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lalbatros
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I was interrested in the general solutions to the wave equation depending on only one spatial coordinate.
For one linear coordinate, the general solution is:
For one radial spherical coordinate, the general solution is:
I thought that for a radial cylindrical coordinate, the solution would be:
Yet I found this is not a solution since I got this residual for the wave equation:
This would indicate that the cylindrical solution applies only to the static case.
Any comment on this surprise?
Did I do a mistake in the calculations, of does that instead mean something?
Thanks.
For one linear coordinate, the general solution is:
a f(x-ct) + b g(x+ct)
For one radial spherical coordinate, the general solution is:
a f(r-ct)/r + b g(r+ct)/r
I thought that for a radial cylindrical coordinate, the solution would be:
a f(r-ct)*Log(r) + b g(r+ct)*Log(r)
Yet I found this is not a solution since I got this residual for the wave equation:
D²(f(r-ct)/r) = a (2+Log(r))*f'(r-ct)/r + b (2+Log(r))*g'(r+ct)/r
This would indicate that the cylindrical solution applies only to the static case.
Any comment on this surprise?
Did I do a mistake in the calculations, of does that instead mean something?
Thanks.
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