Drums and wave equation, a clarification of an assertion

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I have read somewhere something that sounds like that:

'Given the shape of a drum , thanks to well-known formulas, we can deduce all its vibration frequencies and so the sound that it is capable to produce'

My question is this:

since there are almost no regions of the plane for which we can solve explicitly the wave equation ( then I obtain an eigenvalue problem), is this assertion true or expressed correctly? Is this the meaning of this phrase?

Thanks a lot!!