PHYS 221 General Physics II - Calculus Supplement Grist Homework Solution “Waves” A)In order to show that xctySin CosLLπ=is a solution of the wave equation221yy2xct∂∂=we first take the second partial derivative of ywith respect to x: 222 2xctSinCosyxLLSinCosctxxLLππL⎛⎞∂⎜⎟∂⎝⎠==−We next take the second partial derivative of ywith respect to t: 222tSinCosycSinCosttLLxctL∂∂−Now we substitute these solutions into the wave equation and see if it is satisfied: 221xctcxctSinCosSinCosLLLcLLL−=−The 21cand term cancel, so yes, 2cxctiosLL=is a solution of the wave equation12x=! B)At x=0 we get 220100ctcctSinCos
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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.