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Unformatted text preview: ASSIGNMENT 3 Physics 218 Due Fri Sep 17 Fall 2004 Labs start next week. The string lab is in Rock 26 and the sound lab is in Rock 30. To simplify comparing your solutions with others, use ( x, t ) = A sin( kx t ) for the displacement of a traveling sinusoidal sound wave, and use P m for the pressure amplitude and R m for the density amplitude the amplitudes multiplying cos( kx t ) or sin( kx t ) as appropriate. (The subscript m is for maximum.) For air at STP, use = 1 . 29 kg/m 3 , p = 1 . 01 10 5 N/m 2 , and = 1 . 4. 1. Derive the following relationships for traveling sinusoidal sound waves in a gas: (a) The pressure amplitude P m in terms of the displacement amplitude A . (b) The density amplitude R m in terms of the displacement amplitude A . (c) The maximum value of the density (per unit volume) of kinetic energy of a sound wave ( dK/dV ) in terms of the displacement amplitude A . (d) The maximum density (per unit volume) of the potential energy of a sound wave ( dU/dV ) in terms of the displacement amplitude A . (e) The maximum intensity of a sound wave I m in terms of the displacement amplitude of the sound wave A . 2. (a) First calculate the speed of sound c in air at STP....
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