Assignment_4_08 - TA's Name Section Your Name Physics 214...

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TA's Name:____________________ Section: ____ Your Name: _________________________________ Physics 214 Assignment 4 Concepts: Derivation of the wave equation Standing waves Waves on strings Standing waves on strings Sound waves Standing sound waves in pipes Reading: AG Notes on Mechanical Waves (from website); Y&F, Vol. 1, Chapter 16 Assignment: Due in lecture on Tuesday, February 19. Please turn in this sheet stapled to the top of your work. Physics Problems: 1. Sound waves in a thin solid rod travel at a speed determined by Young’s modulus (the squishiness along the direction of the rod) rather than the bulk modulus. (Can you think why this might be?) Consider a sound wave traveling along the length of a thin solid rod of cross-sectional area A, Young’s modulus Y, and mass density (per unit volume) ρ 0 . Let x and x + x be the equilibrium positions of the ends of a short segment of the rod; s(x,t) and s(x + x, t) are the displacements of the ends of the short segment from their equilibrium positions. (a) What is the change in length of the segment when the ends are displaced? (b) Find the (tensile or compressive) force that must be applied to each end to produce this length change, using the definition of Young’s modulus: F/A = Y L/L 0 (c) Take the limit x 0 to obtain a relationship between F(x,t) and s(x,t). (d) Write an expression for the net force on a segment of equilibrium length x. Then apply Newton’s second law and take the limit x 0 to derive the wave equation and to
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This note was uploaded on 03/31/2009 for the course PHYS 214 taught by Professor Thorne during the Spring '08 term at Cornell.

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Assignment_4_08 - TA's Name Section Your Name Physics 214...

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