The problem of hearing the shape of a drum is well known as a mathematical problem.
But what about as a problem of (1) physics and (2) human perception?
Suppose you have the kind of membrane used with a kettle drum but without the kettle. One musician tries to adjust the pitch and loudness, etc., so that the square one and the circular one sound as similar as possible; an opposing musician is allowed to hear but not to see, and tries to identify the round one and the square one by the sound. And so on with other shapes.
And if unaided human perception doesn't work, how much analysis can be done with electronic gadgets?
Later note: I find a comment below, saying this isn't actually a mathematical question. As I pointed out below, an answer might bear upon the mathematics. A simple-minded stereotype says mathematics can shed light on the things it's applied to, but not vice-versa. But that is known to be an error.
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