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Sound Waves

Consider the wave equation

when the solution s admits spherical symmetry, ie, s(t,x,y,z)=v(t,r), where ... , the wave equation becomes:


making the substitution

for some twice differentiable function h, show that (1) becomes

hence, show that the general solution reads

for any twice differentiable functions f and g.

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Solution Preview

look at partial v(r,t) with r yields -1/r^2 [f(r-ct) +g(r+ct)] +1/r[fr(r-ct) +gr(r+ct)]

Then multiply this by r^2 to get:

-1[f(r-ct) +g(r+ct)] +r[fr(r-ct) ...

Solution Summary

A wave equation is investigated.