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sharklasers45
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Homework Statement
Is it possible to find a solution to the wave equation on a circular membrane such that the shape remains constant, but rotates at a fixed rate in the angular direction?
Homework Equations
The Attempt at a Solution
I've tried separating variables, and assuming the solution only depends on theta, but the time dependence is oscillatory (which comes out of the normal separation of variables process), so this doesn't represent rotation in time.
And by writing the wave equation in polar coordinates, I can't get rid of the r dependence even if I assume the d/dr derivatives are 0 because of the 1/r^2 multiplying the theta derivative...