1. wavesoln - PHYS 221 General Physics II Calculus...

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PHYS 221 General Physics II - Calculus Supplement Grist Homework Solution “Waves” A) In order to show that x ct yS i n C o s L L π = is a solution of the wave equation 22 1 yy 2 x ct ∂∂ = we first take the second partial derivative of y with respect to x: 2 22 2 xc t Sin Cos yx LL Sin Cos c t x xL L ππ L ⎛⎞ ⎜⎟ ⎝⎠ == We next take the second partial derivative of y with respect to t: 2 2 2 t Sin Cos yc Sin Cos tt L L x c t L Now we substitute these solutions into the wave equation and see if it is satisfied: 2 2 1 x ct c x ct Sin Cos Sin Cos L LLc LLL −= The 2 1 c and term cancel, so yes, 2 c x ct i o s L L = is a solution of the wave equation 1 2 x = ! B) At x=0 we get 2 2 01 0 0 ct c ct Sin Cos
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This note was uploaded on 01/09/2010 for the course PHYS 221 taught by Professor G.r.grist during the Spring '09 term at Skyline College.

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