Phys 2214 Assignment 4 2011

# Phys 2214 Assignment 4 2011 - TA's Name:_ Section: _ Your...

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TA's Name:____________________ Section: ____ Your Name: _________________________________ Physics 214, Fall 2011 1 Cornell University Physics 2214 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: Y&F, Vol. 1, Chapter 16. Assignment: Due in second section meeting the week of September 26. 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) 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).

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## This note was uploaded on 01/02/2012 for the course PHYSICS 2214 at Cornell.

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Phys 2214 Assignment 4 2011 - TA's Name:_ Section: _ Your...

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