMBNiIOJqw7Jly9Tcqa2VMAW3ePHiqkJgGDZsGNKkSYMuXbroV2hUrVoVI0aM0I\/sE5u4vv12Hrje9tNTAO97VzD9l2Ho0\/9HNKr6ESo0+16lU1zT5\/ss6kX86+fO+OCLtuqlWL9gFDK+ngbZ83yAsbOXIsTcnA5+fBWl3suMiSsO4LcR3fH71jPwv+eGvJnS4osGLfDT0JGYM28+9hzV5okorhUa99ErIL5oPuja8FO8\/NLLcPmsHrYfu4jzexchQ\/pMaNHuG4wYMx7zF\/yOc1ee7rmS8ID7cMmdCb+uOIjJwwdi9cKJyFnyK9y7fAT12\/ZXw2ls5e\/ZsBw9u\/fA0AG9kOHNd3DUU6sA7rjuRLZMWbD11BX0bdsIRzyf4Na\/f5t\/hzfRrP03GD76F\/xm\/v9nLj89RCgkL8ePH1ejPY8eab8liSmu\/MueK0eHLDRq1AgjR+qjHQYYieuhDfOx66QnGpTPhxYDpmmJkWFo+L\/3MXPDKXVoJK7fT\/xbHW36Ywxq12uENp16YsPuY1HPf0xxfcv83B29ZW0sUFzzVWys3jUS1XM195rrueQ19xIn6L3a5xPX8g17m8UrFNWLZMQvi\/ap9PlDO8ZZXE3hQWhbrQTyF\/4Ix6754PaJdUifKTvqtuuvhpVhvneNYpkx9q896vrfh3eOEley469RyJQtF1p9O8bcDAZCfe+gXJ6MaGLu0VuuEewj4mrD5s2b1RyQ7bDwl19+qawZLfBcuXLl1Do9iwEG54poEWk7rGWPuIqrKcwXTSoXw\/B56xEUHIJJ3zeJVVzLqJ6r+T7Xr+D2DU\/8OrwnMqR7HYv30xLZhJkDv0aJT+qgVdvu8A2LRMADDxTM\/DomLNmt3cSGmOLKnqGHuzvOn9iLr2tXwNtFKmH\/1qXIkCEbdhoZlDyFCdMHtERJszB\/9+NYRAbfRbGsGdD06+b4+4BmzLV70S8o\/L96uOflh7vn9+HtzFZxNUUEo0sdF9Ro1Aadvh+lKoY7J9chbdoM2HT6lrpGcEwePHigxPXkSasxzaxZs5S4fvLJJ6hZsyayZs2KOnXqqGkXQjuB999\/X72P9njseQw50qdFjfrN0blzZ3Rs3xpFS5TDTbPSuB3ZgOIF8qPnj6Mx9LtOaNV7FEL0biXF9atvLMtfNHEdNH29+X3zQtXShdGm+wAsW7ka\/2zdDlf3G+oqimvmt3LhwuMwhAc9QpWiOVD2s5oYPHIcbvuG48Le5ciQNi2+bNgaI8wNApei76FRn0nqfxz95y+8kzkz6jUznxv1MyoWex+1e4xW96W4ujT6Vl1Hcc38wZewLKWluFZu1t98zoSf2lVFroKlzL3L\/mj8hQs++Ly1+fto4pq\/XAME2hFXsnvROHxUt5t6Z0wRQahbNo9eJxAThnSojpwFtHs3qVEOxT5riWClvECI93WUK1oQ289YrLZN2P7XeGTK8BoKla6Ebt\/2xfAJMxEfu+nUgIirDTRcSpcuHby8NOG7cOGCEtsbN7SXzMLUqVNVS9syx+rn56eGk3fufPaC8LiKa2TwE1QrmQvNeo\/AoYP70KxKqVjFtVzdHuYedwCqFc2F2RuP4d61UyhTKD+2ndXE7\/6lfXjnrTcwZYXWAkZkKIa0rYE3s+bGyKkLcPDAfixYuEIJdExxvXZkHfIUrwT3W4\/wz8KxZpFsjEeP76HmR\/nxfrHymLdkDfbv3o6\/Nzwt1BaeeOzFm6+mxaqjWlmO6lYLBSo1RaDqtpp73DMH4e08ZbBx5z4smj4Mr7+RI0pcyfFNv+GNN7Jgi\/6ihwd7oX7FAni3yIeYu3AlDuzbjSVrtqlzguNAoaxbt240I0Aa7u3atUstb6PFsJubW7QGLR1I5MiRI5oRVExMEeF49PCBEm9LePTEO+qZDfDzxo3r13H\/waOouVAS4OsNHz+r8ZuP12MEBIUq4enXuQnqfFUDFSpUgEuZEsiYJZf5\/bmFyIhQPHxovU+A7xNcv3ETvlFGfJF4ePc2bt25p4z9Av184K0MDokJXo\/u47b5XIDlnK92LsjfF16+muVvaHAAHprzb0E7p10XFhKI69evqe9HY0PL9ww1xx97+UR9ZyOUUaJ+H+Ln7aWNFOnw3jcM7q1hgre5LrQtP1oLP3l4D55Xrsa4VoiJiKsNrAi4xpUvPdmxYwfGjRsXzYqR0DqYDiW4BIecPXsW7777bpQox0ao1w1MHD8JN3Uzewv+D69j6rTZeBxgrWTOH96mFtxPX7AEB3ZswJylm9XDfPfScUyat1wb2jFz7uAWLFq7y3zOhBN71mPMmHGYPn0adh2\/aF3sbgrFmmVL8STQ2s4M8XuEBTMm4KfBQzB5zp+4fk8Ts1N7N2DJem2oiHCpwJJ5UzD+18mYNvs33HyoVXqPb17CxDEjMGTYCPy5fAMemXud9jBFhmHJH39GtbL5HbYdti5XCPV\/iOnjR+Hn0eOw\/8i\/mDl1CjwfaEsoSHigN5YsXQ1zpzsKn\/tXMHH0SAweOhzzl6zDw1j+v5B87Nu3DyVKlFCiGhe6du2qnnu+j0mF277laPnt2CixiAwLQJsaFbH+2FU9RRCeDxHXGNAoiR6X7HqHMeC7775D9+7d9SNBEGyhDQPfj759+9pdC26BBlB0j2gZIk4qLu5bgXey5US37wdhzNgxGPxjP\/w0YX7UPKogPC8irjGgH1S2stnajgu0dKQRVMyhY0EQrHANOY0BHz58qKcYQyMmOp5IckwROLV\/C34Y0B9DR03EKbdrMuQp\/CdEXA04duyYWlrzrGEsLtOpX7++Gj4WBEEQBAsirnagsMZlzieph68EQRAEx0fEVRAEQRASFOD\/8wyGpH4KkaMAAAAASUVORK5CYII=\" alt=\"\" width=\"471\" height=\"158\" \/><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><strong><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><\/strong><\/p>\n<p style=\"margin-top: 5pt; margin-left: 54pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><strong><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><\/strong><\/p>\n<ol class=\"awlist29\" style=\"margin: 0pt; padding-left: 0pt;\" type=\"i\">\n<li style=\"margin-top: 12pt; margin-left: 54pt; margin-bottom: 5pt; text-indent: -54pt; line-height: 150%; font-family: 'Times New Roman'; font-size: 16pt; font-weight: bold;\"><span style=\"width: 38.9pt; font: 7pt 'Times New Roman'; display: inline-block;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><u>Amplitude(A):<\/u><\/li>\n<\/ol>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><em><span style=\"font-family: 'Times New Roman';\">The maximum displacement of the particle of medium about their mean position is called amplitude<\/span><\/em><span style=\"font-family: 'Times New Roman';\">.<\/span><\/p>\n<ul>\n<li><span style=\"width: 34.45pt; font: 7pt 'Times New Roman'; display: inline-block;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><u>Time Period(T):<\/u><\/li>\n<\/ul>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><em><span style=\"font-family: 'Times New Roman';\">The time in which a particle complete its one vibration to and fro about mean position is called time period.<\/span><\/em><\/p>\n<ul>\n<li><span style=\"width: 30.01pt; font: 7pt 'Times New Roman'; display: inline-block;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><u>Frequency(\u00a0<\/u><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"13\" height=\"27\" \/><u>):<\/u><\/li>\n<\/ul>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><em><span style=\"font-family: 'Times New Roman';\">The number of waves produced in a medium per unit time is called frequency of the wave\u00a0<\/span><\/em><\/p>\n<p style=\"margin-top: 5pt; margin-left: 72pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">i.e.<\/span><span style=\"width: 16.45pt; font-family: 'Times New Roman'; display: inline-block;\">\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"49\" height=\"38\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0\u00a0<\/span><span style=\"width: 20pt; font-family: 'Times New Roman'; display: inline-block;\">\u00a0<\/span><span style=\"font-family: 'Times New Roman';\">Unit:<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"38\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0<\/span><span style=\"font-family: 'Times New Roman';\">or<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0<\/span><span style=\"font-family: 'Times New Roman';\">Hertz (Hz).<\/span><\/p>\n<ul>\n<li><span style=\"width: 30.9pt; font: 7pt 'Times New Roman'; display: inline-block;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><u>Angular Frequency(w):<\/u><\/li>\n<\/ul>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><em><span style=\"font-family: 'Times New Roman';\">The rate of change of phase of wave is called angular frequency of the wave<\/span><\/em><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">i.e.<\/span><span style=\"width: 16.45pt; font-family: 'Times New Roman'; display: inline-block;\">\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"125\" height=\"38\" \/><span style=\"width: 36pt; font-family: 'Times New Roman'; display: inline-block;\">\u00a0<\/span><span style=\"width: 36pt; font-family: 'Times New Roman'; display: inline-block;\">\u00a0<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Unit:\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEcAAAAbCAYAAAAu\/JKTAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAOeSURBVFhH7ZhJKHZRGMdNZcpKhoQyJFlQWIi9YWNKJDLbGUMpSSzE0soGJYkMxUaZIhYWKEoUFpQiSoYixPP1f+5z3RfvvR99utR3f3XrPf\/zv+55\/\/ec85yXA1noEWmFo48VjgFWOAZY4Tw\/P9PMzAwtLi6K8sr\/Gw5CGR4eppiYGHJwcKCOjg7peeXnwllZWaHS0lK+GhoaRDWPsbExmp2dpdPT098XDpicnOSBVVdXi2I+l5eXvzOc5eVlHtjc3Jwo5vNrw8GMwcCOjo5EMZ9fG056ejo5OjrSw8ODKJ8jIiKCnJycPnWtra3JXfb5azj39\/dUV1fHppGREe6B1t3dzVpgYCDv7racnZ1ReXk59wcFBdHU1BRtb29Tfn6+ON5i6w8ODuYlhftSU1PFofHy8sKbZXx8PPt9fX2poqKC9vb2xPF9GIZzd3fHD4cpLCyMQkND6fr6mhISEigxMZHc3NwoNzdX\/Arz8\/P8VrKzs+nm5obOz8\/Jx8eHH9LV1SUuDdWfk5Pz6vf29mZ\/T0+PuDSysrLI3d2dtra2uD00NEQuLi5UU1PD7e\/EMBzMELxVEBsby3U\/LS2NZwHo7OykhYUF\/gxOTk74jxUVFYmi0NTUxDpmhC16\/srKStY3NjZEUcCsgV5bWyuKQklJCQ0ODkrr38FSPjg4oIGBAX4evvPOzg4dHx+Lw2bPeXx8ZBMunBj1QL+np6e0NDB49F1cXIiioOfH8kPf1dWVKApqOFjKT09Pon4\/mDEI5v01PT0tDptw1MNQUlKSKB+5vb1lT0ZGhiga0dHRFBAQIC0FLCH4MzMzRdHAUo6KipLWW1paWvi+8PBwWl9fF9V0tHDUM0d\/f78oHxkfH2fP6uqqKAr7+\/usV1VViaKg58f0tedXweyZmJhgD67W1lbpMRUtHPXMoe4\/9lCrzfvSi5IMfXR0VBSFr\/rfg5mKzRnepaUlUU1DCQdvytXVlfz8\/FjVo7i4mAdqW1Ix0\/Ly8lg\/PDwUVcGev6+vT9cPX29vr7QUdnd32dve3i6KaSjhoJxjAHFxcazqgeUBn7+\/P597UKGSk5OpubmZdZTozc1NKigoYD9+XNr6GxsbKSUlRddfX1\/PJdsWlHF41bJuIko4WEoYQFtbG6tGeHl5sdfZ2ZkKCwtZw28jnGOglZWVsabyFX9ISAifb6DjHpyePTw8+F8LP4C251h8wArHACscA6xwDLDCMcAKRx+K\/AO8SKJwqmBoRgAAAABJRU5ErkJggg==\" alt=\"\" width=\"71\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">.<\/span><\/p>\n<ul>\n<li><span style=\"width: 35.34pt; font: 7pt 'Times New Roman'; display: inline-block;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><u>Wave Length (<\/u><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"14\" height=\"27\" \/><u>):<\/u><\/li>\n<\/ul>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><em><span style=\"font-family: 'Times New Roman';\">The distance between two successive crest or trough is called wave length.<\/span><\/em><\/p>\n<p style=\"margin-top: 5pt; margin-left: 72pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><em><span style=\"font-family: 'Times New Roman';\">Or<\/span><\/em><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><em><span style=\"font-family: 'Times New Roman';\">The distance of a crest and trough is called wave length<\/span><\/em><span style=\"font-family: 'Times New Roman';\">.<\/span><\/p>\n<ul>\n<li><span style=\"width: 30.9pt; font: 7pt 'Times New Roman'; display: inline-block;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><u>Wave number<\/u><u>\u00a0\u00a0<\/u><u>(<\/u><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"13\" height=\"27\" \/><u>):<\/u><\/li>\n<\/ul>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><em><span style=\"font-family: 'Times New Roman';\">The number of wave present in unit distance is called wave number<\/span><\/em><span style=\"font-family: 'Times New Roman';\">.<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">It is equal to reciprocal of wave length<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"16\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">.\u00a0<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Thus<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"210\" height=\"38\" \/><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">S.I. Unit:<\/span><span style=\"width: 12.88pt; font-family: 'Times New Roman'; display: inline-block;\">\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"44\" height=\"27\" \/><\/p>\n<ul>\n<li><span style=\"width: 26.45pt; font: 7pt 'Times New Roman'; display: inline-block;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><u>Angular Wave Number or Propagation Constant(K):<\/u><\/li>\n<\/ul>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><em><span style=\"font-family: 'Times New Roman';\">The wave number multiplied by phase 2\u03c0 is called angular wave number.<\/span><\/em><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">i.e.<\/span><span style=\"width: 16.45pt; font-family: 'Times New Roman'; display: inline-block;\">\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"62\" height=\"38\" \/><\/p>\n<ul>\n<li><span style=\"width: 22.01pt; font: 7pt 'Times New Roman'; display: inline-block;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><u>Wave Velocity or Phase Velocity:<\/u><\/li>\n<\/ul>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><em><span style=\"font-family: 'Times New Roman';\">The distance travelled by wave per unit time in its direction of propagation is called its wave velocity or phase velocity<\/span><\/em><span style=\"font-family: 'Times New Roman';\">.<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><strong><u><span style=\"font-family: 'Times New Roman';\">Relation between Wave Velocity, Frequency and Wavelength:<\/span><\/u><\/strong><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 200%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">As\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"232\" height=\"38\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 200%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Or<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"98\" height=\"38\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><span style=\"width: 7.12pt; font-family: 'Times New Roman'; display: inline-block;\">\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"104\" height=\"42\" \/><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 200%; font-size: 16pt;\"><span style=\"font-family: 'Cambria Math';\">\u27f9<\/span><span style=\"width: 23.55pt; font-family: 'Times New Roman'; display: inline-block;\">\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" 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alt=\"\" width=\"59\" height=\"27\" \/><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 200%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">So\u00a0<\/span><span style=\"width: 15.1pt; font-family: 'Times New Roman'; display: inline-block;\">\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"416\" height=\"27\" \/><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><strong><u><span style=\"font-family: 'Times New Roman';\">27 Speed of Transverse Wave:<\/span><\/u><\/strong><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; text-indent: 36pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">It is found that speed of transverse wave is directly proportional to tension in the string and inversely proportional to mass per unit length of the string\u00a0<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">So<\/span><span style=\"width: 19.1pt; font-family: 'Times New Roman'; display: inline-block;\">\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"78\" height=\"56\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><span style=\"font-family: 'Times New Roman';\">where<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"47\" height=\"27\" \/><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">In case of solids the speed of transverse wave is<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"63\" height=\"56\" \/><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Where\u00a0<\/span><span style=\"font-family: 'Cambria Math';\">\ud835\udec8<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0is coefficient of in rigidity and\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"13\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0is the density of the solid.<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><strong><u><span style=\"font-family: 'Times New Roman';\">28 Speed of Longitudinal wave in liquid and Gases:<\/span><\/u><\/strong><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">In longitudinal waves, the particle of the medium oscillates forward and backward in the direction of propagation of the wave. They cause compression and rarefaction of small volume element of the fluid. So speed depends upon Bulk modulus and density of the fluid. So speed can be expressed as\u00a0<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAE8AAABQCAYAAABYtCjIAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAYKSURBVHhe7ZtrSFRNGMftYoSpmJhQEmhevlSEFl1AKhURKgNBDEFQ\/FRI+SkJog9RGZGFfogkIcJATDGCNE1BEdRExYpCKim0AsHSpBBJsnn9P\/uMezvr7p6zuy\/tmR+MOs\/M8Zz9secyz8wJEQpd\/P3796qSpxMlzwBKngGUPAOYVl51dbUvivnk1dXViZCQEF8U88k7fPgwfXijmPK0VfIMoOQZQMkzAOS9fPmSa\/oxrbz3799zTT+mlLd\/\/34lTy+43il5OlHyDKDkGUDJMwDkzc7Ocs3KixcvRFJS0koZGBjgFiFu375t1\/bgwQPzynNFeXk5td+6dYsjVhCPiIgQg4ODVFfyHCgsLKT28fFxjli4c+eOWL9+vXjz5g1HTCjv\/Pnzq8rbuHEjtf\/584cjQnz58oViY2NjHLFgOnmnTp1yKe\/bt2\/UduzYMY5YxK1du1Z8\/vyZI1aUPBv6+\/up7cKFC1T\/+vUr1V+9ekV1R5Q8G3BHRdvDhw\/Fs2fP6O\/W1lZudcaU8uLj47lmT3Z2NglLSEgQmzZtor+bm5u51RlTyuvt7eWalcXFRZIFaWByclKsW7eOYrY3D1uUPGZiYoJEnThxgiNCHDp0iGIfPnzgiD2mk5eamqopr6uri0RdvnyZI0J0d3dTbO\/evRyxx3TyIENLXkVFBbUNDQ1xxMK2bdsoroWSt8yyBBEdHU1tv3\/\/5qiFS5cuUbysrIwjVpS8Zd69e0dxlLm5OY5awKhCtjnOe5he3tLSkrh\/\/\/5KaWxs5BYLTU1NK23IpNhiSnm+QskzgKnkyQdhX2EqeTLR6SuUPAPYycOdB0MR22wpwNju7du3TsnAQIPc2sjIiBgdHaW\/cbze4Dd5nz59omUIu3btoh10dnZSB4z5Dh48KI4ePUrxmZkZigeSjx8\/igMHDlA2JDc3d+WB1tWY0xV+k4eDwgVV5rEePXpEHZC2ljNNyDKsdsCxsbG0raclJyeHt3QN9hcWFkZzC5L29nYRHh7ONc+BPMfnOCM4XfPu3btHH8wxe4phy5o1a7imzd27dymh6GlpaWnhLV2TmJgoNm\/ebJcWmpqaEjdu3OCa5\/hd3tmzZ0ne\/Pw8RyxUVlaKtLQ0rgWGp0+f0rF0dHRwxBha8uRZoLPYy9uzZ4+Ii4vjmpWoqCgxPT3NtcCASwkO0lfXWfwvR3m4tustz58\/t8rDqYkdpKenc8RCfn6+OH36NNdck5GRQfI9LWfOnOEttUlJSaHj8fau6goteUawO21xY8AOTp48yRHLwBjXOsdUjRa+vmFs376d+vkK\/C+\/ycNpiR2UlpZS\/ebNm1T\/\/v071QPNvn37aP8\/f\/7kiOVZD3dfPfhVnpz03bJlC\/2OjIwUv3794tbAgyUOOA4UTETj94YNG8Tr16+5h3dge1\/idLc9fvw4rQJ6\/PgxR\/5fGhoaxI4dO2g6sLi4mKP68Lu8YEbJ08n169eVPL0oeQbQIw8TPteuXaMZNK3pSiVPAzxh4MaJOduamhpx5coV2ragoIB7WDCVPPn86g685LJ161a7YeHFixdpsGA7RDWVPLyd7Y76+nr6lmH5hS3Dw8MUl6k6oOQ5cOTIEacUGFDy3Mj78eMHCdI6veVaFkxHSEwjDx\/cnby+vj7qV1tbyxEriDuOqZU8G\/DuBfo5vkaAxDDimN+xRcmzISsri\/phVagEqTgkgvHyiiOmkvfkyROuOSMTwaGhoWLnzp20Fhnpq5iYGJpHWVhY4J5WTCVvNeSyWnw7e3p6xLlz50RJSQlNUi1L4l72BI08zKbhw+PdCS3cyWtra6M+3uQK\/3l5mFnbvXu3qKqqog+PojXn4U4eHk\/kSnhP+eflYX5ZTsQjYQpJRUVFVJdgUeJq8iAbjyGuFm67IqiueXhfVn77bHEnD0tp0Z6Xl8cRzwgqeQBzzhCRmZnJEffy9BJ08gBE4U1FiZLnBfK1J7k8BPLkm4y+JCjlAchDwZyvkuclycnJJA9LR5Q8L5HpJVmUPC\/BaEHJM4CSZwAM35Q8A2C5rz8whTx\/oeQZgOQt\/0hRxfsihIj5D\/4pr00ZpAqCAAAAAElFTkSuQmCC\" alt=\"\" width=\"79\" height=\"80\" \/><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">In case of solids<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"98\" height=\"56\" \/><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Where\u00a0<\/span><span style=\"font-family: 'Cambria Math';\">\ud835\udec8<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0is modulus of rigidity.<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><strong><em><u><span style=\"font-family: 'Times New Roman';\">2<\/span><\/u><\/em><\/strong><strong><u><span style=\"font-family: 'Times New Roman';\">9 Speed of Sounds: Newton\u2019s Formula and Laplace Correction:<\/span><\/u><\/strong><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">The speed of sound wave at constant temperature can be given as<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"65\" height=\"56\" \/><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 200%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Also<\/span><span style=\"width: 5.77pt; font-family: 'Times New Roman'; display: inline-block;\">\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"137\" height=\"27\" \/><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 200%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Differentiating both sides, we get<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 200%; font-size: 16pt;\"><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"140\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 200%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Or<\/span><span style=\"width: 19.12pt; font-family: 'Times New Roman'; display: inline-block;\">\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"118\" height=\"27\" \/><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 200%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Or<\/span><span style=\"width: 19.12pt; font-family: 'Times New Roman'; display: inline-block;\">\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"152\" height=\"47\" \/><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 200%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Or<\/span><span style=\"width: 19.12pt; font-family: 'Times New Roman'; display: inline-block;\">\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"190\" height=\"38\" \/><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 200%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Now Newton\u2019s formula for speed of sound in a gas<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 200%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"63\" height=\"56\" \/><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 0pt; line-height: 200%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">At S.T.P.<\/span><span style=\"width: 12.43pt; font-family: 'Times New Roman'; display: inline-block;\">\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" 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alt=\"\" width=\"325\" height=\"27\" \/><span style=\"width: 36pt; font-family: 'Times New Roman'; display: inline-block;\">\u00a0<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 0pt; line-height: 200%; font-size: 16pt;\"><span style=\"font-family: 'Cambria Math';\">\u27f9<\/span><span style=\"width: 23.55pt; font-family: 'Times New Roman'; display: inline-block;\">\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"246\" height=\"56\" \/><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 0pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">The above value is 15% less then experimental value (331<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"54\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">) of speed of sound in air at STP.<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 0pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Latterly Laplace pointed out that sound travel adiabatically not isothermally by this Newton\u2019s formula modified as<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 0pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"88\" height=\"56\" \/><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 0pt; line-height: 200%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Where<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"246\" height=\"56\" \/><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 0pt; text-align: justify; line-height: 200%; font-size: 16pt;\"><span style=\"font-family: 'Cambria Math';\">\u27f9<\/span><span style=\"width: 23.55pt; font-family: 'Times New Roman'; display: inline-block;\">\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" 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\" alt=\"\" width=\"254\" height=\"56\" \/><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 0pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Which is close to the experimental value, hence Laplace correction is justified.<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><strong><u><span style=\"font-family: 'Times New Roman';\">30 Factor Affecting Speed of Sounds in A Gas:<\/span><\/u><\/strong><\/p>\n<ol class=\"awlist37\" style=\"margin: 0pt; padding-left: 0pt;\" type=\"i\">\n<li style=\"margin-left: 54pt; text-indent: -54pt; line-height: 150%; font-family: 'Times New Roman'; font-size: 16pt; font-weight: bold;\"><span style=\"width: 38.9pt; font: 7pt 'Times New Roman'; display: inline-block;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><u>Effect of Pressure:<\/u><\/li>\n<\/ol>\n<p style=\"margin-top: 0pt; margin-bottom: 0pt; line-height: 200%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">As<\/span><span style=\"width: 18.22pt; font-family: 'Times New Roman'; display: inline-block;\">\u00a0<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"72\" height=\"56\" \/><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 0pt; line-height: 200%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">At constant T<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"137\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 0pt; line-height: 200%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><span style=\"font-family: 'Times New Roman';\">Or<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"136\" height=\"41\" \/><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 0pt; line-height: 200%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Or<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"122\" height=\"41\" \/><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 0pt; line-height: 200%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">When pressure a change, then density is also changes in same ratio, thus there is no any effect of pressure on speed of sound waves.<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 200%; font-size: 16pt;\"><strong><u><span style=\"font-family: 'Times New Roman';\">(ii) Effect of Density:<\/span><\/u><\/strong><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 200%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">If\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"22\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0and\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"22\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0are the density of two gases, then speed of sound in them will be\u00a0<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 200%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"81\" height=\"56\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><span style=\"font-family: 'Times New Roman';\">and<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFEAAAA4CAYAAACFdBSkAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAXTSURBVHhe7ZpbSBRfHMfN1CBFDMvygiJCRlkY4uVBMaHEJ0EQBSkfii4EgpaX0JeIJHoJ9EEN0qiIEhEj1AdvUZCipQUhGWSmeb9lZmZp\/f58f3tmHbdx13VH\/+vufODgnDN7Znc+njmX3xkH0rAYTaIKaBJVQJOoAppEFbA7iZ8\/f6Zbt26pmuxOYkpKCjk4OKibxLXtBtz0qVOnRE4dNIkqoElUAbuUqDZ2JfHt27eaREt58+aNJtFSNIkqAIm7du0SOaKfP39SWVkZXblyhb5+\/SpKiX78+EGZmZn0+PFj+vXrF1VUVFBhYSEfz8\/PU3l5OZ8fGxvjz9udxPj4eJEjys\/Pp0ePHrHYjIwMUUp08uRJ8vT0ZJmnT5\/mz6AFP3nyhJKTk\/nvoUOH9K3ariTipuUSJVAWFxfHx+Pj4+Ts7ExTU1Ocn5iYoIWFBa6bkJDAx+DZs2eaRDkFBQV6iYGBgdTQ0MDHEq9eveK6PT09ooSorq5Okyjn2rVrLBGPLfo6Q27cuEHh4eEipwPX2bNnDx\/bncTW1laRWwYS09PT6ciRI\/T3719RusyJEyfo7NmzIqfD1dWV3r17x8d2J1EJSMS50dFRUbIMBhecS01NFSVEx44do6KiIpGzI4lDQ0OrSsSjWVlZKXIr6erq4nptbW1UXFxMDx48oJGREXFWh91LxGjr6OjIwVolIC4yMlLklLF7iegLUY7HVonY2FgO5BpDf1V0qNPT0zwvkoPyyclJTlsZSAwNDRW5ZZ4\/f061tbUitxKsTnbv3k1RUVH06dMnUfovLBHi0C\/4+vryf6WxsZFPQmp0dDTt37+fy6UJ6HpZWlqiubk5s9Li4qKobRlPnz5VlKgGLBFzIPQNTU1NLOvevXt88uLFi\/Tlyxc+3rlzJ3V2dvLxemlpaeHrm5OqqqpEbcvAtTZUosT9+\/f5yzo6OkSJDrSG7du38wLcEgYHB6m0tNSs9PHjR1HbMjZN4uXLl\/nLZmZmRImOO3fuUFBQ0D8T0e\/fv9Pw8DD3HdaOksScnBwutziJ6zFhYWHk5eUlcsv4+fnpZ+d\/\/vzhiSd+0N27dzlchGP0qZBqreBmNwr9lfHI4osiIiJEiY7c3FxKTEzUt0JIxGgln92\/f\/+e6yLuZgyEoo4fP25WwuhpKfjNmyLx27dv\/EUI90hgoHFycuJzxsAjjbolJSWiRBkMTDExMWYlDEaWglnBpkjEPBBflJaWxnksb3bs2LGmjh2RXtQ1XA5ZC5su0dvbm9zd3flYaUFuSH9\/Pwcxm5ubRYn1sWkSwdGjR8nFxYVb1lrAY75t2zb95NxagUQfHx+RU591\/3uwmkF\/WV9fL0qsl76+PuuTiEn3gQMHVoSPMHpLu1\/WBh5lcyQiGIERfa2sS2J2djbvdr1+\/VqfENg8d+6c+IR1sVaJt2\/f5ljB1atXKTg4mHf11oLZEtEKAwICFJOpKc7\/BSRmZWWJnDLnz5\/Xb1aB7u5ucnNz4\/7UFOvuE7cSpkZmhMnQv8uXuwMDA1yvt7dXlKyOTUhEK8MNrzbImZJ44cIFDgPKYwMvX77kelIoDpv4eXl5\/Hrx4cOHufuS2NISsTDAjV66dIn\/hoSEiDMrMSURa\/+bN2+KnI6kpCQ6ePCgyBE9fPhQP9hgZoJr\/v79m\/NbWqI8eiS1RuyJGGJKIubG8vCftPD48OGDKFkJArwIVEstd0tLlIOoO25cSRhioavx4sULruPv788BEmwV7Nu3j99lVAKvmWB\/Gi9DSdiMRIC3uyAE4Tk5xiSeOXOGI\/uQgoFldnZ21TkiRmxEtKTHWMKmJALD1oi3u4xJRKTIsD9UAuE+vAkhIR+EbE4iXpGDxOrqas4bkyjFGdvb20WJMvictIknT9J2ic1JBB4eHnyTeESNScQmHAYkw+0Qc7FJidevX9e3FkjcaGxSIti7d69e5EZjsxKxjtckqgB2LjWJFlJTU6NJ3CpoElVAk2gxRP8Bucj7Agvly98AAAAASUVORK5CYII=\" alt=\"\" width=\"81\" height=\"56\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 200%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAABYAAAAbCAYAAAB4Kn\/lAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAC5SURBVEhL7ZQxDoMgGIWJ4Y6ex4s4srDA5GLiysYmJhxAFzmAA39b8webiNSkNSYNX8Lw3vANPAKBi8jiQBYHsjhwr3gcRyiKAiilsCwLtmlOia21QAhZzzRN2KY5JfbeQ1mWUFUVNp\/5s\/HqugatNaYNKSW0bYspzqGYMbaO9XoN7\/R9H4ac5xnbPYdiznlUPAxDEDvnsN2TvAohBBhjMG10XQdKKUxx7hnvG7I4cJ34+cE0vz++eQCyyAcD\/+5G4AAAAABJRU5ErkJggg==\" alt=\"\" width=\"22\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><span style=\"width: 28pt; font-family: 'Times New Roman'; display: inline-block;\">\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"77\" height=\"56\" \/><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Hence at constant pressure, the speed of sound in a gas inversely proportionality to the square root of the densities.<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-left: 18pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><strong><u><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><\/u><\/strong><strong><u><span style=\"font-family: 'Times New Roman';\">(iii)Effect of Humidity:<\/span><\/u><\/strong><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 200%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">As<\/span><span style=\"width: 18.22pt; font-family: 'Times New Roman'; display: inline-block;\">\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"73\" height=\"56\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0<\/span><span style=\"width: 24pt; font-family: 'Times New Roman'; display: inline-block;\">\u00a0<\/span><span style=\"font-family: 'Cambria Math';\">\u27f9<\/span><span style=\"width: 23.55pt; font-family: 'Times New Roman'; display: inline-block;\">\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"68\" height=\"42\" \/><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">As the density of water vapor is less than that of dry air so sound travel faster is moist air then dry air.<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-left: 18pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><strong><u><span style=\"font-family: 'Times New Roman';\">(iv)Effect of Temperature:<\/span><\/u><\/strong><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">For one mole of a gas,<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"79\" height=\"27\" \/><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 200%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">If M is molecular mass of the gas and<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"17\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0is the density then<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 200%; font-size: 16pt;\"><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"54\" height=\"38\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><span style=\"width: 32pt; font-family: 'Times New Roman'; display: inline-block;\">\u00a0<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 200%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">or<\/span><span style=\"width: 22.67pt; font-family: 'Times New Roman'; display: inline-block;\">\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"55\" height=\"41\" \/><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 200%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Or<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"78\" height=\"41\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><span style=\"width: 7.12pt; font-family: 'Times New Roman'; display: inline-block;\">\u00a0<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 200%; font-size: 16pt;\"><span style=\"font-family: 'Cambria Math';\">\u27f9<\/span><span style=\"width: 23.55pt; font-family: 'Times New Roman'; display: inline-block;\">\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"60\" height=\"41\" \/><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 200%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Or<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"83\" height=\"56\" \/><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 200%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Clearly<\/span><span style=\"width: 24.91pt; font-family: 'Times New Roman'; display: inline-block;\">\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"66\" height=\"32\" \/><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Hence speed of sound in a gas is directly proportional to the square root of it absolute temperature.<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><strong><u><span style=\"font-family: 'Times New Roman';\">(v)Effect of wind:<\/span><\/u><\/strong><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">As sound moves with the help of wind or air, if wind in direction of sound then speed of sound increases and when wind flow in opposite to direction of sound then speed of sound decreases.<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><strong><em><u><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><\/u><\/em><\/strong><strong><u><span style=\"font-family: 'Times New Roman';\">(vi)Effect of Frequency:<\/span><\/u><\/strong><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">The speed of sound is not affected by the frequency of sound.<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><strong><u><span style=\"font-family: 'Times New Roman';\">(vii)Effect of Amplitude:<\/span><\/u><\/strong><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">To a large extent, speed of sound wave is independent on amplitude of the waves.<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><strong><u><span style=\"font-family: 'Times New Roman';\">31 Displacement Relation for a Progressive Wave:<\/span><\/u><\/strong><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><strong><u><span style=\"font-family: 'Times New Roman';\">Progressive Wave:<\/span><\/u><\/strong><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; text-indent: 36pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">A wave which travels from one of the medium to another is called a progressive wave. It may be transverse or longitudinal.<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><strong><u><span style=\"font-family: 'Times New Roman';\">32 Plane Progressive Harmonic Wave:<\/span><\/u><\/strong><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">During propagation of progressive wave, if particle of the medium vibrate simple harmonically then motion of wave is called plane progressive harmonic wave.<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">The displacement travelled by simple harmonic progressive wave is<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"268\" height=\"27\" \/><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><strong><u><span style=\"font-family: 'Times New Roman';\">Phase and Phase Difference:<\/span><\/u><\/strong><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><strong><u><span style=\"font-family: 'Times New Roman';\">Phase of Wave:<\/span><\/u><\/strong><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">The phase of a wave is a quantity which gives us the complete information of the wave at any time and position.<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0<\/span><span style=\"font-family: 'Times New Roman';\">Suppose a harmonic wave is given by<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"271\" height=\"27\" \/><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 200%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Where phase of wave is<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 200%; font-size: 16pt;\"><span style=\"font-family: 'Cambria Math';\">\u2205<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"150\" height=\"27\" \/><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 200%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">The path difference \u2206<\/span><img decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"12\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0and phase difference \u2206<\/span><span style=\"font-family: 'Cambria Math';\">\u2205<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0of the wave are related <\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 200%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">as<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHUAAAAmCAYAAAD6HtTlAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAYuSURBVHhe7ZtbSJRNGMfNTLPUREWyC5EyU4QQOqFeVBIJXUhFZBpEGBYYpVBKiKDdhFKU3nS8SA0tQy+UogOhgqhUEFhapoYpJnYuD53z+fo\/O2O77+67u326ri7zg4GZZ+bd153\/zOzzzIxupHA5lKguiBLVBVGiuiBKVCs8fvyYzp07RxcvXqS8vDy6evUqff36VdTOXJSoOjx69Ig8PDyos7OTy58\/f6bw8HBau3Ytl2cySlQdIGJzc7MoGcBsdXNzo7dv3wrLzESJ+g9kZGRQUFAQ\/fr1i8utra0UExNDixcv1k1DQ0PcdjpRotrJwMAAL8c1NTVcxmzNzMykT58+sdAoj42N0f379ykkJITzSM5AiWoHcI4WLlxIly9fFhZT5s+fT+Pj45zfv38\/rVu3jvPOwqVF3b59O82dO9dqysnJEa0t8\/37d\/4dLS0tFRZTOjo6aM6cOZzHsoy2V65c4bKzUDPVCj9\/\/iR3d3fdGQpSUlJ4GQYjIyMssLPDHiWqFbZs2ULZ2dmiZKCkpIS6uro4\/\/v3bwoMDOTZCp4\/f06+vr5sr6ioYJszcJioVVVVtHv3blGafTx9+pSXUvw+yrR06VK29fT0cJvjx49zeXR0lMsvX77k8urVq6mhoYFtzmDKRO3u7qY7d+7QrVu3qK+vj0ewHNGzkbt379KFCxcsJunVvnr1ir+rMR8+fKAfP36IknOYtKjYSluxYgWPUG2SI1gxvUxKVMxOiBcWFkY3b96kN2\/e8MhFGfbg4GDRUjGd6IpaVlZG58+fFyXLhIaG0oIFC1hMyfDwMM2bN4+DdAi7Y8cOUaOwRn19PWVlZYnS5NAVFbMMougxODjI9bt27RIWA8nJyXTs2DHOIyj38vLivMI6mCDW+vtfsPgply5doiNHjvBLbty4IaymYLMb9XCOjPHz86Pe3l7OHz16dMr+UFemsbGRV0X01ZkzZ4T1\/2OxxxGLFRQU8Ev0REEchjopIMB5Y3x8vCgR\/86izZMnT4Rl+pB\/u7MT+tEWt2\/f5r6Tz+jx8eNH3txAm8rKSmE1xMtRUVFsf\/\/+vbmo8Fjz8\/M5j0AaDb99+8ZlYyyJumrVKmpqahIlw5kk2tgSddu2bZSYmGh30m4IWALO2kxItmYetiFlPB8QEMD9hZ0pLWiHKAMkJCTwIQL2m7E1uWbNGtq6dSv5+PjwLpiZqGfPnhU5ogMHDvBLcPqvRYqKIB08ePCA\/P39J46lgFxSXrx4ISyWiYuLo5UrV9qd0tPTxZOzn+rqapEjHgDoL+mT6FFXV8ftnj17Rnv37qUTJ06IGgMmosKLPX36tCgZwMNIWtra2theXl7O5dTUVCouLua8BNtscrNbYQ72iOG7GKPX38bInaudO3fSxo0bhfUvJk\/DrdaCpREfgH1NY3jt\/mPHUiDz7969E7UGPD09ydvbW5QUWhBBaMnNzeW+rK2tFRZz5MnRkiVLOITUYiKqJdVlvImkBSMF9g0bNlBaWpqwGsASiTpst9ni2rVrfFxlb7LnM2cDOEzXAk9Yr78luGqD39\/IyEhhMWXiyfb2dpEzZ\/ny5fwSeF\/GYIbiygbqcCHr1KlTdOjQId7Qhu3gwYOGhjZYtGjRxBexJ23atEk86Tj27NnDsePmzZuFZWox9j20rF+\/nr9nS0uLsPwFnm5sbCz\/fWiDmxdaJkSNjo4WOXMePnzIH4AZqQVxLLwu2eFIeOm9e\/dEC9tgCcHoszc5ek8ZgxW3CHFFBd+nv79f1EwdOKDXA0d5eC+8Wi2FhYU8ceQ+AcIhLSzq69evuWANKZgWhDGImeBef\/nyxeknFFNN3B\/PHF7mdCP7Ww4ohDOITJYtW8Z9jYmA+sOHD3M9wiIMRsAq2bPxHhERYSYq4lecG8r7Oa4Ilt+pFhXHkrZISkri\/sbZLSYd8ggZEYdK4McgusBKef36dWE1Wn4V5uBmIDrTGTN1MihRdcCuDq6EOmKmOholqgXgF+D4EM6eo7xfR6JEtQAOJRBWAK0fMRtQomrAviuOD2UcCVGd8a8Tk0GJagQ8SIgor3wCeP379u1jT1O7+TJTUaIacfLkSb4gYByi4YSpqKiI72PNFpSoLgfRf0QYPRBt516jAAAAAElFTkSuQmCC\" alt=\"\" width=\"117\" height=\"38\" \/><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><strong><u><span style=\"font-family: 'Times New Roman';\">33 Principle of Superposition of Waves:<\/span><\/u><\/strong><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; text-indent: 36pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">According to principle of superposition of two waves the resultant amplitude of the wave moving though a medium is equal to the algebraic sum of all the amplitudes of the waves. i.e:<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"294\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">.<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">When crest falls over crest and trough fells over trough then resultant amplitude of the wave adds up and when crest falls over trough and trough falls over crest then resultant subtract off. As shown in fig.\u00a0<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><strong><span style=\"font-family: 'Times New Roman';\">5.6 REFLECTION OF WAVES<\/span><\/strong><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Suppose<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0<\/span><span style=\"font-family: 'Times New Roman';\">a pulse travelling along a stretched string and being reflected by the boundary.<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0<\/span><span style=\"font-family: 'Times New Roman';\">the reflected wave has the same shape as the incident pulse but it suffers a phase change of \u03c0 or 180<\/span><span style=\"line-height: 150%; font-family: 'Times New Roman'; font-size: 10.67pt;\"><sup>0<\/sup><\/span><span style=\"font-family: 'Times New Roman';\">\u00a0on reflection. This is because the boundary is rigid and the disturbance must have zero displacement at all times at the boundary. By the principle of superposition, this is possible only if the reflected and incident waves differ by a phase of \u03c0, so that the resultant displacement is zero. This reasoning is based on boundary condition on a rigid wall. The phenomenon of echo is an example of reflection by a rigid boundary.<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">If the boundary is rigid, the pulse or wave gets reflected. If the boundary is not completely rigid, a part of the incident wave is reflected and a part is transmitted into the second medium. The incident and refracted waves obey Snell\u2019s law of refraction.<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">To study, a travelling wave or pulse suffers a phase change of \u03c0 on reflection at a rigid boundary and no phase change on reflection at an open boundary.\u00a0<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">let the incident travelling wave be\u00a0<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"217\" height=\"27\" \/><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">At a rigid boundary, the reflected wave is given by<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"464\" height=\"27\" \/><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">At an open boundary, the reflected wave is given by\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"458\" height=\"27\" \/><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Clearly, at the rigid boundary,<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJgAAAAbCAYAAACA5kZXAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAXRSURBVHhe7ZlbSFRdFMcnRVMjxEC8BUbZxYdQFCQyK\/ASiZhRSZEkiheE0hBEEHzI9FEtglDoJbCLhOWDKURJN3sQUsO84UN5ybQyzS5eSnf816yj08xpPMfxzPj1nR9sZvb\/nLNnz5q191prj0Ho6GiI7mA6mqI7mI6m6A6moym6g+loiu5gOpqiO5iOpugOpiNLVlaW8PX1FQaDQQQFBYnCwkK+og7dwXQsiImJIcd69+6dWFhYELdv36Z+Tk4O36Ec3cFMgBH\/79y7d4\/s8OzZM1YEOdn27duFi4uLeP\/+PavK0C1qgu5gQkRFRZEdJicnWTFSXV1N+sWLF1lRBll0bm5OuLm5kYeGhITQBYn+\/n6Kxbh24MABVu1DcnKycHV1FevXrxcfPnxg1UhkZCTNaceOHazYzmo6WF9fH80bczx79iyrRhoaGkhHu379OqtrAz8\/P7LDzMwMK0ZaWlpIP3bsGCvKIIt6e3tT586dOzTI3bt3qS9x69Yt0ltbW1mxpKqqiu5R0zo7O\/lpS1JSUkRPT4\/o7u6me4uLi\/mKkampKdKjo6NZsR2Mtxq8efNGJCUl0fuwsDAa9+fPn9SXSEtLE+vWrVMdckzJzc2lsdW0+fl5ftoSXJPuM6e3t5f0ffv2saKMP0YaGBigQc6cOcOKkYSEBFpt1iZ38+ZNqjbUNKxyJfj7+9O8kAtItLW1CWdnZzExMcGK7cgZ1lZqampoXMxXAt8Di\/ro0aOsrIySkhJZu1pr1n7Dt2\/f0lzl7ICFAN0mB0OohCMh\/JiyefNmcfXqVe7Zn9jYWPpyX79+ZUWIQ4cOifDwcO4tAUNg57NGR0cHbfnmDZ8hp798+ZKfVA9yGexUFy5cYEWIoaEh+ixbxtUCzR0MxMfHiw0bNix6Oozg7u5uEZPtiRQKsMNKYPcaGxvj3hKJiYli79693JMnNDR00ZBKmq153saNGym3kSgvL6cFstbAsYT0nc2RFoXNDlZRUUEDDQ4OUj8iIkLU1dXRe2t0dXVRHqamjY+P89PWefHiBc0Jr6CoqEgcPnyY3puDlfbx40fuqUPOsKuBlDiDb9++UUGF3cJWnj9\/LmtXa800zZAD80SbnZ1lxYiUgx0\/fpwVZVhY9NGjRzQQXp8+fSp27dpFoXM5MHlpckqbtSTflOnpabq\/srKS5oKQY26A0dFRUVtbS800lKoBn6EFp06dWhy7rKxMpKen03tTsHtg7lIxMDw8TH0UOX9jtZN8sG3bNrrvy5cvrBh5+PAh6aWlpawow8Ki2Lkw0KVLl8TOnTtFe3s7X3EsgYGBVCIjhN+4cYPVJRDCMzMzae4rDed4VgsaGxtpbBQknp6eFhUlTspTU1PFpk2baKGeO3du0XkePHjAd9mHkydP0ue+fv2aFSP5+fmkq616LSz669cvGsjLy0ucP3+eVceDUO3h4WE1H8rIyKCKd6Xge2sBHB5jY5E8fvyY1SVQSCB07d69Wxw8eHDxOAiL3N6578jICBV6W7duXQynKFQwf\/PTBSXIWhSJHELjjx8\/WHE8p0+fpi8pl9hL4O+MK1eucE89WjkYQFFy4sQJ7smDHezy5cvccxzYcXHAjcW8f\/9+OlJB5DBPS5RgYVFUCziBXq7UtzdYUfX19dyzRCqjX716xYp6tHIwhDmMbS3\/wZkg7vn8+TMrjgXFCBJ7+AHy25Xyh0XhoQhDa+3viyNHjlBeYq0CQqWLH2i5KsnefPr0STg5OdEPZo28vDzNHNyRGPCD3L9\/X3z\/\/l0EBASoLkO1AHkHEnnkg3Cu4OBgvvJ3EFqQ46CCxJaOytNR4PgAfxfhKALRQMmB6p49e0R2djb3\/h0M165do5WDHKGgoIBlx4Iwhzmh4UDSvOqSA4ewPj4+Ii4ujhzTkeCMDnNHNJBL6uXYsmWLePLkCff+HQw4Z8Gf3I5c8eYgD8EZEPLB\/yLNzc2iqanJ4Y6+FkCIbNKb3rRpC02\/AfvoHxh37Nz+AAAAAElFTkSuQmCC\" alt=\"\" width=\"152\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">at all times.<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><strong><u><span style=\"font-family: 'Times New Roman';\">34 Stationary Waves:\u00a0<\/span><\/u><\/strong><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><em><span style=\"font-family: 'Times New Roman';\">When two identical waves of same amplitude, frequency travel in opposite direction with same speeds along the same path super impose each other and resultant wave does not travel in the either direction called stationary or standing waves.<\/span><\/em><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><strong><u><span style=\"font-family: 'Times New Roman';\">35 Standing Waves and Normal Modes<\/span><\/u><\/strong><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Consider a wave travelling along the positive direction of x-axis and a reflected wave of the same amplitude and wavelength in the negative direction of x-axis. With \u03c6 = 0,\u00a0<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">We get:<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"548\" height=\"27\" \/><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">The resultant wave on the string is, according to the principle of superposition:<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"274\" height=\"27\" \/><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAWYAAAAbCAYAAABP7SW9AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAABDpSURBVHhe7dwDkCVJFwXg3X9t25z1xtq2bdu2bcfath1r27ZtG\/nHl1M5kfPmsef1zoueOhEV3Z31XlVW5s1z7z03qwcJJUqUKFGiYzAIFL+XKFGiRIkOQEnMJUqUKNFhKIm5RIkSJToMJTGXKFGiRIehRxDzH3\/8Ed5+++2+jh9\/\/LE429n44Ycfit9C+Pvvv8OHH37Y5xl+\/fXX4kyJEu3DP\/\/8E3766afirxB+\/\/338O6770ab89P5EgMWPYKY33rrrTDmmGOGWWaZJSy\/\/PLxuO+++4qzrQFRvvrqq+Gbb74pWroH+rzFFluEpZdeOvz111+xzQK58sorw9RTTx0mnHDC8Morr8T2gR3mYt111w2XX355HKOeiM8++yy89tpr3eqM\/\/3333DvvfeGFVZYIey3335Fa+\/xPeaYY8L4448f5ptvvvDLL78UZ0p0BRzbzjvvHI499tjw9ddfF6194+WXXw5TTDFFX8cdd9xRnO0hxPz66697kHDggQdGo3IksmsVJ554YhhhhBHCrbfeWrS0H6496aSThiOPPLKviBlE+rPPPnuYbrrpak7qwAaG\/sQTT4TlllsuLLnkkuGdd94pzvQcrL766mH00UcPn3\/+edHSfhxyyCFhqqmmCjfddFM\/DoBTcP8111wzZm4l+g\/vv\/9+2GGHHeI65gwr8eeff8a5dpx33nmRv6699tribA8j5sMOO6xo6TqOOOKIsMwyy8QIpjtw9913h5FHHjlceumlMYKpxMcffxwmmWSSSELVzvckvPnmm2GVVVZpOjPgcGUZ00wzTfjoo4+K1vZA1HjwwQfHPv3X4HhWXXXVsOGGGxYt7YeIeOyxx47ZYDWI1oYccshw0kknFS0DFmzCfHSaJHn22WeHnXbaqam1aV7PPffcMMwww4RHH320aO0X1113XUnMAxJffPFFjFg23njjmhH9gw8+GJ9FGtSTwbAPOOCAMNFEE0VdvVkg0Jlnnjmsv\/76bZU1ELJxv+WWW4qWnoOnn346DDHEEOH8888vWvrF4YcfHp9fZtIJIOnpzyeffFK0DHjIMnr16hU22GCDoqU5bLLJJlGq+O6774qWvtHxxMw7PvbYY+Gaa64JDz\/8cPj+++\/DBx980DB1bYaYDeqLL74Yr20AeDBRcSp0vPHGG+H666+P5+k\/CQhEQeSGG26In0ltDObmm2+OhiwtaQbHHXdcXCDPPvts0dIvTjjhhPC\/\/\/0v3HXXXfFvYyL11C\/Hl19+Gdv1Qf8RySOPPNIX0TOA22+\/\/T9bZPpRbQHpo7n77bffipbe+Pnnn+M8i+BIOldccUV8NilfMxLUxRdfHIYffvjwwAMPFC39j+4i5m+\/\/Tbamue78cYbw3PPPRedi7EB59hjPrfApnzW3Kd2EoNI0ueTLTaC+6y00kqxZlHLTn1m2WWXDWOMMUYfKUVGkmzOmKQ5tF6sN+uB\/JGeA6xV7e2QmrqTmNmYvldz7J5T\/\/PnMu7m8aijjgqDDz54WGuttfqMjes0gsBj6KGHjtl4NbRMzCbnhRdeaPpgNHZIdAWPP\/54mGuuucKMM84YUwUFvJlmmilMPvnk4cwzzyw+VR2NiPnTTz+NRTYp8I477hjWWWedqCPzfmniSQjSatex8MHk+H2jjTaKnxXt0n2vuuqqMP3008drmCjpTSNwDHPOOWeYe+65IzFVAwOQ0ooiGTkg5tQv90ztImtyh3PDDTdcdBLw1VdfhcUXXzyMOOKIYZtttolt3QlF1sUWWyzOfyWMn+cRGScH6Censemmm8ZnUmzadddd4yHtS5+rhyT3SP3bpYd2BzGLVNnz\/PPPH3bZZZc4L+QC85ZI4aWXXorz7d5pbtmHMZNZjTbaaJEItB100EFhggkmiM6d7eUBRC3QOtnCtttuW7T0C6Qz5ZRTxv6lfhlja2+wwQbrc39zI+r2N1sea6yx4vVB0OMabFGRtn\/RXcRsNwqC3G677aoWOZGy53jqqaeKlt6Z7gUXXBBmmGGG2CdyGnvdbbfd4hw3g6WWWioGIZVBCrRMzGnxNHuYqK54S5Edj67yLkoGhCRlZYCiq3poRMwGka4r8gWEcfLJJ8f0IveaW221VTT6ZPAInZMQaWy99dZhvPHGCxdddFFcWPrMePRv5ZVXbhjpuabiCjLJvXEOC8RCRt7JwRmHeeedNzoWiwV8\/8knn4yemOFONtlkMbU36Z5h7733jgVGn+lOIDHOSmRXC5zYKKOMEhdujgsvvDAuehFWq0DGCyywQHSWHFE70B3EPNtss8W5S4U287PGGmtER59gLjkZhJvsgt7LPpEhW0CYCsWCChoxex500EHD0UcfHT9fD4hUBiYrqQXkMtJII4U99tijaOlNUKOOOmosYCUCY+P3339\/7Nc999wTtVOEJViZZ555Yt0EKVs3\/YvuIGb9tj4UWq2rarDWBTsLL7xwXyRqbtjcxBNP3E\/htBlwtLW05paJmbE+9NBDTR+i3moeoR4Mlge2wHmmBNdZaKGFIukksq6FRsSMOJFiXtBDgldffXXxV2+jY1yi6nw3BIIUKYgSRB7rrbdeH4JkvOOMM050KI0iPRGtPp566qlFS7+w6ERUnAEwcHrW9ttvX3MM3HfFFVeMOzksVHpWVwynVZBjOOJLLrmkaOkdrZuDJMNAWuCiiwRGzukbu644ckBOiL1dWwq7g5iHHXbYsOCCC\/bltEXI1kkC6YDjQhYJ5pTzYYeyJAHEvvvu24cgOTPPjhQbgZP2XPWi67QrgNQCzzzzTFx7p59+es2Ag1wm0jePgg2fbSfaTczGk46OZ957772iNURHo8iYc8\/xxx8fA658ntg2e+VYu5KlyRI502rrvyM1ZgthqKGGCoceemifiAHocAYC6TRCI2I+66yzouRgq5X9w9UgJRO10NoqjdGCsEBE3bnHo4NL3U455ZSipTZE2vpYbzElY0Sw9KtZZ501XruRPKTibgxJCs3uJrE7RHRT66Bt1gLiEMXJaPKxYnz6b7wTkIs95sY+GbTx5EjsO++q9EXvc69qW5EagfOSluaHBet6otfKc3bpdKXQyIkjUGkze64G9s8Zs\/9KyDLY17TTTtvXvJpvfa21wyLHZpttFj9bzwFuvvnmcX0IHuzKcL9m9PslllgiEpgotKvzaLso26gc8yTvCJQqz9WTZWqB1EYWMnY5zwi4jH++bfWyyy6L95bVJcgQ6MRd3bUiK3FNDrYSHUnMNmLrQmVBDOlptwAboRExMxq6koKRAoc0sTLCRSpSPl61ErR2C0wRJf9eWiDN6EzNELNUVfTEIEgn+tNIxoE0se7RLGi7vlPrkLLVgohKNEjzzGEfOeOVPSUoXCHmRRZZpA8xG0+SUVcWWAJdXz9JJa3CjhdklB8iIddDEpXn9tlnn6YLvDmQsXqGeUT8+QsECcbMfavNc3LUIrgcZC1BQqUNV0MjYpaZzjHHHJGMOQm\/I7Bmsi6ZnWsnibAr4KT32muvfsZ80UUXjdeWjVaes35bASLefffd43PltRBBhZdqBAn5WKorufc555xTtPSOorV1VR40\/r5Pn65Ey8RMX\/IwzR6VaUIzkDKRCPKIwAK2UCzyPC2uhUbEDAZe2iu1RAp2SORIJMszViINnJdPEky2iEGBpBmdsxExWyB0LRECeUfxge7npYB6oJWRauhX+++\/f9HaGCIE0Wyto9bWHhA1eJacaBAX7d145C9JPP\/8830koGT8d955Z\/x+ve1bjXDGGWfEa5ibdqC7dmUICkSiHB1JR+qcgyMQMFSTqjhn85rvrjFvZDlBQjNoRMxIFTmRzNi0VFvKXU0LzWFXiDdURdqVz9QOtFPK4GTIpdZWnrnInq0xEX8eRSNxgVj+kpnIWlBnbXQFyb6qFeRbJmYGRX9p9kB2tNtWYOeFB841HkUEbaSMVEjIB64StYiZR5Tu5em2qixDZFQ5SCbuWen93ddgWjx5pTbtDLBAXL9e\/yANPkKpBs\/JSBQewAJkSBZurTQaGar2i\/JVyUkZXU0pW0GK8uwMSRAZGw8Frxy2\/\/lsrkWLtKXo6fvGjmNuNIY5Uh\/y6Lx\/0E5i5ixdL4dIi9wkK0pItih7MZf584sktVfWPEhQrmNcodGYsQ\/PVUv2uO222+L50047Lf5NAzc39Zw8p+21buQpIGslIGgW7SRmTo9sRgbJJQs8g4DtBkpIJM6WE\/cImnr16hULsUnn19YKSbNTz1OZZULLxPxfQNFDF0TGIkUFCN4bUdpewvDs060XOdciZtE7w3Y+wYBK25BYQtI86cgGW7SQNDbRu6IgJ5FXcvXJAlFt9RmRRr3IGaknPa4a0sTl0o2dFsja7gvkn9524zwc7ukVWs8krbRrxGct8rT1qjtAPmDQycjMEV2avJHrzhaVMUXW+T\/NkYnJWiwMi4YmbVxa0XHpxKLJVjO0WmgnMQtoSAK5\/IHwOPd8L6uIDbGJxtiQDCIVltU8RMa2jebkmzI79mm90KbrSRpqFCLgWjUD3ye1kA7B3NF3kZD7mjdO1++yHzao2MdO9dkuIjKV7wnKuhpRVqKdxKxvAigZS9pBxNZwDJtNNSLPiCTZdi5pslGbECgC+iMjlNG3kq3RrY0zmaQSHUnMiBhhGTQLWPHNBNOWGC35wCKsV9SqRcwiMsRmf7S90GQEjkCRL0+\/TJx9hvRdhup+aYEgY8UBskUORurzimAiBguGodYCT42kSDfV9DsFP0QvzU9gnAhMlIW4UuFC\/5CwrVjJcFXqk25Lt0fa+YJuJzgyz21+RG76Za+uvhtrOwHc3++cWuXLEJ7LmNJJRTEWSP5yRSNwRBwAe8kjoP5BO4nZeJiLtddeO2YKFj6iVsxN+34hZRnGgN1tueWWfTIegYj+VNZYODELXBZHrxTx1oPdGByC9LwS7DXtr032DqJs97D2VltttShZISfjbe3oZ7Jh+nsqiiGrdr30005iBlww7rjjRrnQLhRatd1OggPjr81OH9t2BQ5sLME4yRA4OJEzkmbfrcC6NA\/VXkjpSGL20LQcEyxiSKmCiFA0asAaLb5axMzbMxQLw\/UVGaQt1V4Bdg3psaJSrq9KZ3xPFJRDv+0NFTUipHqknLDnnnvGNLFychAoQ6Qn5\/osr64QSCZiWD7nME4Wf76YfFa7Z5DuNlMY6h8YI7KMsfEzRfPGUVRo7hhctbkTSXpeBE57z6PpZsApcuTu0S7n005iNoeuQ9ozPvrJVqrJfGoaHLuxyudMRua7Iu0c1gcSFNE1s1WQXZJERHspk0lArq5lfeTZCh1WgdSRdjGZR06CjeXzJULWrj95Ztq\/aDcxsxN2o5\/mQ0CIfI25uTLWnkO2XM2m9MN4+G6rmrp7GH\/zUG1ddiQxtwO1iLnToJ8iXRv5myHyEv3CokHoXudu9rXkZoDwRIbtemGlk0DGUKRrFF13Ejg389GKvNWpkP2QR2rtICqJuQNAUqEdtivlG9hgq56CmTfhujsr6CkwTnZnqK3kGVmJ7ofsgoRFos1rDjlKYu4ASCeluN7HT29alWgOUndFWkXRVuWPgR3Gy55q20Wb+R8bJfofdHljrrZUT5Lp8cSsIOQfvzga7cMckCBjSNNUs\/2TnzLyqw9aKC2fgXu5INUhSrQG46ZopRBZ+dJKifZCUREfKfpVK2xro+070l7zHkfMtg15NTc\/mn01eUCCflbvVdkSvaFII6qw171dxb6BFcZP9JwXjku0H94kVlCuVUsSQSs45keeyURiLlGiRIkSnYRBBvk\/jbOdc6Xk8VMAAAAASUVORK5CYII=\" alt=\"\" width=\"358\" height=\"27\" \/><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Using trigonometric identity we get,\u00a0<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAPEAAAAbCAYAAACtFGntAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAA3TSURBVHhe7dsFbBxHFAbgKzMzp8wMKrdpykwqMzNzq6qYMjOozMygMkhlZmZm5k71TXbc9fr27uzaiV3tL51ij\/d2Z948+N8\/m1qoUKFCn0YVxBUq9HFUQVyhQh9HFcQVKvRx9GgQ\/\/nnn+H555+P\/\/YGfPbZZ+H999\/PfqtQ4f+BHgvihx9+OCy77LJhrbXWCt9++202OmRx9913h8UXXzzsuuuu4dNPP81GKwwJSOxvvvlm\/Lzzzjvht99+y\/5SobPokSC+9NJLw3TTTRcuuOCC8Msvv2SjPYe\/\/vorvPHGG+HLL7\/MRsrxySefhO222y7MNtts4dlnn81Gew9+\/\/338Oijj4bjjjsu7LzzzmHHHXcMxx57bHj33XezK\/4f+OGHH8Kpp54aJp544jDffPNFllSha+j2IL711lvDGGOMEa666qrw999\/Z6M9iw8\/\/DBMMMEEMXm0Aolls802C\/POO29LgT+48Prrr8fkMv7444ftt98+3HTTTeGggw4Ko4wySph00knDk08+mV05+PDBBx\/EOS299NLhp59+yka7Bx999FEYd9xxwxJLLDHYfOX\/iG4N4i+++CLMPPPMYcMNNwx\/\/PFHNtoeNkvlLKJsvBl876ijjgqjjz56ePrpp+M9WrmP3niiiSYKe++9dzYy5PHggw+GWq0WjjzyyLY1WN8JJ5wQhh566LDGGmsMdmd\/7733wmSTTRbmn3\/+8OOPP2aj3YPnnnsurleiqtAcYgo7O+OMM7KRQejWIEaPONtjjz2WjbSHirnXXnuFFVZYIZx11lltgpfKeNhhh4Ull1wybmyreOutt+IzRx111DDiiCOG5ZZbLqy88sph8803b0rPBIO5TDLJJPE+vQEvv\/xy2GabbSLlz4NNRhtttDDttNP2GpGwO8AHhhpqqHDddddlIxUa4amnngpjjTVWuPDCC7ORQYhBTFR4\/PHHw\/XXX99BveXgjHzNNdfEICyDLNG\/f\/9Ivb755pts9F98\/\/33YaONNgq333572HTTTcN4440XXnvttfg9QtPCCy8cK2NneiNUj4Amm6+44orhxRdfjB9iSSvV+L777ovfPfPMM7OR3oknnngiJio2qrcuNrRP6PfNN98cf5YYH3rooaaV23c\/\/\/zzKC75SCCJNrtHGkd9070IlWk8tSO+o2p\/\/PHHsa9vButYb731woQTThjbCCA2XnvttdHXfJKe4rlpfYltJZjvjTfeGF555ZVspBzW6nrzpjFgjkVBzTV80DXWU9ZCmMPXX38d75Ps891337Xkd+xHw6kH9ykKwebIrpgYf8U8k42++uqrUDNJQcSggoijmEyCQDHmyzfccEM22hEWg3Z5UFm1SAahEg877LDh6quvDuedd15YbbXV4sQ9q7N44IEHYjZXkTsLCUsyoaA3go3hJCpiq5\/urO7otTWedtpp2ci\/YLc999wz2n7dddcNO+ywQ2xp9JnERU5ZBnu2wQYbRPvvtttuYZlllgmTTz552HjjjePfJW2tEXY1zzzztNHpRx55JCyyyCLRJ\/bZZ58oxK2yyirRf8YZZ5xI+cqcP8G9aBKSfgokATb77LPH+5pLcmZ+Ym2e6f7sC6+++mpYYIEFwkgjjdQ0EQuaTTbZJK6VjWaaaaYwzTTTxIBIsGdbbrllPFVxDR3AaYbEkvdpa7Nu1xEexc5UU00Vi1ijQgfmzOZXXnllNtIe9hqb\/PXXX7OREH2PuMlXJb2ddtop7LHHHvEjVmsq5L333ttGL0cYYYQYZHksv\/zyYYoppuiQIfJQEVHaVnpMC7VoBjXhrgRvwiGHHBJGHnnkSDU6C5l0jjnmCHPNNVf4+eefs9GOoKROOeWU0bla\/Qii7oBN79evX3Rq88jDnAWcluCuu+5qq5RoqsDDfMoqscDBXmaddda24zaOuu2228bgSrA3AjsfxIDFDD\/88G1HdpR+wttiiy0WhhtuuFgdG8F9+drWW2+djYTIoKaffvooOtqbBGsTON458J1jjjkmMoBVV101JrYrrriioXqvolrTmmuuGRkhqJ5EtS222CL+rvrOPffcsWBhJsDeAhQLwnASBg4cGMXG1Day8UUXXRQTaaPk\/dJLL8VnnH\/++aX74tnsWux7rUEMKjjFat+uJ0Z1OeDJJ5+cjYQY6b58+OGHlz4Y7rjjjvhdQdUMHIhQQoy6\/\/77s9GugSNScxsFYRk4BiecYYYZIrUqA+dGadHTVj8c7r9CW0I\/UK3qOQc1XhXiyPm9MS6Izz333GykI9CzqaeeOjp3nnkJnmeeeSb7LcRgEejFIH7hhRdi8lxooYXa2d6pBD\/gL40gKFyXKqg2SGVztJZodBHmaR6S\/wEHHBCOOOKIhkwD2EVhEfyEwzxQc1TeNQITO7zsssuyvw6CQHXastRSS7VVR3tCo5BgE8yZ3crmjvYuuOCCMWmlOWs7BKuj2HwLgo3kEykotMMMM0yH4IZ2QSwTapwJQwn6EBmm2ZtOnQli2dCCVJD\/UoUZA71aaaWVspHOgcGJaVhBMxo0uMFhiFxsXy8hCJxFF100MoSijnDooYfGvSCUlcH9BQ3HRTM5ZL0k3SyIt9pqq2xkEFBrz3ZE1gjou+9LOGeffXasUEXaWoQKpDIKSDS\/yEzqAXt0b61FUTBMEED8gC\/RafKQ6PmHZwpEOPjgg2N7I4FJDK0kEklt7LHHbhf4ErMYsKb8urEucZjXlrAPFZp9i2gXxCnT6TNUSzfW67hBvQ3Oo9Ugdk9HCjKbaqG\/6ir0Oe4hK3cFnEAy0R+lDeoNYCNrwoDYp57t0UG0lQPk\/86hBgwYEJ2jmZOrQhR9NuTAqLngzKOzQSzh8AMJqAzmqEXT32F\/krBz8Lfffju7ohyCQdvWKoNTJNhCy1RmD8mc8q+nT0JdHii+NaW\/uY+eWVCh2nzZOsqCWSKwl3rs\/F55p4Lti3qOhDLmmGO2sUPJi73MEYMqol0Qu3jttdeOk5bd9T2yTSsOLkPoE3bZZZdspD6IFOuss06kKXoSDXsRjIHqYAaNQE2XEVEwkFH1G60q3NY1yyyzRAfNCwlFcN4555wzOnqrH\/1aV2CTUUwtQr7PLQK94liqQh6cm2N5frMKAdZtn+0Julbs\/3oiiN2HSLP66qvH31Vg+2g\/G0FACkbJq0h7y5DeByg7NQFBrLXwwlA9RlYMYpBo9bgYhaqpUu+3334d+lXQKvg+MSyPo48+Oo4Xq6t5SGpp\/9Ie0Fnq7Wm7IAYBIQuoAL6ETrcC0jhqp3IXH4T6Ce7TTz89OoMqYiPTm0Ay2yWXXNJGNUyaQ9mwRpD9bD5ayeEJOZynniHrQebX21ALGwEroRNgGa1+CB1dgd7bq4jnnHNONjIIgtneJNqVesq8uspuKqsKkV6gKEsCbJRPXK4TTOzOngk9EcQStGtSAkJhBTXVtQyqGVFHn09VbnRtHolOC4p6uoJ181eVjkZTfCvO9wmLdJNUyflzsqt\/rVnb4xkEqCLSSzz5l1pSdbXX+ZZSC+TavF0lAcmVEp5AAEt9dIcgvvPOO+NNqMZulOT\/ZrAYPZZATupegkkykGzHSRPI6UQDyWLfffdtcyqOYw6OShrBxlIT3VvlkglbnS\/ccsstkc5IIL0BnAQVRi9VEKqxjwRpjoIzbRw1XgKzTxzN9bQMYg+6KfmyhZdoUuDncc8994QZZ5yxHWuxh56RD2KULrGVfBA75qkXxFRqe9coiE855ZRYTdORpX3U1niGls7vSTH3HD+nIxVr0jO6lr0IcfylDNYk4M1JEkwJ3r9scNttt8XfTzzxxHhNUZBTKIiHqcomG+X9GFBqQVxPJdeLW69r0l4QwVBsLUVqI6zNEa2YyPfmaa8JevQk32WDxFQ7BLEzKZUYhWilR8mDo8nkeToGHM99k7yfYEGeYZMYJ0HGNOndd989GymHhVtwmWhRBtmXOKLP6Ox3ewrODjlS2QdNTyxHQDmXZG9BRtFUSWV9bY0XarAfLwTUAwd2zwMPPDD2WVoLynL+zNWecBh0UcBLJsCZKaqezbFS4jTOB9yXM9ZTat0T83HPvFgq2Zi36qzPv\/zyy+M4fUZhUIUFNxx\/\/PGxMqls2gDrbgTOjk1gXejvxRdfHANbhU7\/CQbVdjymGChk7IEuO71wPp2SnflbH8bDTyURrFWBYvNkizzYBZX2fD7NvhRu+22tGKQ20EmL\/t3z80DxMQEiJPbq57wm0CGIUQMZotGLHWUQpBaMInflyAcs2JEAp6lHTboLMjxHUrl6C+gFGEnZpygwYjjotOph3\/xNkKOcggFtLYPEqTIJAuenEpozUwFhD4Ajr7\/++tHZffbff\/8YSCoDKmhMRUyvAbKpCmGcluK8ughzJOSYc54hCCIV2noET1qnQHV9vgAInJNOOikeC0kyeZuUgQjKhubFR903T2PBfbVNEpPAoto70in20oLQSyEYk8CVlFzX6D0Kwc22bEgHSvPGdBwRmpt9KzslsZf2lH2Kb3u1C2KTJTa4uB4FawUEKy8H5KlLZ8CQsm4rr9F1FZ7B2XzKxI4KFfoKahwaNdOLOIiWefO9T1eg1KN4KEQrynYR9ShJd4EgI4P6NHrLp0KFvoKa3kBFQjMoy0VRqqugQHuHVjNf7IWHFAhZaCCa918TVYUKvQU1KqIgxsuThN5dwPlV4lZ6lsEBQkt3r7FChSGNGiEkHVtUqFCh76FWoUKFvoxa7R9pgiO88IPpLAAAAABJRU5ErkJggg==\" alt=\"\" width=\"241\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">\u2026\u2026..(1)<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Here The terms kx and<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0<\/span><span style=\"font-family: 'Times New Roman';\">\u03c9t appear separately. The string as a whole vibrates in phase with differing amplitudes at different points.\u00a0<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">The wave pattern is not moving to the right or to the left so called standing or stationary waves. The amplitude is different at different locations. The points at which the amplitude is zero are nodes and points at which the amplitude is the largest are called antinodes.\u00a0<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">The most significant feature of stationary waves is that the system cannot oscillate with any arbitrary frequency but is characterized by a set of natural frequencies or normal modes of oscillation.\u00a0<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><strong><u><span style=\"font-family: 'Times New Roman';\">Normal modes for a stretched string fixed at both ends.<\/span><\/u><\/strong><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">First, from Eq. (1), the positions of nodes (where the amplitude is zero) are given by<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Sin kx = 0 . This implies<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"247\" height=\"27\" \/><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Since<\/span><img loading=\"lazy\" decoding=\"async\" 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alt=\"\" width=\"116\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">,\u00a0<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">we\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" 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alt=\"\" width=\"412\" height=\"38\" \/><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Taking one end to be at x = 0, the boundary conditions are that x = 0 and x = L are positions of nodes.\u00a0<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">The<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"63\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0node condition requires that the length L is related to \u03bb by\u00a0<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"283\" height=\"38\" \/><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">In the same way, the positions of antinodes are given by when<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0<\/span><span style=\"font-family: 'Times New Roman';\">:<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"66\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">= 1<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">This implies\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"344\" height=\"27\" \/><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">With<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"63\" height=\"38\" \/><span style=\"font-family: 'Times New Roman';\">,\u00a0<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">we get<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0<\/span><span style=\"font-family: 'Times New Roman';\">x =\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"98\" height=\"47\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" 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alt=\"\" width=\"277\" height=\"38\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0<\/span><span style=\"font-family: 'Times New Roman';\">.(4)<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Thus, the possible wavelengths of stationary waves are constrained by the relation<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"317\" height=\"38\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">With corresponding frequencies<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"335\" height=\"35\" \/><\/p>\n<p style=\"margin-top: 12pt; margin-bottom: 12pt; line-height: 150%; font-size: 16pt;\"><em><span style=\"font-family: 'Times New Roman';\">The lowest possible natural frequency of a system of stretched string fixed at either end is called its fundamental mode or the first harmonic corresponding to n = 1 given by<\/span><\/em><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"80\" height=\"35\" \/><span style=\"font-family: 'Times New Roman';\">,\u00a0<\/span><\/p>\n<p style=\"margin-top: 12pt; margin-bottom: 12pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">The n = 2 frequency is called the second harmonic. n = 3 is the third harmonic and so on.\u00a0<\/span><\/p>\n<p style=\"margin-top: 12pt; margin-bottom: 12pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Generally, the vibration of a string will be a superposition of different modes; some modes may be more strongly excited and some less.\u00a0<\/span><\/p>\n<p style=\"margin-top: 12pt; margin-bottom: 12pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Musical instruments like sitar or violin are based on this principle. Where the string is plucked or bowed, determines which modes are more prominent than others.<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><strong><u><span style=\"font-family: 'Times New Roman';\">Normal modes of oscillation of an air column with one end closed and the other open.<\/span><\/u><\/strong><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><span style=\"font-family: 'Times New Roman';\">A glass tube partially filled with water illustrates this system. The end in contact with water is a node, while the open end is an antinode. Taking the end in contact with water to be x = 0, the node condition (2) is already satisfied.<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><span style=\"font-family: 'Times New Roman';\">If the other end x = L is an antinode, Eq. (3) gives<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"194\" height=\"42\" \/><span style=\"font-family: 'Times New Roman';\">for<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAALQAAAAbCAYAAADVh6UJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAXTSURBVHhe7ZpNSBVfGMbVMvtQslJTEhdaLuzLIDdmYppYimKLghRRi2pRiBsJWigoJSi6sYWiIih+QBmiC1tUKwWxSMVFWailid9Gmp+p77\/n9Yze7IrOvXMv0\/2fHxy588zMe48zz33nnPeMHUkkNsLq6uqINLTEZpCGltgU0tASm0IaWmJTSENLbAppaIlNIQ2tMa9fv6Zz586RnZ0d7d27l65evUqDg4Nir3m0t7fTiRMnqKenRyjqWVxcpJKSEoqMjCR3d3fu54EDB+jSpUsm93NlZYVqa2vpypUr5OXlxTFdXFwoIiKCent7xVHWQRpaQ1paWvhmVlRU0PLyMhvE29ubPDw8aHJyUhylHpgwPj6e7O3tOb453L59m2NkZGTQz58\/uZ\/Nzc20a9cuk2Pn5ubyucXFxbSwsEC\/fv2i1tZW2rdvH\/+oJyYmxJGWRxpaQ5ydnf8yRWNj47qBTKG6upoOHjxIhYWFbA5TTaeQlJREgYGBnFUN8fHx4divXr0Sys7JysqiU6dOia0Nrl+\/zjHr6+uFYnmkoTWis7OTb15+fr5Q1kB2gn706FGhqCMnJ4dmZ2f5s6urq9mGHh8fN5ox7927x7ExHNGKhIQEjllTUyMUy6M7Q+OmOTo6kp+fH2\/jkXj58mXWnJycaGRkhHW9kZ6ezjfv7du3QtkAOtrY2JhQTEMLQ2+Fr68vxx4aGhKK+YSFhXHMb9++CcXy6MbQeARikoLxV1xcHO3fv58zE8Z2d+7coaioKL44aWlp4oydk52dzeeqaf39\/eLsnXHy5Ek+7\/cFFcoGeMRjX3d3t1BMw1KGRtLA9UbC0AJcgydPnvC9q6qqEqp10FWGxuQHYHYMc6NC0NHRwRoyM25mSkoKb6uhqKiIjh8\/rqqpzSp4omxl6Bs3buja0GfOnOG4mNCZw5cvX6isrIwOHTpEx44ds2pmVtCVoRVwcdHKy8uFQlz+gVZQUCAUffGvGhqTTcR89+6dUEzn7t27FBwcTKdPn16fwKLaYU10a2hkaEMqKytZRy1WjyCro3\/GDB0bG8v79GZopQLz7NkzoWjH169fyc3NjeN\/+PBBqJZHd4bGLBwXAbVNQxITE1lH7VQtyD6okapp09PT4uydgbIV+mfMtGfPnuV95tZjtTQ0EgNiWXKMi+uI78C9sxa6M7QygTOsZiwtLfG4LDQ0VCjqsMakMC8vj897+vSpUNbAJBc6VtDMRStDDw8Pcxnx0aNHQrEMnz594v6Gh4cLxfLoztBYht29e7fYWqOvr48vTGZmJm+bW\/6yBMjoDg4OvAhiyOfPn7nvDx48EIrpaGXoixcvUkhICP\/YDEFfsUiilvv37\/8x31Ewd1HJFHRnaJSOMKEw5M2bN3xhkAW\/f\/\/Oj\/C5uTmxVz8EBARwPzHbV0hOTuany+joqFDWwHFqszZ+LDivq6tLKH+CfUeOHBFbxqmrq+PjSktL6eXLl+sNK5Kenp508+ZNcSRRU1MTH\/v48WOhGAfH4N2Nzcv758+f530DAwNCIZqammLt2rVrQtkaHLdnzx6xtXEummFSw3dDA7oy9Pz8PL+vgBUmQ2ZmZvjmo+MxMTFWfTdADeg\/SmCovyID4jNMaKyCoNyY7Whra+OsiayqvMsB06ampv6VFbeLiXrz4cOH148z1gyrSIqhHz58KBTjKItKeLpeuHCBG34c+K7NPz7FlLg+24Hj\/mlD44Kj0zDGZlAj\/fHjBzosFP2C1TbM7DEON\/a\/QMMN2ElNHbVcxNqqKWCegZh4420rsHhlLIZhwxNQ4fnz5xzzxYsXQtkarCFg3qPEwTh985AG4P9BzM2vCBgDcT5+\/Ci21vyhxMdnBbx9CA3obsjxf0Cp\/SrvaGhBQ0MDx8RETCuio6MpKChI0yRy69YtLslaKjFJQ1sZLBBhSLJ5TG0OiIWYWtboUff39\/cXW9rw\/v17HpZYEmloiU0hDS2xKdjQv\/80yyabbbTV2v8Art3fTXxR26cAAAAASUVORK5CYII=\" alt=\"\" width=\"180\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">..(7)<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">The possible wavelengths are then restricted by the relation:\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"139\" height=\"60\" \/><span style=\"font-family: 'Times New Roman';\">for<\/span><img loading=\"lazy\" decoding=\"async\" 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alt=\"\" width=\"183\" height=\"27\" \/><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">The normal modes \u2013the natural frequencies \u2013of the system are<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"335\" height=\"42\" \/><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">The fundamental frequency corresponds to n = 0, is given by\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"19\" height=\"35\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0<\/span><span style=\"font-family: 'Times New Roman';\">.\u00a0<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">The higher frequencies are odd harmonics, i.e., odd multiples of the fundamental frequency:<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"100\" height=\"35\" \/><span style=\"font-family: 'Times New Roman';\">, etc.<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><strong><u><span style=\"font-family: 'Times New Roman';\">Stationary Waves may be of Two Types:<\/span><\/u><\/strong><\/p>\n<ul>\n<li><span style=\"width: 38.9pt; font: 7pt 'Times New Roman'; display: inline-block;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><u>Transverse Stationary Waves:\u00a0<\/u><em><span style=\"font-weight: normal;\">When two identical transverse waves travelling in opposite direction overlaps then transverse stationary wave is formed<\/span><\/em><span style=\"font-weight: normal;\">.<\/span><\/li>\n<li><span style=\"width: 34.45pt; font: 7pt 'Times New Roman'; display: inline-block;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><u>Longitudinal Stationary Waves:\u00a0<\/u><em><span style=\"font-weight: normal;\">When two identical longitudinal waves travelling in opposite direction overlap then longitudinal stationary waves are formed<\/span><\/em><span style=\"font-weight: normal;\">.<\/span><\/li>\n<\/ul>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><strong><u><span style=\"font-family: 'Times New Roman';\">Characteristics of Stationary Waves:<\/span><\/u><\/strong><\/p>\n<ul>\n<li><span style=\"width: 38.9pt; font: 7pt 'Times New Roman'; display: inline-block;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>In stationary waves, the disturbance does not propagate in forward.<\/li>\n<li><span style=\"width: 34.45pt; font: 7pt 'Times New Roman'; display: inline-block;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>All particle of the medium except at nodes execute S.H.M.<\/li>\n<li><span style=\"width: 30.01pt; font: 7pt 'Times New Roman'; display: inline-block;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>The distance between two nodes or antinodes is<img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"32\" height=\"27\" \/>.<\/li>\n<li><span style=\"width: 31.8pt; font: 7pt 'Times New Roman'; display: inline-block;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>The maximum velocity is different at different points.<\/li>\n<li><span style=\"width: 36.24pt; font: 7pt 'Times New Roman'; display: inline-block;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>There is no any energy transference in stationary waves:<\/li>\n<\/ul>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><strong><u><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><\/u><\/strong><strong><u><span style=\"font-family: 'Times New Roman';\">Nodes and Antinodes<\/span><\/u><\/strong><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">The patterns of standing wave such that there are points along the medium having no displacement are referred to as nodes.\u00a0<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">There are other points along the medium that undergo maximum displacement during each vibration cycle are called antinodes,\u00a0<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">A standing wave pattern always has nodes and antinodes appearing alternatively in them.<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><img loading=\"lazy\" decoding=\"async\" style=\"float: left;\" 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\" alt=\"\" width=\"722\" height=\"249\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><strong><span style=\"font-family: 'Times New Roman';\">36 STANDING WAVES IN CLOSED ORGAN PIPES: ANALYTICAL TREATMENT\u00a0<\/span><\/strong><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><strong><u><span style=\"font-family: 'Times New Roman';\">37 ORGAN PIPES:-<\/span><\/u><\/strong><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">An organ pipe is a wind instrument which is used for producing musical sound by setting the air column inside the pipe into vibrations. Practical examples of organ pipes are\u00a0<\/span><strong><span style=\"font-family: 'Times New Roman';\">Bugle, Trumpet, Flute, and Clarinet. Shehnai, Saxophone etc.<\/span><\/strong><\/p>\n<p style=\"margin-top: 0pt; margin-left: 21.6pt; margin-bottom: 0pt; text-indent: -18pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: Wingdings;\">\uf046<\/span><span style=\"width: 2.93pt; font: 7pt 'Times New Roman'; display: inline-block;\">\u00a0\u00a0<\/span><span style=\"font-family: 'Times New Roman';\">An organ pipe consists of a hollow wooden or metallic cylindrical tube of suitable length and suitable diameter. A small narrow tapering tube M is attached to one end of the pipe is called\u00a0<\/span><strong><span style=\"font-family: 'Times New Roman';\">mouth piece<\/span><\/strong><span style=\"font-family: 'Times New Roman';\">. The other end of the pipe may be open or closed as shown in Fig.<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-left: 21.6pt; margin-bottom: 0pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">If the other end is open the pipe is called an\u00a0<\/span><strong><span style=\"font-family: 'Times New Roman';\">open organ pipe<\/span><\/strong><span style=\"font-family: 'Times New Roman';\">, and if the other end is closed, the pipe is called\u00a0<\/span><strong><span style=\"font-family: 'Times New Roman';\">closed organ pipe<\/span><\/strong><span style=\"font-family: 'Times New Roman';\">.<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-left: 21.6pt; margin-bottom: 0pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Inside the pipe, near the mouth piece, there is a slanting wooden block B. The size of the block is so adjusted that a narrow slit L is left between the surface of the wooden block and the wall of the organ pipe. L is called the\u00a0<\/span><strong><span style=\"font-family: 'Times New Roman';\">lip<\/span><\/strong><span style=\"font-family: 'Times New Roman';\">\u00a0of the pipe<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-left: 21.6pt; margin-bottom: 0pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">When air is blown into the pipe from the mouth piece, it strikes the sharp lip L and throws the air on either side of the lip into eddies.<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-left: 21.6pt; margin-bottom: 0pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><span style=\"font-family: 'Times New Roman';\">The eddies so generated at regular intervals produce a musical sound of definite frequency called\u00a0<\/span><strong><span style=\"font-family: 'Times New Roman';\">edge tone<\/span><\/strong><span style=\"font-family: 'Times New Roman';\">.\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-left: 21.6pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">The vibrations in air travel to the other end of the pipe and get reflected, these reflected waves superimpose upon the freshly generated vibrations of air column. When frequency of edge tone becomes equal to frequency of vibration of air column in the pipe,\u00a0<\/span><strong><span style=\"font-family: 'Times New Roman';\">resonance<\/span><\/strong><span style=\"font-family: 'Times New Roman';\">\u00a0occurs and the sound produced is the loudest.<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><span style=\"font-family: 'Times New Roman';\">The frequency of the sound depends upon the size of the pipe and also on pressure with which air is blown into the pipe. The eqn. of longitudinal stationary waves set up in a closed organ pipe is<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"284\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026 (1)<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><span style=\"font-family: 'Times New Roman';\">At the closed end of the pipe.\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"77\" height=\"27\" \/><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">So<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"198\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">From (1)<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0<\/span><span style=\"font-family: 'Times New Roman';\">S= 0, i.e. A node is formed\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">At the open end of the pipe of length L<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0<\/span><span style=\"font-family: 'Times New Roman';\">S=L<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0<\/span><span style=\"font-family: 'Times New Roman';\">an antinodes is to be formed, i.e., S=max.<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">From (1) S will be max.\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">When<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"335\" height=\"35\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">where n = 1, 2, 3&#8230;..<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"313\" height=\"41\" \/><span style=\"font-family: 'Times New Roman';\">\u2026\u2026\u2026\u2026\u2026\u20262<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><strong><u><span style=\"font-family: 'Times New Roman';\">First normal mode of vibration<\/span><\/u><\/strong><u><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><\/u><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Let<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"31\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">, be the wavelength o corresponding to n = 1.\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">From (2)<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"164\" height=\"41\" \/><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">The frequency of vibration in this mode is given by<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"186\" height=\"38\" \/><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">This is the lowest frequency of vibration called\u00a0<\/span><strong><span style=\"font-family: 'Times New Roman';\">fundamental frequency.<\/span><\/strong><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">This mode of vibration of one node and one antinodes as shown a.<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0<\/span><span style=\"font-family: 'Times New Roman';\">The note or sound so produced is called\u00a0<\/span><em><span style=\"font-family: 'Times New Roman';\">fundamental note or first harmonic,\u00a0<\/span><\/em><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><strong><u><span style=\"font-family: 'Times New Roman';\">Second normal mode of vibration<\/span><\/u><\/strong><u><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><\/u><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Let\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAABoAAAAbCAYAAABiFp9rAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAHqSURBVEhL7ZTNi0FRFMBloRSysJR8JFnZIpZsyV42svCXULIcllZ2NiTZ2EnsZiclSSn5Kh8lX2fmnDkZb543kyezmfnVfe+ec9\/td7v3vKuAX+B8Pr\/+i2TxR0Sn0wnS6TQEg0HI5XKcfQyRCCXRaBR8Ph9YrVZQKBQwGAx4VD4i0WKxgEqlQv3ZbEaiWq1G8SP8eEZ2ux3K5TJH8vlR5PV6f0fkcDieL4rH43RGTxU1Gg2SKJXK54mWyyXo9XoqcTyjTqfDI0LeJ8N6vYbNZsMZaUQi\/I9CoRDodDoYDofgdrtFoul0CrFYjBaRSqUgEAiAxWKBZrPJX4gRiYrFIm1ZPp+n2Gw2i0Ttdhv8fj9HH+DitFot7Pd7zggRiEajEUk8Hg9nbotukUwmae5qteKMkIvocDjQlaPRaGA8HtMggqJWq8WRNC6XCyKRCEdiLqJEIkErwsv0GhQVCgXqh8NhnED9a7LZLN0geH1JQaJ6vU4So9HI6U9wlSqVCpxOJ3S7Xc5+UiqVwGazwXw+58xtSLTdbmk1WKpfwSrEcsf3V6rVKphMJslzueaydffS7\/fBYDDAbrfjzPfIEh2PR9rqyWRCfWxYTPjP9Xo9\/kqILFEmkwG1Wn2zSRWE7K27FxK9P2rPb+eXN3zlKwzjlJNvAAAAAElFTkSuQmCC\" alt=\"\" width=\"26\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">be the wavelength corresponding to n=2.<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><span style=\"font-family: 'Times New Roman';\">From (2)<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"292\" height=\"41\" \/><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">The frequency of vibration in this mode is given by<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><span style=\"font-family: 'Cambria Math';\">\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"277\" height=\"38\" \/><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Thus, the frequency of vibration in 2nd normal mode is thrice the fundamental frequency,\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">This mode of vibration of two nodes and two antinodes as shown in fig. b. The note so produced is called third harmonic.\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">It\u00a0<\/span><strong><span style=\"font-family: 'Times New Roman';\">is the first overtone produced in a closed organ pipe<\/span><\/strong><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><strong><span style=\"font-family: 'Times New Roman';\">Overtone:<\/span><\/strong><strong><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0<\/span><\/strong><span style=\"font-family: 'Times New Roman';\">These are the notes\/sounds of frequency twice\/thrice\/four times \u2026.the fundamental frequency\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAsAAAAbCAYAAACqenW9AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAADpSURBVDhP7Y8rDoNAEIbXQAgBDQrLBbBIuAOCIBAcBInEobAk+DpOQMIRuABBIMDxtx22j22bPlyb9Esmmce3mxmGD\/jL1\/ysnOc5ZFmm6PueBifCMIQkSaiqCqwoCjRNQxJjDEmScG0jCALqD8NwWWNZFmr6vs87G5qmQVVVyoWdj7LnebzaUBQFcRxTLsiO48C2bV4BbdvSByeeypZloSxLXt3IURSd5SzL4Lou1nWl+shDues6GIaBaZr4ZONO1nUdpmnSg1sEOU1TOqiua94REeR5njGOo7DnNYL8im+RD8fs3ot1twfvrj8z+36mtwAAAABJRU5ErkJggg==\" alt=\"\" width=\"11\" height=\"27\" \/><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><strong><u><span style=\"font-family: 'Times New Roman';\">Third normal mode of vibration<\/span><\/u><\/strong><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Let\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"21\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">, be the wavelength corresponding to n = 3<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">From (2).<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"288\" height=\"41\" \/><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">The frequency of vibration in this mode is given by<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"256\" height=\"38\" \/><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">The frequency of vibration in the 3rd normal mode is five times the fundamental frequency.<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><span style=\"font-family: 'Times New Roman';\">This mode of vibration of three nodes and three antinodes as shown c. The note or sound so produced is called fifth harmonic, this is the second overtone produced in the closed organ pipe.<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Proceeding as above, the frequency of note produced in nth normal mode of vibration of closed organ pipe would be<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"115\" height=\"38\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">This is\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"100\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0harmonic or\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"100\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0overtone.<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><strong><u><span style=\"font-family: 'Times New Roman';\">38 STANDING WAVES<\/span><\/u><\/strong><strong><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><\/strong><strong><u><span style=\"font-family: 'Times New Roman';\">IN OPEN ORGAN PIPES: ANALYTICAL TREATMENT<\/span><\/u><\/strong><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">An open organ pipe is open at both ends. Therefore, antinode is formed at each end as shown in Fig&#8230; Proceeding as in the case of closed organ-pipe,\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">And setting S= max at\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"58\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0and at\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAC8AAAAbCAYAAADszNYXAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAFmSURBVFhH7ZQxq4JQGIZdIqjNZsWh8WJLkENj5FCjQ\/+hxak\/0RA01dTe0hLc0dlZaBZxDHIRzND33r57Ci45nNtwPYIPfHp85Rwe5POTUFHyPP+o5cugli+LWr4savmyqOXL4pe853loNptoNBrY7XYsBeI4RrvdphKJp\/z5fMZgMKBwPB5DlmVa3243Wq\/Xa3Q6Hcp4MQwDkiRxl67rbCcfhW2z3W7pMN\/30e\/34TgOe\/M3LMtCt9vlrslkwnbyUSh\/Op1IfjabwbZtlopHoXySJCSvqirSNGWpeBTKh2GIVquFXq\/Hkvc4HA7YbDbctd\/v2U4+XuSv1yv1+XQ6pa9\/nzTv8u8\/7Hw+x2q1wvF4pAPv41NUnvLD4RCLxeI5LqMoIvnlcknPpmnSXSRIPggCEtU0jdrmwWg0olxRFLiuy1JxIPksy3C5XO4PLP7hkYs6cV56vkrU8mVRffnvy2cVC4D2BVINwXgwQy+IAAAAAElFTkSuQmCC\" alt=\"\" width=\"47\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">L<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">We get<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"62\" height=\"38\" \/><span style=\"font-family: 'Times New Roman';\">\u2026.(1)<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><strong><u><span style=\"font-family: 'Times New Roman';\">First normal mode of vibration<\/span><\/u><\/strong><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><span style=\"font-family: 'Times New Roman';\">From (1).<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"144\" height=\"38\" \/><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">The frequency of vibration in this mode is given by<\/span><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"216\" height=\"49\" \/><span style=\"font-family: 'Cambria Math';\">\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">This is the lowest frequency of vibration and is called the fundamental frequency. There are two antinodes and one node as shown.<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0<\/span><span style=\"font-family: 'Times New Roman';\">The note or sound of this frequency is called fundamental note or first harmonic,\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><strong><u><span style=\"font-family: 'Times New Roman';\">(ii)<\/span><\/u><\/strong><strong><u><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0<\/span><\/u><\/strong><strong><u><span style=\"font-family: 'Times New Roman';\">second normal mode of vibration<\/span><\/u><\/strong><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">For n = 2. From (1))<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGkAAAAmCAYAAADHjLWDAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAT3SURBVGhD7ZrZK3VfGMd5I6LMFyJDpsyKKNwoLrhQJOUGJQqRyEzJjURy5x8QkiJEEUohQ7gyD69ZyBwyrt\/v+5x1OJx98PNzOvvszqee3taz1\/Luvb9nredZz9p6TIeoeXl5+asTSeToRNICdCJpAZIRaXd3l9XU1LCKigr6NykpieXn57Pz83PeQ8b19TWLjY1l\/v7+LC4ujt3c3PAr4kUyIjU2NrLw8HD29PRE7cfHR+bo6Mh8fX3xkOST09PTw\/T09Njh4SH3iBvJiHR3d0emSHBwMIkBwRTBDIN42oKkY5KrqytLSEjgLRnPz8\/M1NSUJSYmco\/4kaxI9fX1NIsQgxQ5OTkhf3t7O\/eIH0mK1Nvby\/T19ZUEAlNTUyTS7e0t94gfyYkEgUxMTAQFAllZWczNzY23tANJiTQ5OcksLS3Z5eUl98gSCjmIR5hFkZGR3COjo6ODTU9P85b4kIxI2A8ZGBiwubk5dnFxQYYU297e\/nVpu7q6IpFaW1upDe7v75mnpyfb39\/nHvEhGZGQVkMAIXt4eKA+eXl51O7s7GQDAwOsu7ubhYWFMQcHB7ouViQjErK2g4MDQfv3IamP0DXY2dkZXRcrgiJh115SUsJCQ0NZbW0t9+pQF6urq2x4ePjVNjc3+RUZSiIhuKK2FR0dTWs1loeNjQ1+VYc6wCogr47Ex8dTPFVESSSkrvJMRx5o+\/v7qa1DfaSmptK7xj7uI1\/GJA8PD9p76FAvgYGBJBImxke+FAlxSSeSesE2AAJBKCE+FQkbQWdnZ9GLhAf8DdPUhnZ2dpb+\/+LiYu55z6cioYKMwb8pUlBQ0LsX85W5uLjwkaqJior6FVteXuZ\/URgvLy\/Be1Rl3z0OaWhooP7Nzc3c8x6VIqFKjIGGhoa\/KlJVVRUFye9aUVERH6l5ysrKBO9RleGU+DskJyfTu15fX+ee9wiKtLOzQ2cuOF5GTJqZmeFXdKgDKysrZm5u\/nqq\/BElkXCKGRAQwOzs7Njp6SkLCQlREgkiIp\/Pzc1lTU1NLD09nYLe4OAg76Hju6DigVkUExPDPcooiVRXV0eDUNsCTk5OSiKNjo4q1bsw68zMzChT+QzU2LBZ\/q5lZGTwkZonOztb8B5VWU5ODh+pmqGhIXrflZWV3PPGwsICFRLeibS0tEQDUG2QIySSEJmZmTRWKM9XRB2Jw1esrKywxcVF3vo56kgc8GUT+o6MjHDPGzh22draehMJM8DIyIhZW1u\/Vo0BRBofH+ct1fj5+dFnVGJhe3ubZjZ+oTjGODo6otNaVXsRTYEqPERSPAMD8gkDXkVC7IETnzspgn0S4g5ilYWFBdX2PoKMDf0UxdU0OEtKS0vjLRmImXhGfKMnBlB9x\/14e3vTe5UbBDM2NqYfFSCR2traaAZBqI9gXbWxsaEsT0gEjEXpSEwCqaKvr48e\/OMHk5oANVIfHx9676qsvLyc+iolDv+FlpYW+hVog0AAGWtERARvaQ8\/FmliYoIeWlGg4+PjL7M7TVFYWEhJizbyI5EgxJ8\/fyhNn5+fJxsbG6PsZ21tjfcSD9XV1XReo638SCSUahDwhExsR9Eo5eAbcW3mf8UksdPV1cXc3d3fLcl7e3u0b9ImJCsSlmTUH1NSUlhpaSlZQUEBs7W1fa2maAuSFQmfa6FyImSoPWoTkl7upMLLy8vffwA4vslQtWirKgAAAABJRU5ErkJggg==\" alt=\"\" width=\"105\" height=\"38\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">The frequency of vibration in this mode is given by\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"221\" height=\"53\" \/><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 0pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">i.e., frequency of vibration in second normal mode is twice the fundamental frequency. there are two nodes and three antinodes as shown in Fig. The note so produced is called second harmonic or first overtone.<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 0pt; line-height: 115%; font-size: 16pt;\"><strong><u><span style=\"font-family: 'Times New Roman';\">(iii)<\/span><\/u><\/strong><strong><u><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0<\/span><\/u><\/strong><strong><u><span style=\"font-family: 'Times New Roman';\">Third normal mode of vibration<\/span><\/u><\/strong><u><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><\/u><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">For n= 3.<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">From (1 )<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"158\" height=\"38\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">The frequency of vibration in this mode is given by<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"214\" height=\"43\" \/><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">i.e., frequency of vibration in third normal mode of open organ pipe is thrice the fundamental frequency. There are three nodes and four antinodes as shown in fig.<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0<\/span><span style=\"font-family: 'Times New Roman';\">The note so produced is called third harmonic or second overtone.\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">In general, the frequency of vibration in nth normal mode of vibration in open organ pipe would be<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFQAAAAeCAYAAACyqDnLAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAQhSURBVGhD7ZhLKHVdGMeJYoBSFLlEyoABAxkQcr8MXDNBFDFhgGTiNpNEScIAZWBiIDMpigED5JYkpOSWcs\/99nzf\/znPfo9vOzjvd\/b7dmL\/atV+\/muvvdf6773Weva2IR1N0Q3VGN1QjdEN1RjdUI3RDdUY3VCN0Q3VGN1QjdHE0KqqKnJ0dKTDw0NRfi6aGBofH085OTkS\/WwsNvT5+ZlsbGxoYWFBlJ+NxYbOzc1ReHi4RDofGvr4+EgbGxt0fX0tipH19XUut7e31N\/fTxMTE1JjHezt7dH29rZEBk5OTmhra4teXl5EMYKxHB8fS2QE10Hd1dWVKF9j0tCZmRmKi4sjV1dXns7qC0JDQSetjdLSUoqNjeX+TU5O0tPTE5WVlf3qM2aTYur+\/j7FxMSQj48P2dvb0+7uLusKubm53GZ+fl6UrzFpaF9fH93f31NPTw9fcGlpSWoMQPP09JTIMgICAsjPz8\/sUl1dLS3fU1RURLOzs3yMPjY2NlJJSQk1NTXR8vIyhYSEsL6zs8PndHd3083NDV1cXLCObOUtiqFHR0eifM2nayhed1xweHhYFGKjoSUlJYliGZ2dndTR0WF2GRsbk5bvebs8oY81NTV8fYWKigrWDw4ORDGgbKzqvQAxHsLr66soX\/OpobgxbjQ4OCiKUVNPD2tienqa++ju7i6KAaR20NXrKGLoYWFhohC\/tXZ2djQyMiKKeXxqKMCN6uvrJSIKDg6m0NBQiayT7Oxs7vfp6akoxGspDMrKyhLFCN5AnI+xKdTV1XFsahObmpoiFxcXk7n3l4ba2tr+MhSbkJOTEx9rRWZmJmVkZJhd2tvbpeXHYDNFv9+CNRSmYdlQozb07OyM229ubnKsgDcf4x8fH+fz\/5ehmDYwVFlnkEppia+vL3l7e5tdKisrpeXHODg4vHvwbW1t3P+1tTVR\/otiKMaZmJhIzc3NUvMeZR+xyNCIiAhqaWkR1QimEvTk5GTO5e7u7qi1tZWio6NpdHRUzvp74IFjsF1dXaIYUJYBgJ19dXWVjxVQFxQURA0NDZSXlyeqaSwy1MvLixsjLzVFeXk5T4XAwEDq7e3lp7uyskIFBQXk5uYmZ\/09YAj6e35+LoqBhIQE1pEC4mGrZxrSQNRjHPio+QyLDEVul5qaylPBFIru7+9PkZGR\/PUEhoaGyMPDg4\/\/JsXFxfyzRg0eclpaGhUWFnJCr6a2tpZSUlLo8vJSlI+xyFBzQOKLGywuLopieOKYZt+RP24ovudxA9xIAbF6l\/wu\/HFDkdulp6dLZPipgG9joHVWYA1gU4OhSPnUaGIoNp+BgQGJiN9M5HH5+flcfufTzdrBvuDs7MyGYozIgqKioqRWA0MfHh74n6j6j9Tv\/vb6Ltj8+\/Yc6UWr8nr0D41l91HU4Ci6AAAAAElFTkSuQmCC\" alt=\"\" width=\"84\" height=\"30\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">The note so produced would be called nth harmonic or\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"68\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">th overtone. It would contain n modes and\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"77\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0antinodes.\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><strong><u><span style=\"font-family: 'Times New Roman';\">Special cases:<\/span><\/u><\/strong><\/p>\n<ol style=\"margin: 0pt; padding-left: 0pt;\" type=\"1\">\n<li style=\"margin-left: 35pt; margin-bottom: 10pt; line-height: 115%; padding-left: 1pt; font-family: 'Times New Roman'; font-size: 16pt;\"><strong>Comparison of closed and open organ pipes<\/strong> shows that fundamental note in open organ pipe <img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHIAAAAbCAYAAACgJtvvAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAYVSURBVGhD7ZlbSBVdGIY1FTLK0lJJrFCDBKmIrDQCocTIY6mheKADkYXoTRFYJEHUTUrdaCriRTeeQKuf0KAbIZLwIiw1rSg7ohd20jyVfvV++xvdM3tm3Pu3v9R\/P7B0r3d9M3tmveu8XcjJvGdycnLMaeQCwGnkAsFp5ALBaeQCwWnkAmFGIx8\/fkwdHR2Sc6IlJiaGTp8+LTk1z58\/p9bWVnry5AlNTEyIasuLFy84TkkfPnyQEgvPnj2jM2fO2OjWGBr55s0b2rlzJ0VERNCjR49EdWINjHJxcaHu7m5RiLq6uig5OZl8fHxo165dlJqaSu7u7rRs2TKqqamRKDWvXr2i9evX870SExPp06dPUmLh27dvdP36dfL09KSioiJR1egaiRaycuVKunr1Kv348UNUJ1o2b95Mrq6ukrNw6NAhNqSxsVEUovfv37MJ0EdGRkRVk5CQwOVoCEb09vaSr68vnT9\/XpRpbIz8+vUrt6bMzExRnBjh4eFBhYWFkrMAI\/fu3Su5abZt28ZGVVdXi6ImLCyMy4eGhkTR5\/79+xx37949USzYGImxeOnSpTQ+Pi6KEz1KSkq4QrUj1vDwsG6vO3bsGMdXVlaKMg3qetGiRbRlyxZRzMG8DI+sv1tlJHojvuzgwYOiqMnJyeFWuGTJElGmUcpu3rwpytwG89vixYv5mS9duiQqUV9f35R+9uxZUW1Zt24d15W9BAQEcLzeoufhw4dcdvHiRVHMaWpq4vi2tjZRNEY+ePCAA7TdFmDhgzEaL4qYgoICKbGgtLjZrnAHBgb4Po4k7fA2E6WlpZSVlcWfcf2OHTv4c2dnJ+3evZs\/b9++nYc7PVAPuA7x9oDFC+I3bdokippz585x+e3bt0UxZ3R0lOfmvLw8UTRGolfhhgg0AzEbNmyQnAVM1mjJs10c4aWxgnMkXbt2Ta52DAyDeJfjx4+LMs3GjRunTNUSFRXF142NjYlizPfv32nt2rW0fPlyVLaoalJSUvh+aCD2EhISwtco91QZ6e\/vT35+fpIzRmskHtbLy8u0Z6DS5hroUXgXbUNAY0SLt95WKOBdV6xYQadOnRLFGAyjaOAw0WwRgzp3tBNs3bqVn12Zj1VGosBeIzFHKNy6dYv3SRgWtWAuSk9Pnxq+5hINDQ38Lnfu3BHFAqaW4OBgyam5ceMGX\/P69WtRjLlw4QI38JcvX4piy7t37\/h+SUlJothHdHQ0X\/fx40fOz9pIrLhCQ0OpoqKC8wo4jUhLS6MjR45wvL1GYlgvKytzKFlP+o6gzE3avRt6IypYD8ydGNaMhkmFqqoqvnd7e7so+mBeRJzeRh\/PoNc5wG83sri4mPbs2cOfrenv7+ehBQnx9hr5JxY7CocPH+brlcoAqKCTJ09KTg1OuxBfV1cnij5oWIhDj58JbO4Ri\/2hFuzn9YZ3EB4eztfpDq0Yd3ECMRO4AYzEl+P\/4OCglNjiqJF\/ktjYWH42ZUuQkZFB+\/bt48965Obmcvznz59FsQUVizo5evSoKNM0NzdTdna25CwoCyftsdzbt2\/5aM8ILPKsn11lJHoXCs0OZwFisJdcvXo1z4FmzAcjy8vLefGGSjZacGCR4+3tzSc3Zly5coXvGRcXx\/txJWHRgyHb2sgvX75wrHY+xvSC79LbrwNMZzAZU5eCysinT5\/yjXHGakZ8fDzH3b17VxRj5rKRWHni2XCujGFQad164KADsdi8G4HeqJypGiXM6QC9WumNMMx6O+Xm5sb6iRMnOFYL6h3lLS0tomiMRKtDQGRkpCj64ARIOxQYMZeNxLNhfrRn2Y8eFRgYaGr2r8rk+5klZY+O79Qrt056R31g\/\/79XKfW+32VkQDHPxgCftdPV3PZSHvBfIV3uHz5sih\/D+x94Q9WxdbYGAmw78PZIFrYbFkIRmJrgHfASvxvgpMknBLBHy26RgJ03zVr1vBvaf8WLJ7w4yrmDaT8\/HxeWMwn0BBXrVpFBw4cEOXPg2fAGTbmTmyZ9DA0EtTX11NQUNDUBP1\/BIuS2tpa09OZ\/xoMp+gQPT09otjCRv760+RM8z1N\/vMTPJoun65TehMAAAAASUVORK5CYII=\" alt=\"\" width=\"114\" height=\"27\" \/>\u00a0has double the frequency of the fundamental note in closed organ pipe<img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"100\" height=\"27\" \/>.<\/li>\n<\/ol>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Further, in an open organ pipe, all harmonics are present whereas in a Closed organ pipe, only alternate harmonics of frequencies<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"113\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">. Etc. is present. The harmonics of frequencies\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"120\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0are missing.<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><span style=\"font-family: 'Times New Roman';\">Hence the overall musical sound produced by an open organ pipe is richer than the musical sound produced by a closed organ pipe.<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">2.<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0<\/span><span style=\"font-family: 'Times New Roman';\">Harmonies are the notes\/sounds of frequency equal to or an integral multiple of fundamental frequency (<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"12\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">). Thus, first second third&#8230;. harmonics have frequencies\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"75\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">respectively.\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">3. Overtones are the notes\/sounds of frequency twice thrice four times the fundamental frequency\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB0AAAAbCAYAAACAyoQSAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAKJSURBVEhL7ZUxSGphFMfVkGxtUajFoUECsclFRHCKdGuyTQKHXFxMcDIEFwe3xsBJFFxEGmqKwMElGtIQEUJ00MpUhLQ8vXPu8ep99+qz4r239AOR+zvfd\/\/3fnzfuSr4D\/yE\/lV+QuH5+RlisRhcXV2xWQ6fzweVSoWvlFEMTSaTsL6+DpFIBJ6entj+mdFoBOl0GlZWVsDv97OVIwvFQJVKBcVikc3neXl5AaPRCPv7+2ykSEKr1SpotVo4Oztj83UeHh7o4ROJBJspklCn0wkmkwne39\/ZfI9AIAA6nQ6GwyEbATG02WzSk4XDYTZScDKugtlsZjNlc3OTaoPBgI1AuVyme56enrIREEMzmQwNuL29ZTPFYDDQ\/9HREY2p1+t0PUGv14NGo5GtEG4s9Ht7e2wExFC32027bhGFQoFC8\/k8G6AgdMFgkI0Uu91O9fF4zGYmFAuTN5oHviGOy+VybACur6\/J1Wo1NlI8Hg\/VW60Wm0+GttttGodNY4LL5ZIt3yzHx8c05+7ujs03Q0ulEqytrUGj0aBrJb4d2u\/3xVA8BhaLBVKpFFeVOTg4oDmKy7u7u0vbfhGzoXgGDw8PuTIfh8NBc3AnTxBDsQthEc\/WPCahW1tb9Javr69cUebt7Q1WV1fBZrOxERBDsQXiDUOhEBs5uKQ4ZmNjAzqdDtv53N\/f0\/h4PM5GQAzFc4RPr9RxZsGvTq\/X46vFnJycUGi322UjIIYiNzc3NCibzbL5Oo+Pj9SNvF4vmymSUCQajVLwZ76jv4NdCldsZ2eHjRRZKIJNH3fy5eWlZNctAx4NtVoNVquVjRzFUAQPPHabi4sLNsuxvb1NPXoRql8b6Pzf\/sbnH2pVC71FudHHAAAAAElFTkSuQmCC\" alt=\"\" width=\"29\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0Thus; first second third overtones have frequencies\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"88\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0.respectively and so on.<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 0pt; line-height: normal; font-size: 16pt;\"><strong>Problem A pipe 20 cm long is closed at one end. Which harmonic mode of the pipe resonantly excited by a 430 Hz source ? Will the same source be in resonance with the pipe if both ends are open? Take speed of sound in air 340 m\/s\u00a0<\/strong><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 0pt; line-height: normal; font-size: 16pt;\">Sol. Here, <img loading=\"lazy\" decoding=\"async\" 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Tp\/GQnQdM7LTnXOqwclRchTLRsr5\/nGpnbLu3cAI3AqIhLdqEUBHe576d8odoYKGUREGC2+pRltkCkMs11T2zN6VfwLnpRkoO5o548M1Wa49577437DJUNgDh22GGHbrYpH638LEnS9dOnfHM2Z6e8PEeuakAgUSraMslG7EyxIYBXX301jtWD90WumveNiKKTIFaVjfrBkonD33q2tQgshwTm\/zTCHoiz1mZw80ckmEPXSR78nI2bQfJnD1uwciBmdi3\/SsLzEgMHH3xwt543eAYkqTqoB1uv9OqOPfbYeH\/xqn2UJ2eIhFehwn8RlIGVOoqhFUVfofOQkpaFymZ941ZQEV6F\/yQoNttrqJKyKq3Q\/0APmUJXXvcEKsKr8J+FvlOn7nWs0Br0wK20KoV7AhXhVahQoSOhl6qHbBdJq333ZqgIr0KFCh0JbQkLVT1FdtCrQoUKFQYM9Or1P1M1ridnbQuSAAAAAElFTkSuQmCC\" alt=\"\" width=\"316\" height=\"27\" \/><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 0pt; line-height: normal; font-size: 16pt;\">Fundamental frequency of vibration in a closed organ pipe<\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 0pt; line-height: normal; font-size: 16pt;\">\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"244\" height=\"38\" \/><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 0pt; line-height: normal; font-size: 16pt;\">Hence a source of freq 430 Hz may excite resonantly the fundamental mode of closed pipe.<\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 0pt; line-height: normal; font-size: 16pt;\">\u00a0If pipe is open at both ends, fundamental frequency<\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 0pt; line-height: normal; font-size: 16pt;\"><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"254\" height=\"38\" \/>.<\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 0pt; line-height: normal; font-size: 16pt;\">Same source of frequency 430 will not be in resonance with the pipe open at both ends.<\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><strong><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><\/strong><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><strong><span style=\"font-family: 'Times New Roman';\">39 BEATS<\/span><\/strong><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><em><span style=\"font-family: 'Times New Roman';\">This phenomenon of alternate variation in the intensity of sound with time at a particular position, when two sound waves of nearly equal frequencies and amplitudes travelling in the same direction superimpose on each other is called beats.<\/span><\/em><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">The time interval between two successive beats (I.e. two successive maxima of sound) is called beat period. The number of beats produced per second is called beat frequency.<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">For example, when two sounds of very close frequencies, say 256 Hz and 260 Hz reach our ears simultaneously, we hear a sound of frequency 258 Hz, which is the average of two combining frequencies. In addition, the intensity of sound heard increases and decreases slowly.\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">The number of beats heard per second is equal to 4. This is the difference in frequencies of two incoming sounds.<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">40\u00a0<\/span><strong><span style=\"font-family: 'Times New Roman';\">FORMATIONS OF BEATS<\/span><\/strong><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><strong><span style=\"font-family: 'Times New Roman';\">(a) Graphical method<\/span><\/strong><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Suppose we have two tuning forks A and B. Let the frequency of fork A be 6 and frequency of fork B be 8. Let the waves of compression and rarefaction given by the forks A and B be represented by curves (a) and (b). crest represents a compression and a trough represents a rarefaction<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Fig. (c) Shows superimposition of the two waves from forks A and B\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">And in Fig. (d), we have represented the resultant wave according to the principle of superposition.<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Thus one beat is formed in 1\/2 second between P and R. Similarly, another beat is formed in the next 1\/2 second between R and T. Hence number of beats per second is equal to two, which is also the difference in frequencies of the two forks A and B.<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><strong><span style=\"font-family: 'Times New Roman';\">(b) Analytical Method<\/span><\/strong><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Let us consider two waves of equal amplitude\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"12\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0and slightly different frequencies\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"21\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0, and\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"21\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0, travelling in a medium in the same direction.\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Let the time dependent variations of the displacements due to two sound waves at a particular location be<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"340\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">And<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"329\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">According to superposition principle, the resultant displacement s at the same time is<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAXUAAAAbCAYAAACDdB9WAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAABDBSURBVHhe7dwFbCRHEwVg5w8zMynMzBdUmDkKk8LMpDAzM3OiMDMqzMzMzMz96+tMO+O5hVnT3fnmSaM7t2d3p7urXlW96nVbqFChQoUKfQYVqVeoUKFCH0JF6hUqVKjQh1CReoUKFSr0IVSkXqFChQp9CBWpV6hQoUIfQn+k\/t1334VLL7007LbbbmGbbbYJe+65Zzj11FPDyy+\/HP7555\/srt6Dz3z11VfDcccdF7bffvv4TIceemi45pprwjfffJPdNejg\/fffD6eddlrYbrvt4lwOOOCAcNlll4VPP\/00u6NCV8Fm3n333XD99deH8847L9qKda8weCLZww033BDt4eqrrw7vvfde9tu+hw6k\/vTTT4cZZ5wxzD\/\/\/OGMM86ITrHmmmuGIYccMqy22mrhr7\/+yu7sHfz555\/hiCOOCOONN17YbLPNwnXXXRfOP\/\/8MN1004Whhhoq3HTTTdmdgwbOOeecMP7444e11lorXHHFFeHKK68Ms8wyS\/jf\/\/4Xjj\/++OyuwQcnnXRSGHfcccPFF1+cjXQdbHaBBRYIk046adh0003DFltsESaccMIw9thjh2OPPbbXbbhCeUh22MMFF1yQjXQdOGLBBRcMk0wySbs9TDTRRGGsscYKRx11VJ+0h3ZSl\/UidA6Rz4B\/+umnMNVUU4Xdd9+91zN1kVVAOfroo8Pff\/+djYYYaYceeujw9ttvZyPdi2eeeSYcdNBB4ffff89Guo5HH300jDbaaGGXXXYJf\/zxRzYaYgU0zDDDhDvvvDMbGXxw5JFHxn0U7LoLK6ywQhhhhBHCY489Fu3V9corr0RHHmWUUcJzzz2X3TnoQZKjWj3rrLOykdbxwAMPxERpYISgyx7OPPPMbKTrWGWVVcJwww0X\/S\/Zw+uvvx4mnnjiMPLII8dEdlDGgQceGA477LAOwamd1O++++7Q1tYWjjnmmGzkP5A7OElvwkOqDmTpb775Zjb6Lz744INo3N1JunmcffbZcS1+\/PHHbKTr2GuvveJ7Pvnkk9nIv0DwG2+8cfjqq6+ykQpdwdprrx122GGH7Kf\/oDqy\/t1ZFfQ22I7EgDzaWUhWkNnggvXXXz\/KnEWsu+660R66syrobZCQVCAk3DzaSf3aa6+Nk8T8AwMQ9nLLLRfL5hdffDEb7R30BKlvueWW8T1lSoMKVGmeVxXh\/\/Drr7+GJ554IlZLMuBG8JoPP\/ww6pkC8ddffx2zTfj888\/juOuHH36IY6qxdL\/LvTKrL7\/8Mv787bffxp87A6W39Sd7NYIq9d57743za3Q9+OCD2Ss6wjM\/\/\/zzUQYq6vjW7uabb45XK7bFFz7++OOw8sorxzmoXNNztNpX6gqpJ3u444472p\/fnAQbfYtW7UEik+zhiy++aN\/3vD189NFH7eMSoLw9mHtn7SH5o35WI7C5++67r8Pe17rq+bU5vPHGG5FfVQj55zV3yTRZuZWkzuv4j8TWHPQ903NY33ZSV4YofaaYYoqWSZTBMeSy10svvRSNoRFMPj305ptv3k4qvYGeIHWNXu+50korRXLrblhP61prvetdn3zySfbq\/qFxK+OV+epf0Pw\/++yzmOHQI83llFNOye7uCFUWZ1lyySUjmcqUZphhhjDNNNPEAMHQGeDUU08d3yfJCb\/99lskLNmocaR4+OGHh379+sUSWv8BobSK77\/\/PswxxxxhnHHGiQ5WDxry9Ff38YXRRx896vEuROiZJphggvjzHnvskb3qP9gDkhJ79R7mZ04J1pQMZB1acWISnXWx7noy\/GLXXXeNV6s22llSt\/fsYZ111olr43kQi0xY4mVtTjjhhOzujmAPgil72GSTTcK2224b7cH63HbbbdHXkd60004b3+f000+Pr7N2JBn7YJzcSgfX82MPM888c3x9qxA05pprrvjcr732WjbaP5DwQgst1G4P7LKePZBVizBvtk3HJ\/fYP2uWkJ7DnjayyyL4hcMrPpekuNVWW7Xbg2DZTuoMcoMNNogPqhEp00hRtBlstteVvcYcc8xoqM0g8k8++eSRVFZfffUYnXsDPUHqNmLOOeeM77v00ktHAu5OIOlk\/GUvJ5xqgZMxmocffjiuOQls5513jk3zCy+8MGYuM800U119+pFHHolGj+BSL+Stt96KTbDLL788\/gxIwHMUNWKym3HNcZ\/HmZ1aoJUj559\/\/jm7sxyU2F5b1B7zQPwqQ4QiC+eEtH4lrmuNNdaITmQefq6VIf\/yyy\/xtT4j+QRiSJB1IhK6f1qXsrAPnkmQbfW1eXSG1NmDJqa5sWMklAK+gwv3339\/DLj19OnHH388kg8ZNz27PUWIeTlMkmDNEqknsDvjEgSf57X2dMQRRwyzzjprywmfz2QPBx98cF174PvsgR889NBDsfHu8EiyB3NnD8i4nj3gT2uj0hIEzeH222\/Pfvuvzc0222ydsmkVBB9cZJFFot3l0U7q4MF23HHHuFgjjTRSOOSQQ0rp1hbZhpe9NC3KTkJpN99888UFEd0tcL6E6Qn0BKkDA1hiiSVi85dB33LLLdlvug6GbV1rrXe965133sle3T\/Svmsaa+QKrrJrTmn9ZW71gj7jt37+zUMFqMxOQPDuK5L61ltvHccvueSSbORfwmTA1o29lcULL7wQyVCgaLSfkhrByNzYmOwsJR4+e7LJJovvUZZQTzzxxDgHgTHhqaeeinvfGR33rrvuiq9lm11BZzP1ZA\/Wkz1YD9l33h7yBwDyEBytRbGyk9jkM9errroq3lck9VSxC\/DJ92Xxiy22WM2eWyP4TDo0KauRPXj\/ZA\/6iewhKRjsYcopp4zvUS8oFOHQh2zfHBJk1aOOOmqnJG\/PIolzgKWIDqQONoY+xhGGHXbYGKkGNGz8TjvtFEsu8lBRq0ywAUm\/KgPvu\/jii8cyLn8pkRmR00DF39VaxFag5HL6gGPY0GLG7vcIl3xx0UUXRcIbUN8RAMRqLWRJZSs3zy8psI4yq6SRFtGM1POlMfKQHSmBy55YIAvOO++8Yamlloo6bFkgZJmnbAg4t0Sn2JBqBM7rqGqSB+yfTHX66afvQGQJ5mfdBOZaSDZTbLTXA6IjJRXtFwl6ruK4SzbZDGnPNtpoo7okXoT1Yw8y23PPPbeuPTQj9byvWK\/11lsvVgB6PGVA\/iLl8fl8ctEMOBAXpGwcyZvPPvvsE38uA2sw\/PDDdzi6rOEtWOTtnDR7zz33RP9XnVqvWgpF2gfBooj+SB0YoPOdHpxTdHfG2hmInIjFROjTeXhekYu2RNpxLLMMOC2SpoHmLzqaz3Eqpfi7rmZKILrvu+++0bmUsQnmqNSUEZKeaN5OI5Etbrzxxuyu3oN11VBijAinLMyPQSrTZSeI7OSTT+6vTG6F1MF+CIRliI0Dyuw5cKPeQRGeXd9DFpYCKUccYoghWmpyI3NzTydVkAgtvZil+zwlOUlG4Nhvv\/2y3\/wHBCYweb2MuAwENIlQ0X5JgJ6rOO7yvYlGsB70cMkVWaEszNG8VVnJHgTOIq+0QuqAD1QdZU7m+VLloosuGm2CDFYW1n7VVVcNyy+\/fLs9sGX2QIYsC8+OT\/fee+\/4M6UCt0oU0vtaD9zD51SjnpNEyo+KNo83xhhjjJo9gZqkDkoMmo0yq1mW47geMi17KV0aNSjqQZNMtsIA86DtKisRO6mmLKnXQ0\/JL3moKDgHAk9g\/LfeemuHSsTacwYNKQZWD4yGRFJrvetd+++\/f\/bq2mB4sj0NrFYyXWCoCMgXjLxeAJtnnnk6NMh7itTTMdHZZ589lritAPkinXzTT3MY4bbS3BQEVbpI3b5Za7p8MbuVkcnGVB+cvhapW3vSo0YjG+kKunL6hT0svPDC8XsrrWS6wB5UKCQYPTv2MPfcc3cI9D1F6ipMDVr6e70qvx7suSw9f9R7ww03jPZQq+KqB1KnqiKRurP4eCrPMSQuKkn+IAViN\/d8VcCHkD8tni5fRJsmhiZYESIbZ\/TiZvq3TIOxlL2UefWMggNoYCC3ItKmF0mAwbhMVjQemEhd6ZbXhhOeffbZ6PT1mpUJNlWmLnCmiF4LCNTJgFrrXe+i0zaCso8hrrjiitlIOTDOPPkot5dZZpm4phrwCT1B6tbIiQlBS\/M4Dw7arNnudI5sMq2N6kmwVLb7f1nQnlU4SJ1\/IIZaJJD2lD8gqFqkbh5IROad4P6y8kce9r2zpC5Asodll102GykH9pCX7viVzNce69Mk9BSpqwrIdsXGPvJsZg+Ot7KH1OA0F6d2JI\/FBmUjCMyeAambh8ZrvoleD2Q0VUG+P+XYomRb9ZagMk3P02aTOYpyLYFD0nMZUnfIDa3AoikzbVieGAQZxmQy+WfNY2AjdSSgMYrQ8hmqcZmDTL3RUSYBzpE+mU29OfckEJt1ECxaAYelH+chY\/dezuQmIDxjRVJPZ4iLpE7HbUbqZCt2KxOSjKRLRiNYkL3qgb35DI20lNEJqspfWTZiQmyNKqaEROr8iz036wM0InWJF8d2AkyA1LyWtTcjpFroCqkjOPvCJlsBOUszMJ+UOE3jvRB5gsarsSKpk3yMF0mdDzUjdcTppIv3LNqDv78kWaoH9uAz9IbSWvNDvQGSTCv2kEjd8Ub9i1pJaxE+ny+QaTxzAmlGb0SiITA5kUVmTOvQptmgFKK1ySod9zERkUTGnCej3oBsRhkqi3WkzfMo2Whhjv800jUHNlK3kTZQpOeQmmdOAtBPlbCNdHIOQONUYg2or7YjAHJXq2fDkTr7sVcyCARpTJM7NZtkmSpE6+yUVcrkGK9zyMaRSCICQV3pjyidGsoTRIIxgd8pEaW9bCpdqk7jjjXWg1MvgobPT8\/D+b02leDOaZfJ0MxZcEEo+Wy0HhqROuIQGBzt1cAV5FvR9\/PoCqlbO7bc6qktpO7gBR3e\/puPnoUKKMl67EF\/y77TmfP2kHpckoy07\/aFr0uM+FE9e+BrSeqpZQ\/Wox6QJCJGqul5BFVSmIs9+KZyGXvATTTw9J2PZhAoJEIky2JCxxfIotaEVGgdVb1pDdqwvOyJhihq0W5EUfp0mQjU3ZCp6xRrrDAiz2ThOUazL+0MbKTOEGSVApMz2+bCYP3cqHln3WUwyIVMMyDgGWTSCLcV7RA4HwdF5PRHho+s2FqCE0pIWtASsFPTSYbPiYyTfRCAdSSpGHPJkmoda+RwnDfdV+uqdVogQRC1R8VgSx\/nF6rXfMbUCGwn7XUZNCJ1cBzS+7Gj\/Dq2is6SOsJAHBK9ss3aBN+a9GWtvD2omPJVKlmOHdgjduEECKgKkj0gaGfCZbCIMe2pv+9S61gje0Dg6b5aV6OTcjiHPRRtxjFV9iBJa+WMvLVD1M141fwkstaB1FIL1g4\/ek9JXz6o1W2UDoroLlJXcstOLW5vw+b4GjlCH1AZeoXeRzNS7y4IhokwKwx84P\/kSGfwJTSdQUXqAxnoyAg9\/6UVJatKKpWAFfoeeovUKwzcIAH269evv28iU0\/Kok+QuowaGTobrJFKY6LHKsk6c0JgQEEDlfZOe0tnpV30VKVnRep9DyQCtis700fyJyRUaK0evasw6INkRy7SiE2+79K41zAtiz5B6siQvsUxHF9y+T+NtNW\/CzEgQa\/1pZ00h\/ylW57XzSr0DdCI2a5MLO21b+F25g9VVRi04citU1t5v09XK1\/+61PyS4UKFSoM7mirUKFChQp9BW1t\/wcLaoUcJK3jmQAAAABJRU5ErkJggg==\" alt=\"\" width=\"373\" height=\"27\" \/><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"269\" height=\"27\" \/><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Using trigonometric relation\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"375\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">We get\u00a0<\/span><span style=\"font-family: 'Cambria Math';\">\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"371\" height=\"27\" \/><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; text-align: justify; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">=<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><span style=\"font-family: 'Times New Roman';\">A<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"306\" height=\"27\" \/><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Here A=<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"173\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0represents the amplitude of the resultant wave given by equation. (3).\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Clearly, the resultant amplitude A changes with time.<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">(1\u00a0<\/span><u><span style=\"font-family: 'Times New Roman';\">)\u00a0<\/span><\/u><strong><u><span style=\"font-family: 'Times New Roman';\">The amplitude A will be maximum<\/span><\/u><\/strong><span style=\"font-family: 'Times New Roman';\">,<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><span style=\"font-family: 'Times New Roman';\">When<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"146\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0= max = + 1 = cos n<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"18\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0where,\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHQAAAAbCAYAAACtOKuoAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAASFSURBVGhD7ZhLKHVdGMcP5TpQ7lEUGbiEIgO5jaXIgIgQZSIpTJQIZcZAKcplgoGJiRyZUUKkkNxyv+Re7nfP+\/0fa593O6\/zfWefl3PY3\/nVGqz\/3muddZ7\/2ms9a2nIiqqwGqoyrIaqDKuhKsNqqMqwGqoyrIaqjB9raFZWFnl6epJGo6Hg4GBqbGwUT\/4eqW9jOT09pcrKSoqOjiZnZ2cek6+vLxUVFdHd3Z14yzz8SEMjIyPJxsaGjo+P6fn5mVpbWzmItbW14g3TGBoa0k0SGGIseN\/e3p5GR0fp5eWFrq6u2Ezo6enp4i3z8OMM7e7u5kBtbm4KhdhUf39\/cnR05K9FKZeXl5SUlESpqalUX19vkqE1NTWi9ga+TOgo5+fnQv16fpyhAQEBHCR98HVC7+zsFIrxDAwM0OzsLL2+vnId\/SgxdGtri56enkTtN4GBgdzX\/v6+UL4ejgxmE2a3nZ0dZWZm8oOHhwcKDw9nDc\/MvRcYwsXF5UNDe3p6WC8tLRWK6Sg11BDYFtDX\/f29UL4eDZYrLy8vrsTHx5Ofnx\/vTTCyqqqKwsLCeFDt7e38jiE6Ojr4PSVlenpatDYO7E9SW32wf0FPS0sTiumgn781tLe3l\/tpamoSinl4FxlkaYmJiRQXF6fbo9bW1nhg\/5VF9vf3U1BQkKIyPz8vWhvHysoKjwVFH+nZdzD04uKC+4iKihKK+dBFBkusFKyRkRGhEs3MzLA2Pj4uFMvxEwxFHBMSEsjHx4ezXXOji8zBwQH\/EXyhcioqKlg\/OzsTiuXAqoGxoOizsLDAuiUNxfaVn59P3t7etLe3J1TzoovM2NgY\/5G+vj6hvIFlGPpHWZycpaUlamtrU1SwVysFY0HRR9pDy8rKhGI66EepociQq6urydXVlXZ3d4VqfnSRKS4u5j8iPzMhs3VycqLs7GyhGMYcSRFwd3fntvpIv9\/V1SUU00E\/Sg0dHBwkBwcHk\/7TZ8KRkbJHZLhypqamWNdqtVy35MyTiI2N5TEh8ZCDpQ66KRcL+ig1VLpEaG5uFspvysvLaWNjQ9S+Hjb05uaGB4RgyZGu1CYnJ+no6IhCQkLEE8uxvb1Ntra2fH8rAQ3jxH2qnJiYGNaVnAMPDw+5jYeHh1DeU1BQwM\/n5uaEQhQREUFubm40PDz8rjQ0NPBXu7i4KN58Izk5mfvArZREXl4eay0tLUIhysjIYK2kpITrExMTXJf\/d2nFur6+5joburOzw2JdXR2LEpjtOMijUW5uLj0+PoonlgVHJIw3NDSUM0oEMycn54\/xSYYacymCQMIs9IU2uBTAdSBMkS+jkqGSdnt7y\/V\/K4ivnC83FIHA3omUWx8MGHed0rXYdwFHAiRiy8vLBpMrKaEzZiKiL0NFfnWHiY0+cd0HMFk+aiMv+gklDIZ+cnIilLdTBjR5DoNMGRpWDQAvUF9fX+c6WF1dZQ3bJvgzu1ARuAHDbddngq+jsLBQ1L4fqjUU52kkSp8JltuUlBRR+56o+gv9P2I1VGVo\/kl2tNailvKq\/QWWuqX9QbpOaQAAAABJRU5ErkJggg==\" alt=\"\" width=\"116\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">So\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"170\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">or<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"94\" height=\"38\" \/><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Hence the amplitude of resultant wave and therefore, resultant intensity of sound will be maximum at<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><img loading=\"lazy\" decoding=\"async\" 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\" alt=\"\" width=\"394\" height=\"54\" \/><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Time interval between two successive maxima of sound<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><span style=\"font-family: 'Times New Roman';\">=\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"180\" height=\"41\" \/><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">I.e., frequency of maxima =\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"85\" height=\"27\" \/><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><strong><span style=\"font-family: 'Times New Roman';\">(2)\u00a0<\/span><\/strong><strong><u><span style=\"font-family: 'Times New Roman';\">The amplitude A will be minimum<\/span><\/u><\/strong><span style=\"font-family: 'Times New Roman';\">,<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><span style=\"font-family: 'Times New Roman';\">When\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"146\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0= minimum = 0\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">cos\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" 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alt=\"\" width=\"382\" height=\"35\" \/><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Or<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"110\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"131\" height=\"35\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><span style=\"font-family: 'Times New Roman';\">Or<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"107\" height=\"42\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0\u00a0<\/span><span style=\"font-family: 'Times New Roman';\">&#8230;.. (4).<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Hence the amplitude of resultant displacement and therefore, resultant intensity of sound will be minimum at times,\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAUAAAAbCAYAAAC0s0UOAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAAaSURBVChTY\/iPBYwKooERLfjv37\/tqPjfdgDDxRiM9K4wpAAAAABJRU5ErkJggg==\" alt=\"\" width=\"5\" height=\"27\" \/><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"413\" height=\"55\" \/><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Time interval between two successive minima of sound<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><span style=\"font-family: 'Times New Roman';\">=<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"246\" height=\"41\" \/><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">I.e.<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0<\/span><span style=\"font-family: 'Times New Roman';\">Frequency of minima<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">=\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"85\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">\u2026\u2026\u2026\u2026\u2026\u2026(5)<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Comparison of values for maxima and minima intensity shows that maximum and minimum intensity of sound occurs alternately.<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Combining (4) and (5),\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">we get,<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><span style=\"font-family: 'Times New Roman';\">frequency of beats =\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"85\" height=\"27\" \/><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">i.e.,<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" 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\" alt=\"\" width=\"561\" height=\"34\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><strong><u><span style=\"font-family: 'Times New Roman';\">Applications of Beats:<\/span><\/u><\/strong><\/p>\n<ol class=\"awlist40\" style=\"margin: 0pt; padding-left: 0pt;\" type=\"i\">\n<li style=\"margin-top: 5pt; margin-left: 72pt; margin-bottom: 5pt; text-indent: -54pt; line-height: 150%; font-family: 'Times New Roman'; font-size: 16pt;\"><span style=\"width: 38.9pt; font: 7pt 'Times New Roman'; display: inline-block;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>For tuning musical instruments.<\/li>\n<li style=\"margin-top: 5pt; margin-left: 72pt; margin-bottom: 5pt; text-indent: -54pt; line-height: 150%; font-family: 'Times New Roman'; font-size: 16pt;\"><span style=\"width: 34.45pt; font: 7pt 'Times New Roman'; display: inline-block;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>For producing colorful effects in music.<\/li>\n<li style=\"margin-top: 5pt; margin-left: 72pt; margin-bottom: 5pt; text-indent: -54pt; line-height: 150%; font-family: 'Times New Roman'; font-size: 16pt;\"><span style=\"width: 30.01pt; font: 7pt 'Times New Roman'; display: inline-block;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>Beats are used in electronics.<\/li>\n<li style=\"margin-top: 5pt; margin-left: 72pt; margin-bottom: 5pt; text-indent: -54pt; line-height: 150%; font-family: 'Times New Roman'; font-size: 16pt;\"><span style=\"width: 30.9pt; font: 7pt 'Times New Roman'; display: inline-block;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>For detection of marsh gas in mines.<\/li>\n<\/ol>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><strong><u><span style=\"font-family: 'Times New Roman';\">41 DOPPLER&#8217;S EFFECT IN SOUND<\/span><\/u><\/strong><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><em><span style=\"font-family: 'Times New Roman';\">According to Doppler Effect, whenever there is a relative motion between a source of sound, the listener and the intervening medium, the apparent frequency of sound heard by the listener is different from the actual frequency of sound emitted by the source.\u00a0<\/span><\/em><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">When the distance between the source and listener is decreasing, the apparent frequency increases the reverse is also true. For example:<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">1. The frequency of a whistling engine heard by a person standing on the platform appears to increase, when the engine is approaching the platform, and it appears to decrease when the engine is moving away from the platform<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Thus basically, Doppler Effect is the motion related change in frequency of sound.\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-left: 22.5pt; margin-bottom: 10pt; text-indent: -18pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: Wingdings;\">\uf046<\/span><span style=\"width: 2.93pt; font: 7pt 'Times New Roman'; display: inline-block;\">\u00a0\u00a0<\/span><span style=\"font-family: 'Times New Roman';\">Note that Doppler Effect is essentially a wave phenomenon. It holds not only for sound waves, but also for electromagnetic waves.\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><strong><span style=\"font-family: 'Times New Roman';\">Expression for Apparent Frequency\u00a0<\/span><\/strong><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Let S be a source of sound and L, the listener. Both are initially at rest. Let\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAsAAAAbCAYAAACqenW9AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAADpSURBVDhP7Y8rDoNAEIbXQAgBDQrLBbBIuAOCIBAcBInEobAk+DpOQMIRuABBIMDxtx22j22bPlyb9Esmmce3mxmGD\/jL1\/ysnOc5ZFmm6PueBifCMIQkSaiqCqwoCjRNQxJjDEmScG0jCALqD8NwWWNZFmr6vs87G5qmQVVVyoWdj7LnebzaUBQFcRxTLsiO48C2bV4BbdvSByeeypZloSxLXt3IURSd5SzL4Lou1nWl+shDues6GIaBaZr4ZONO1nUdpmnSg1sEOU1TOqiua94REeR5njGOo7DnNYL8im+RD8fs3ot1twfvrj8z+36mtwAAAABJRU5ErkJggg==\" alt=\"\" width=\"11\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0be the actual frequency of sound emitted by the source and\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"12\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0be the actual wavelength of the sound emitted.<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">If\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAAbCAYAAABIpm7EAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAEQSURBVDhP7ZC9jkVQEMdFQkKl9ByewQPoRaNUKWipvYKnkChupfQINzolhQKJj8LHbGaca6\/sFrbbbPaXnOTMf\/I7xnDwQ\/6FO\/wpwfd9EEWRTt\/3lG3bBrqugyAIoGkaZSRgUJYlRFEEHMdBURTUlGUZpmmCNE0p77ruOlIYhtSo65olB0mSgCRJdL8IpmmSMI4jSw4cxwHP8+h+EXBORVFYdYD\/gyO\/vnoK67rS64ZhsOQAl+G6LqvehKZpSAiCgCUAeZ6DqqqwLAtL3gTcEgpxHFOdZRmtuKoqql98EWzbBsuygOd5eD6frPvJKczzTAIeFNq2ZZ0rp4DgOodhYNX3XIQ7\/EZh3\/fH\/bM\/PgBim6OzddCibwAAAABJRU5ErkJggg==\" alt=\"\" width=\"12\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0is velocity of sound in still air, then\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAADAAAAAjCAYAAADSQImyAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAKwSURBVFhH7Zg\/SHpRFMdFMRKhLUjBXByEJATBQVsKt0ARB8GlWUSEnJzaJXBwFCwRxEEqnHTSVTAC\/zSVLhaIEiUolflOnPO7Wb9fWhb88l3oCxfvPfddvZ\/3zjme+yTAsQRBKPwCzFO\/AP9bNzc34PV6QSKRQKlUItvV1RVsbGzA0tIS3N3diRvA5\/NBp9MBtVoN6XSabHa7HR4fHwnq4uKCDxdaXFyESqXCRgD39\/egUqn4iIFGo0F3+\/r6mlkAYrEY5HI5PgAODw8JYDAY0BhjwOPxUJ8LAL\/fTwCoYrEI6+vr8PT0RGMuAPb39wlAo9FANBqF0WjEZjgBwA3f3t7Cw8MDs7yKC4CPNBUAaTH\/Yr4VsyYCXF5eks9hW11dheFwyGbEp3cA3W6XgqVQKEAoFCKIs7MzNis+TXwCb91GqVRCPp9nI\/Hp0yA2Go1zAyiXyxAOhz9rHwOYzea5AUQikXEsftCmA1SrVSqiuHQhzDxY7SHlLACJROLfO\/NpOz09Zau\/r6kAWIfjj6ysrMwEgNkLffYrrd\/vs9Xf10QATKG4eaxBMAa4SqO9Xg+kUilsbm7iJKytrfEDgBu22Wwgk8mojEDhP\/EsAKKIgYODA\/rivb09Zpkd4Pj4GHQ63ZdarVZjq7+vMUCr1aLNo8u8FQLgIQLVbrfp8yeFVQE+qXq9Th7yovPzc3pLQQCYMnHzcrkcms0mu+SPDAYD7OzsQCqVAovFwqw\/IzwHuN1u2Nraov3h2fhF29vbVLMRwMnJCTidTtjd3WXTr8pms+ByuSAej\/91B35aCoWCUu+LlpeX6ag5diGxS6vVjt8LoRYWFsi9uAHA2Ewmk9R3OByQyWSozw2AyWQigKOjIwgGg8zKEYDVaoVAIECx+jYWuQLQ6\/XvjrfcAEyTIAiFZxR\/ouYlLYHaAAAAAElFTkSuQmCC\" alt=\"\" width=\"48\" height=\"35\" \/><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Let us now consider a situation, in which medium, source and listener move in the same direction from S to L with velocities<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"141\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">,<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0<\/span><span style=\"font-family: 'Times New Roman';\">respectively,\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">As a result of the motion of the medium, the sound waves in one second travel a distance\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"120\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">This is the resultant velocity of sound along SL.<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><span style=\"font-family: 'Times New Roman';\">Further, the distance moved by the source in one second\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"113\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0along SL.<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAABsAAAAbCAYAAACN1PRVAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAC6SURBVEhL7ZKxCoMwFEXj7l\/lpwIFl\/yKY3EKdFIIODkGR0fzBy6K5LaUR9wMoUFKmwMJvDPkwCMMF+Gcu+fYx+RYEnIsCd8bK8sSRVFgWRYycUTFGGPvY4whE0dUTAgBzjlN8fzxB2maBl3X0XQwjiPqusa+72TCnMa01v5TzPNMFljX1fuqqsiGOY31fe8ftdaSBbZt815KSTZMcI1t22IYBpoOpmmCUirdGlOTY0n48djrelxz3O0Jv8cVENrm3CsAAAAASUVORK5CYII=\" alt=\"\" width=\"27\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">Relative velocity of sound with respect to the source =\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"156\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">So the apparent wavelength<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"154\" height=\"39\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0\u2026\u2026\u2026\u2026.(1)<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">These waves of wavelength<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"21\" height=\"29\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0travel towards the listener, who himself moves through a distance\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEoAAAAbCAYAAADbAhkjAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAOcSURBVGhD7ZdLKHVRFMdv5DmkSBlcQpEBKa\/BFcXAwPs5YCZTJcljcBkZGhpIMaVIeRR5pcRYjCjkWd7v112ftax9z9nuPc6mr4\/bd3616+z\/\/t\/TOf+7zjr72MBCCSsoRaygFLGCUsQKShErKEWkoA4ODmBlZcU9tre3ecUTFe\/19TUUFBRAc3MzK76LFNTx8TFkZ2eDzWaDjIwM2Nvb4xVP0JuVlUXezMxMr96bmxtaT0pKYsV38Xj0Ojs76eaGh4dZMaa9vZ28IyMjrMiIoNLS0ljxXTyCys\/Pp5vDijHDzHt4eEjr\/f39rPguUlAvLy\/g7+8PMTExrBij4g0PD4fKykqe+TZSULu7u1QB1dXVrBizs7ND3pqaGlY8WV9f56N\/Dz72wcHBEBAQQP1WgFUeGRlJektLC6vmSEFNT0\/Tzbe2trJizOTkJHnb2tpY+T5YnXiur4zPbnJ+fh7y8vLg9fWVvHa7nfSNjQ3Iycmh45KSElpTRXKKRr66usqKMR0dHeRdW1tj5ftgUHFxcV8aPT09\/GtjRFDJycmsaBQVFUFFRQXPzJGCio2NpZJ8enpixRjsTaren+L5+ZmCys3NZUUjPj4elpaWeAbgcrlgc3PTPT7elzso3BziSVNSUlgxRnhTU1NZ+Z3c39\/Tdfb29rLyDraYqKgoClKAQXV3d5O\/oaGBVQ13ULizRpO3t9TJyQkcHR3xDGBra4u8VVVVrGigV2VroQcvsq+v70sDvwbMmJmZoevUtweslMTERJidnWVFA\/1BQUFenxJ3UOPj43TSwcFBVjTwrbGwsMAzgLGxMfIODQ2xopGeng6Li4s8U+NvN3OB0+kkr57Gxkaoq6vjmQwWSUJCAs9k3Gepra2lk+7v77PyDlZHYGAgXFxcsGLuvby8ZOVnKS4uhpCQEDrGxt7U1ER\/5MPDA2l6ROMvLy9nRYaCEk0vLCyMRIEoU1wTz7Pw4mZSj96LFfIbwKD8\/Pzocww\/ozCkq6srXpV5fHyka5+bm2NFhoIqLS0lE77F9K9g\/DdQxz2HQOw\/sHLMvD\/NxMQEXVNoaCgMDAxIzfsjy8vLdE9YWd6goM7Ozj4dt7e3ZEa8revH3d0dO38H5+fnXpvzR\/C7FXfsRsid7j8GK8\/hcPDsna6uLhgdHaVjK6g3cHuCQem3DKenp6SJl5gV1BvR0dEQEREB9fX1NMrKymheWFjIDisoZWxvZTdlDbPhmvoDjoLntzP12JAAAAAASUVORK5CYII=\" alt=\"\" width=\"74\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0in one second.<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0<\/span><span style=\"font-family: 'Times New Roman';\">Relative velocity of sound waves with respect to listener<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"183\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Apparent frequency of sound waves heard by the listener is<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"146\" height=\"40\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0\u2026\u2026\u2026..(2)<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Using (1)<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"158\" height=\"42\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0\u2026\u2026\u2026\u2026\u2026..(3)<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><strong><span style=\"font-family: 'Times New Roman';\">Sign Convention<\/span><\/strong><span style=\"font-family: 'Times New Roman';\">. All velocities along the direction S to L are<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0<\/span><span style=\"font-family: 'Times New Roman';\">taken as positive and all velocities along the direction L to S are taken negative.\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><span style=\"font-family: 'Times New Roman';\">As case the medium is moving in the opposite direction from listener to source,\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"31\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">is negative.\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><span style=\"font-family: 'Times New Roman';\">Now the effective velocity of sound waves\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"64\" height=\"27\" \/><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Hence, observed frequency is given by<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"155\" height=\"42\" \/><span style=\"font-family: 'Times New Roman';\">\u2026\u2026\u2026\u2026\u2026\u2026.(4)<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">In case medium is stationary,\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"52\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">0.\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Therefore, from (3) &amp;<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0\u00a0<\/span><span style=\"font-family: 'Times New Roman';\">(4)<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"114\" height=\"42\" \/><span style=\"font-family: 'Times New Roman';\">\u2026\u2026\u2026.(5)<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><strong><span style=\"font-family: 'Times New Roman';\">Special Cases<\/span><\/strong><span style=\"font-family: 'Times New Roman';\">.<\/span><\/p>\n<ol style=\"margin: 0pt; padding-left: 0pt;\" type=\"1\">\n<li style=\"margin-left: 21.5pt; line-height: 115%; padding-left: 1pt; font-family: 'Times New Roman'; font-size: 16pt;\">\u00a0<strong>If the source is moving towards the listener but the listener is at rest,<\/strong><\/li>\n<\/ol>\n<p style=\"margin-top: 0pt; margin-left: 22.5pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Then<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"34\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">, is positive and\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"59\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><span style=\"font-family: 'Times New Roman';\">Therefore, from (5),\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"108\" height=\"38\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"131\" height=\"29\" \/><\/p>\n<ol style=\"margin: 0pt; padding-left: 0pt;\" start=\"2\" type=\"1\">\n<li style=\"margin-left: 21.5pt; line-height: 115%; padding-left: 1pt; font-family: 'Times New Roman'; font-size: 16pt;\"><strong>If the source is moving away from the listener, but the listener is at rest<\/strong>,<\/li>\n<\/ol>\n<p>then <img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"20\" height=\"27\" \/>is negative and <img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAADsAAAAbCAYAAADCifeFAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAMCSURBVFhH7ZY\/SOpRFMclsBKTFyRFg2aQ0RC1iGBDtegoQdjoFC0NLUYOgRA1ObWFokg0tIT9GV5IFNHQULZERjVFQRBoiQap1Xmd47GfaZrP98g\/9YELnu85P7nf3+\/ec68Ivg\/yH7NVyo\/ZauXHbLVSHWYfHh5gaGgIGhsbQSQSQW9vL3g8Hs6+Uflm4\/E4KBQKUKvVEAqFIBaLgcViIdNLS0tcRVS+2ZmZGTJ2c3PDSvIFyOVykEql9NWZyjeLRpubmzkSGB4eptzBwQEraWbtdjvU1tbSuLi4YBVgbm7uTY9Go6yWD2hIpVJxJDA+Pk45h8PBCpsVi8VwenoK29vbVOB0Oik7MjICW1tb9FsikcDOzg79LhadTkf\/X+hobW3lJz\/m6emJ6rq6ulgRQA+Ym5iYYCVjGa+trVHB3t4eKwL19fVwd3fHUXGYTCbo6OgoeODLyYff789pdnd3N79Zm81GBembHcEH6+rq6E2mwM6HqwHH5eUlq1\/LP5k1GAy0XDPp6emBlZUVjpJcXV1BU1MTyGQyOD4+ZvVrOTk5yWl2c3Mzt9nn52dKdnd3s5LE5\/NBW1sbtfN0Xl5e6BA3Go2sfI7X64WFhYWCx+LiIj+ZG5xze3s7RwLYmDDncrlYSTOLnRaTer2eFYDr62v6eoFAgBUBXMZYn3Fw5+V\/NygE61paWjgSGBsbo9zh4SEraWaDwSAlsYkgePwolUpYXV2lOJOjoyOqx+dKCV4eampqso7F\/v5+mt+Hl4qUWa1WC1NTU7QXl5eXOZvN9PQ0vYxSk2pSeIlIsb+\/T1raGYsIZhOJBBXgGBwchPPzc85kg\/u1oaEBBgYGWCkdOJf5+XmaNzbSvr4+mpvVan13erwimEUeHx8hHA5zlJtIJEJ\/7na7WSk99\/f3dAyenZ3l2lrvzRYK7mc0e3t7y0qSzs5OWiFlSnFmJycnsy7fs7OzMDo6ylFZ8vdmNzY2yChevs1mMw2NRkPa+vo6V5UlxX3ZCkUueu1mv7\/DAIBffwA1SOEHyeTgSgAAAABJRU5ErkJggg==\" alt=\"\" width=\"59\" height=\"27\" \/>\u00a0,\u00a0 Therefore, from (5),<\/p>\n<p>we have <img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"226\" height=\"38\" \/>\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"113\" height=\"29\" \/><\/p>\n<ol style=\"margin: 0pt; padding-left: 0pt;\" start=\"2\" type=\"1\">\n<li style=\"margin-left: 21.5pt; line-height: 115%; padding-left: 1pt; font-family: 'Times New Roman'; font-size: 16pt;\">\u00a0<strong>If<\/strong><strong>\u00a0\u00a0<\/strong><strong>the source is at rest and listener is moving away from the source<\/strong>,<\/li>\n<\/ol>\n<p>then <img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"57\" height=\"27\" \/>\u00a0and <img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"21\" height=\"27\" \/>\u00a0is positive,<\/p>\n<p style=\"margin-top: 0pt; margin-left: 22.5pt; margin-bottom: 0pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Therefore, from (5),\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"109\" height=\"42\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"117\" height=\"29\" \/><\/p>\n<ol style=\"margin: 0pt; padding-left: 0pt;\" start=\"4\" type=\"1\">\n<li style=\"margin-left: 21.5pt; line-height: 115%; padding-left: 1pt; font-family: 'Times New Roman'; font-size: 16pt;\">\u00a0<strong>If the source is at rest and listener is moving towards the source<\/strong>,<\/li>\n<\/ol>\n<p>then <img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"57\" height=\"27\" \/>\u00a0 and <img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"21\" height=\"27\" \/>\u00a0is negative,<\/p>\n<ol style=\"margin: 0pt; padding-left: 0pt;\" start=\"4\" type=\"1\">\n<li style=\"margin-left: 21.5pt; line-height: 115%; padding-left: 1pt; font-family: 'Times New Roman'; font-size: 16pt;\">Therefore, from (5)\u00a0 <img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"227\" height=\"42\" \/>\u00a0\u00a0 <img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"113\" height=\"29\" \/><\/li>\n<li style=\"margin-left: 21.5pt; line-height: 115%; padding-left: 1pt; font-family: 'Times New Roman'; font-size: 16pt;\"><strong>\u00a0<\/strong><strong>If the source and listener are approaching each other<\/strong>.<\/li>\n<\/ol>\n<p>then , <img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"25\" height=\"27\" \/>is positive and <img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"26\" height=\"27\" \/>is negative,<\/p>\n<p style=\"margin-top: 0pt; margin-left: 22.5pt; margin-bottom: 0pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">From (5),<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"340\" height=\"42\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n<ol style=\"margin: 0pt; padding-left: 0pt;\" start=\"7\" type=\"1\">\n<li style=\"margin-left: 21.5pt; line-height: 115%; padding-left: 1pt; font-family: 'Times New Roman'; font-size: 16pt;\"><strong>\u00a0<\/strong><strong>If the source and listener are moving away from each other<\/strong>,<\/li>\n<\/ol>\n<p>then <img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"20\" height=\"27\" \/>, is negative and <img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"21\" height=\"27\" \/>\u00a0is positive,<\/p>\n<p style=\"margin-top: 0pt; margin-left: 22.5pt; margin-bottom: 0pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Therefore, from (5), we have<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-left: 22.5pt; margin-bottom: 0pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOMAAAAqCAYAAABBaewwAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAA+aSURBVHhe7d0DkDtJGwbwu+9sq862bdu2bV+dbdu2bdbZtm3b19\/\/1zezNzs7ySabRbLJUzVVm95g0m+\/et63OwOFFlpooc8xECR\/t9BCC32IljK20EKdoCmV8dNPPw3PPfdc8qh+8M8\/\/4Tnn38+fPLJJ\/HvZsaXX34ZnnzyyeRRfeHHH38MTzzxRPj111+Tke5BUynjH3\/8EY477riw7rrrhrvuuisZrR9QwDvuuCOsv\/764cQTT+x2YTcC\/vzzz3DWWWeFtddeO9xwww3JaH3h+++\/D4cddlhYa621wjPPPJOM1o6mUca\/\/\/47bL\/99nECf\/jhh2S0PsErrLHGGmGfffaJi7NZwBgdcMABYYUVVohzUM9wr3feeWeYffbZw1NPPZWM1oamUcZbb701TDzxxOHbb79NRuobH3\/8cZhyyinD7bffnoz0fzz00ENhsskmC++++24yUt+gkKeffnqYb775oresFU2jjPPMM0\/Yc889k0f\/gVXjhVxfffVVHLv22mvDoosuGvbee++qczce+Oyzzw4LL7xwOOaYY+IYT+y9FlhggXDffffFsUqwxx57hKWXXjr8\/vvvyUj\/xoorrhg222yzOIdZfPDBB2HzzTcPCy64YHjxxRfj2KOPPho9qEhHDlctbr755rDMMsuE9dZbLz42xyeffHL8jFNPPTWOVQJGc9JJJw033nhjMtJ1NIUyvv3222GkkUaKAszipZdeiqHgmWeeGUYfffTwxhtvhAcffDCcdtpp0eLNPPPMHRZGZ5DrUeZll102LL\/88vH18tT7778\/KtZRRx2VPLNz8IojjjhiXIz9HRb1eOON12FRi2R22GGHGBIOMcQQ4aabbgrvvfdeOOKII2J+PdZYY4XPP\/88eXZl8Blkvttuu4VRRhkljl133XXh6quvjgaQkleD5ZZbrk2pa0FTKGMqSAIvwjnnnBOmmWaaNs8ISASKCkIQry13fffdd\/G5wMryrISdQu5HaE8\/\/XR8TEl\/+umneJXKCxkLi0X41t\/x+OOPh+GGG64kyy2CMRcvvPBCMhLCI488Eoke8807Fsklf2XnervttosRTApR0O677x4uuuiitsc\/\/\/xzlFG56MRrhKqeWwuaQhnPPfdcX7SdwmSx8847x\/AkFZTJX3XVVWMJBI488siYv5W7Dj744PhcsDAmmmiiaH1T3HvvvVFoGF3w3sKylVdeOXz00UdxLA8efcwxx4wWu7+DxyOjN998Mxlpj8svvzzOaUrskNWOO+4YHn744fhYalAkl\/yVjTKWWmqpsPXWWyePQvS4G2ywQVv+R44U1tooV2Y59NBDw3TTTRe+\/vrrZKRraAplvOqqq8Kggw7azvOloByLLLJI2GqrreJjFvDwww+vKQdAQAw11FBt+aEFsO2224YPP\/wwPk5hMQhrS0HYLHxuBhLnnnvuidHLq6++moy0h\/mbddZZY0ThuvDCC+Pc\/fXXX8kzqocUQAoBDPVOO+3UQenk+htuuGHZdAUDPNtss9VM4jSFMgpxhh122FhQz8MEEjLv99lnn4V99903etJahCw3JeiXX345PPbYY9H65sMvIc3II48crXEpPPDAA2HooYduIy36Myghw3P33XcnI\/+BIiDYRCvIsJNOOikqSS1hIa832GCDxVzxrbfeisru7yyEqfPPP3\/kAMpBvrjEEkuUTDcqRVMoo7BzggkmCGeccUYy8h9++eWXMO+888ayR9oMUIsiwiuvvBIGGWSQmEfsuuuuhVS9sHXGGWcsy9YikqaaaqrwzTffJCP9F+SAMMuG+ynMkciFslLICy64oOaGCBERgznTTDOFjTbaKObyeVm8\/\/77cV3oiCoFa8t9I5RqRVMoI+y1115hscUWKww33nnnneg1u6NWBCwk4cr5SiX+LHs2X8nDYkEuHHjggWUVtj\/h+OOPD3PPPXdc4Hmk7XFffPFFt80Hoyl6KeVhpTdLLrlk+O2335KRjsC+TzjhhOG1115LRrqOplFG3gVjeumllyYjfQvWFDUPPLEcKLsIWf9ZZpmlatq+kcEYilKEofVggJA3Bx10UPLo35JIlgASMjPwWuO6436bRhmBpxKWnH\/++W2sZl8AjS9EooxySvnq6quvHv8n\/DrvvPPCQgstFC13swHJJbznJct5pJ6G0HSSSSYJp5xySpQXY4lbYDgpHqWU1ihflSt7VIMuKaObwT7VWlfpC7hnuVg1XRbdDUqG0MleSh1CaPVNC6AoVGsWUEKRASPVV0Cs5WXEmINQWTmsu+u\/XVJGIZ8WoO5IWltooYV\/0SVlxDjqlpD8ttBCC92DLimjOHm11VZLHvUuNBJjGVtX55d6aSPg2WefLbz\/RrzSrq2uICqjHFDdSyeBRDWfkOrVUxqQ63iuQqi+wL6ALomVVlqpdVVwXXLJJcms\/QuyQ8FLL4499tiY+2ShY4icb7nllmSkd6Cpoej+G\/HKs9\/m3KkASlRa9vJcgIYCc+45URkxVzpPFFS1JNn7l4XdBwOeFmtx3twbl2sPAv2WknDWudLr9ddfT17dQk9AW53IYpdddolNCWkjfAo0\/sADDxyZzFKQohTJrtR15ZVX9ikr2pegK5ybxg\/Mq5bMfGmNPOgWZxiVEZ2MslXA9A91kyxQzeOPP35bo7UP6QwEP\/jgg8f3q\/TKNla30P1AvJEhWl5Hkt7YbAsXC01m5Y6SsDWsSHalLtuiinqCmwV2iiijcWTmQ2SXxTrrrBOGGWaYOEcD\/j\/gGQm0bXmY3YRLgASnANqZN8zCc7U4VXPV2obWQmXQlznDDDPEWma2rUwENO2005Y1tlKYItmVurx\/Jca7v0OkaO\/lxhtvnIz822U1+eSThzXXXDPqSztlVOhUjN50002TkRCuv\/76MMYYY9RtAdqXsAG1t2qePAkr1l2F3kqgM8VVtKgtdvdTjaH0HeaYY452Ow0QD0MOOWTcqlQPSOVaj\/VW813tetPOZwuX9roUNpzTt3TTeztllNCPO+648SgDYNkwRPvvv39VwgY3q0iqI77Sq9reUPfLi9vikt+e1N2gCHJaEYKcqzebtwlLznH00UdHmWQhmmE87ZWspnXOMSS8o+\/hu\/lO9u11JmcGu0h2pS7F82ojHgvXmvOdy+1q6QuYKz2rNjUzXJUaZfNsvs07MIj2s26zzTZtqUI7ZWSJhCmU0Yfa5bD44ot3aeH1dM4oFmfddaxUayi6AnmUXlHkVpGH6mkgQZwD4xjHPCFCmNhR23jMSyVQmkqV0RYzG3cpT2fo6ZyRh8ZR6E+t57TFfTq5wcbiVJnKgYeniKkyXnbZZbEpPmtAB8zXgBlLoPFV\/x1lZI2FMdljDqoB6+a4C\/2XlV6VejfKJ\/G107s3FMNEKuf0ZQsdyDF4r\/SgqywsXGfFyEkqsdaeRxntI5xrrrkixV7JXDJKRbIrdQnFKu0DJlfs4pZbblmzIsrRNHHrK+0pIMJsg8tXH4ognZCjU0bHqTDs6SkFKQqV0VmQTjLLb7asFzAUzkPJ7xMkTPVPi9JJXx6zWsIKe9bsJu8K0NFILPNTC\/Q3ormx1anC3HbbbXEBXnPNNfFxZ3Cwr1Si6MhJjN0444wTP6czUEZbf+QwrHs9eCEe2p7FPD9BjjYd23KWRk+iAw3\/m2yySVvOlYVTEixtp8AVgYHVoyzFSR0O5VLi09RS6REa++23X4wes0RYEVJl1EYq9bv44os7GL92yugLsiYSec3K9RommDChTD5cY6E0FwvBGBUTLhwQbquhEly1sBBWWWWVdixYV6CpWB60xRZbRCVQYhA5yAN5AuFfJZBXDz\/88IWGkrzsSvE5ncEcEr05qReSxHEnc845Z4f7IUNHbDjkS2oCapiUkSIwcHmUU0YGWo58xRVXxFRKxEMeFMt7MmjpwWGdgVxHHXXUTglOiufUOacLqOcWRQvtlNHCY2UUICsNLfoCKHjJvfvNghAtSISG\/MkEIJI8z7EKXdnLSHBTTDFFh9prtUC8mFOCEKp47H7dm\/e2ECsBjzr99NO322eXhXlhPDrLY3Ti6LRJa8f1ABQ\/o5l3Akoxvg\/CQ4QD5o58HcfBqOVRThm9TpQjX+Z4vN5nWis2mls7lea5SMqxxx67pAfOwuZoTROlmNh2ytgoUJtJD5DKw2IVDmAXU2BdCdIkUIgRRhih04vlBO\/3v\/\/9L0YKeVjMRa\/NXjbLZoGFS+tKQCl5xUqFb1HKG4W2RRCiU\/bOwqZ6hPzL6WxFoDzSp+y5sxQHv5EyzFKXdN5tZLC0nSGUlUf2dIX0bCTvkyI9M7dSYJeFntW8phQaUhkRD0K7ImC5bAoVboBQ1gI18V0B5dUhIQetFe6FIUnPeWGN\/Z3vBWW5KV3e84Nx+TxPXwSlF8YoH8I3AhBJ2OIiOI9GeJ4eDsVbWgOljrvoLGcEbX8UOI0ChaZ+jyU\/d+SU99YpsNfWmw3htaIhlZFnEYoVTRAhsIASfrQxxlXDtAXeFfgMFtuZNbXC\/WgrRCjJ\/Q455JAODC0SIW3kZkTyPwdgoTgkqdReUnS7+Sm1eOoZQlBH7helSEgWctVQjXXn4Zy1WgqVKKNcUw7KwJlnIX728CnRhdxUXq+eTSZ5yBUpdHf8qllDKqNJcWpaUewthpdQ66BPGdQiD1MpKLGQUB9nrVDuwcoiIpRmdDflIfxGVvhcCyRPf6PsNfMXMcPyKIp6wgknJCONBaGeH74pYortnRVyIud4T9xGOQNbiTJqlB9ttNEiqUYxyScLhCDjwAAKk4vOuGUQtLmlpwDUgoZURsVpk1hUQ2JVhX1KBl1pViiCBnotgbxWLbB4CFh5olS3jEOPUN8o\/KKOJOGyML0oDBUNUPaioyEbAbptkCH5aAB8XwyyZpJKOrXSs3TKbfUTYtpVITwtiiS8h99HccRG0Zwy8shCHpV3rRUNqYxgG5caWW8QFRQcsSA06o5JLwWfY1EgFNS\/5C9Zr+6QZZ6vaL8hy40FFL7WEgn0NZSmlNdqrenWCnNIHhSfx5566qk7tCIy0sa72hiTR8Mqo4lBYrBKtf7GQSXgydDuthnl62DdBfmj8ovP0mUjZE0Vi4IKmbCJeWXDFiMzGAvERiODccVkK1nkNz\/3JnhLspZDOolA+JwqowhH+iCC0axRLlyuBg2rjKDsIO+yaHsjNGOtsWbyi2r6LSuFRnQ\/ckMh1b5S7+CYf4rmWMe8IspV\/E\/oWxS6NiLSVEMuV0m\/bE9AiiNl0HBAJumPE1E88tGlQ17dpYjQ0MqYolQZoKfg87pTCJ1B6FqKHfW9ezJ07kv0tlwrRU\/dV1TGFlpooR4w0ED\/B1uyMsLYCitCAAAAAElFTkSuQmCC\" alt=\"\" width=\"227\" height=\"42\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0 \u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"103\" height=\"29\" \/><\/p>\n<ol style=\"margin: 0pt; padding-left: 0pt;\" start=\"8\" type=\"1\">\n<li style=\"margin-left: 21.5pt; line-height: 115%; padding-left: 1pt; font-family: 'Times New Roman'; font-size: 16pt;\">\u00a0<strong>If the source and listener are both in motion in the same direction and with same velocity<\/strong>, then <img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"108\" height=\"29\" \/>\u00a0\u00a0 (say).<\/li>\n<\/ol>\n<p style=\"margin-top: 0pt; margin-left: 22.5pt; margin-bottom: 0pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">From (5),<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"63\" height=\"43\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-left: 22.5pt; margin-bottom: 0pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">or<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"58\" height=\"29\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-left: 22.5pt; margin-bottom: 0pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">It means, there is no change in the frequency of sound heard by the listener\u00a0<\/span><\/p>\n<ol style=\"margin: 0pt; padding-left: 0pt;\" start=\"9\" type=\"1\">\n<li style=\"margin-left: 21.64pt; margin-bottom: 10pt; line-height: 115%; padding-left: 0.86pt; font-family: 'Cambria Math'; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><strong><span style=\"font-family: 'Times New Roman';\">If the source and listener move at right. angles to the direction of wave propagation<\/span><\/strong><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><\/li>\n<\/ol>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0 \u00a0 \u00a0 The velocity of source and listener in direction of wave propagation<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0=<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"20\" height=\"27\" \/><span style=\"font-family: 'Times New Roman';\">\u00a0cos 90 =0 and\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"127\" height=\"27\" \/><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0 \u00a0 \u00a0 \u00a0From (5),<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"73\" height=\"42\" \/><span style=\"font-family: 'Times New Roman';\">or<\/span><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\" width=\"53\" height=\"29\" \/><span style=\"font-family: 'Times New Roman';\">.\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">It means there is no change in the frequency of sound heard if there is a small displacement of the source and listener at right angle to the direction of wave propagation.<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><strong><u><span style=\"font-family: 'Times New Roman';\">42 APPLICATIONS OF DOPPLER&#8217;S EFFECT<\/span><\/u><\/strong><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">The change in frequency caused by a moving source\/observer t\/listener is called Doppler shift. The measurement of Doppler shift has been used.\u00a0<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">(1) By police to check over speeding of vehicles,<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">(2) At airports to guide the aircraft,<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">(3) In the military to detect enemy aircrafts,<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><span style=\"font-family: 'Times New Roman';\">(4) By astrophysicists to measure the velocities of planets and stars,<\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 10pt; line-height: 115%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><span style=\"font-family: 'Times New Roman';\">(5) To study heart beats and blood flow in different parts of the<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><strong><u><span style=\"font-family: 'Times New Roman';\">43 Characteristics of Musical Sounds:<\/span><\/u><\/strong><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><strong><u><span style=\"font-family: 'Times New Roman';\">Music:<\/span><\/u><\/strong><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><em><span style=\"font-family: 'Times New Roman';\">The sound which has a pleasing sensation to the ears is called music.<\/span><\/em><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">e.g: The sound produced by sitar, violin and table are music.<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><strong><u><span style=\"font-family: 'Times New Roman';\">Noise:<\/span><\/u><\/strong><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><em><span style=\"font-family: 'Times New Roman';\">The sound which has none pleasing or jarring effect on ears is called noise<\/span><\/em><span style=\"font-family: 'Times New Roman';\">.<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">e.g: The sound produced by explosion, from market etc.<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><strong><u><span style=\"font-family: 'Times New Roman';\">44 Characteristics:<\/span><\/u><\/strong><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0<\/span><span style=\"font-family: 'Times New Roman';\">There are three characteristics of musical sounds<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; text-indent: 36pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">(i) Loudness<\/span><span style=\"width: 27.57pt; text-indent: 0pt; font-family: 'Times New Roman'; display: inline-block;\">\u00a0<\/span><span style=\"font-family: 'Times New Roman';\">(ii) Pitch<\/span><span style=\"width: 15.56pt; text-indent: 0pt; font-family: 'Times New Roman'; display: inline-block;\">\u00a0<\/span><span style=\"font-family: 'Times New Roman';\">(iii) Quality or Timbre<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><strong><em><span style=\"font-family: 'Times New Roman';\">(i)<\/span><\/em><\/strong><strong><em><span style=\"width: 20.9pt; font-family: 'Times New Roman'; display: inline-block;\">\u00a0<\/span><\/em><\/strong><strong><u><span style=\"font-family: 'Times New Roman';\">Loudness:<\/span><\/u><\/strong><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">The amount of energy crossing per unit area around a point in one second is called loudness.<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><strong><em><span style=\"font-family: 'Times New Roman';\">(ii)<\/span><\/em><\/strong><strong><em><span style=\"width: 16.45pt; font-family: 'Times New Roman'; display: inline-block;\">\u00a0<\/span><\/em><\/strong><strong><u><span style=\"font-family: 'Times New Roman';\">Pitch:<\/span><\/u><\/strong><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">It is a sensation which helps a listener to distinguish between a high and a grave note. It depends on frequency. The pitch of a lady\u2019s sound is higher than that of a man.<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><strong><em><span style=\"font-family: 'Times New Roman';\">(iii)<\/span><\/em><\/strong><strong><em><span style=\"width: 12.01pt; font-family: 'Times New Roman'; display: inline-block;\">\u00a0<\/span><\/em><\/strong><strong><u><span style=\"font-family: 'Times New Roman';\">Quality or Timbre:<\/span><\/u><\/strong><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">Quality of sound helps us to distinguish between two sounds of same pitch and loudness. It is due to quality due to which we can recognize one\u2019s friend without seeing him.<\/span><\/p>\n<p style=\"margin-top: 5pt; margin-bottom: 5pt; line-height: 150%; font-size: 16pt;\"><span style=\"font-family: 'Times New Roman';\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n<div style=\"clear: both;\">\n<p style=\"margin-top: 0pt; margin-bottom: 0pt; text-align: right; line-height: normal;\"><span style=\"height: 0pt; text-align: left; display: block; position: absolute; z-index: -65537;\"><img loading=\"lazy\" decoding=\"async\" style=\"margin: 0 0 0 auto; display: block;\" 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alt=\"\" width=\"287\" height=\"422\" \/><\/span><\/p>\n<p style=\"margin-top: 0pt; margin-bottom: 0pt; line-height: normal;\"><strong><em>\u00a0<\/em><\/strong><\/p>\n<\/div>\n<p style=\"bottom: 10px; right: 10px; position: absolute;\">\n","protected":false},"excerpt":{"rendered":"<p>Chapter 15\u00a0 Wave motion\u00a0 Transverse and longitudinal waves, speed of wave motion, displacement relation for a progressive wave, principle of superposition of waves, reflection of waves, standing waves in strings and organ pipes, fundamental mode and harmonics, Beats, Doppler effect. Unit-10(B): Waves 21 Waves Motion: It is a disturbance which travels through a medium due [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_uag_custom_page_level_css":"","site-sidebar-layout":"default","site-content-layout":"default","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"set","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"class_list":["post-2290","page","type-page","status-publish","hentry"],"aioseo_notices":[],"_hostinger_reach_plugin_has_subscription_block":false,"_hostinger_reach_plugin_is_elementor":false,"uagb_featured_image_src":{"full":false,"thumbnail":false,"medium":false,"medium_large":false,"large":false,"1536x1536":false,"2048x2048":false},"uagb_author_info":{"display_name":"sandeep.soni484@gmail.com","author_link":"https:\/\/vartmaaninstitutesirsa.com\/index.php\/author\/sandeep-soni484gmail-com\/"},"uagb_comment_info":0,"uagb_excerpt":"Chapter 15\u00a0 Wave motion\u00a0 Transverse and longitudinal waves, speed of wave motion, displacement relation for a progressive wave, principle of superposition of waves, reflection of waves, standing waves in strings and organ pipes, fundamental mode and harmonics, Beats, Doppler effect. 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