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    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.