vibrations of higher dimensional drums

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?

flag	asked Oct 4 2011 at 15:33 antianticamper 81●3

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 2011 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 2011 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 2011 at 17:50

Browse other questions tagged ap.analysis-of-pdes or ask your own question.

question feed