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The solutions of the wave equation for a circular drum with fixed boundary are well known. What do the solutions look like for a spherical drum in three spatial dimensions? What about higher dimensions?

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You're asking about eigenfunctions of the Laplacian on a sphere. The keyword "spherical harmonic" will be useful in your search. – Aaron Hoffman Oct 4 '11 at 16:16
The 3d "drum" is a ball and is fixed on the boundary (sphere). So solutions will be time dependent functions on the 3d ball which are constantly 0 on the spherical boundary. – antianticamper Oct 4 '11 at 16:43
Sorry. I meant (Dirichlet) eigenfunctions of the Laplacian on the ball. Take e.g. section 10.3 in Strauss. – Aaron Hoffman Oct 4 '11 at 17:50

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