ps05 - Physics 2214 Problem Set #5 (Due 11:15 am, Thursday...

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Page 1 of 3 Physics 2214 Problem Set #5 (Due 11:15 am, Thursday 10/2/08) 1. Use the chain rule to show that the wave equation, 22 2 (,) yxt tx ∂∂ = v can be rewritten as 2 0 yu u uu +− = where uxt + ≡+ v and ≡− v . 2. At t = 0, the wave pulses shown below are moving away from one another. The wave speed is 10 m/s. The right end ( x = 25 m) is free (massless slip-ring boundary condition) and the left end ( x = 0) is fixed. 0 1 2 3 4 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 x (m) Free End Fixed End y (cm) [Note: it isn’t physically possible to have discontinuities in slope. In reality, the kinks shown would have to be somewhat rounded.] (a) Use the principle of superposition along with the boundary conditions to draw the left end of the string (0 x 4 m) at t = 0.6 s. (b) Draw the right end of the string (21 m x 25 m) at t = 0.95 s. 3. Reflection and transmission of sound waves from a boundary between two media. A sound tube of area A is filled with two different fluids on either side of an infinitesimally thin, massless membrane at x = 0. The membrane can slide back and forth without friction.
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This note was uploaded on 12/24/2008 for the course PHYS 2214 taught by Professor Giambattista,a during the Fall '07 term at Cornell.

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ps05 - Physics 2214 Problem Set #5 (Due 11:15 am, Thursday...

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