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Is there software that, when the input is the shape of a drum, will produce the corresponding audible sound?

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  • $\begingroup$ I assume you are familiar with the various research on the topic starting with Kac's paper "Can One Hear the Shape of a Drum?" $\endgroup$
    – quarague
    Commented Jul 16 at 10:17

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The full physics problem is complex, the vibrating membrane displaces the air, which causes a backreaction and signifantly modifies the response. Moreover, the response also depends sensitively on where the membrane is hit. Professional simulators take all of this into account, see for example the COMSOL description.

For a simpler procedure you could just use a numerical Laplace equation solver and pass the frequencies to an audio generator. A worked example using Mathematica is here: NDEigenvalues gives you the resonant frequencies of a user-defined shape of the membrane, AudioGenerator then converts these into sound.

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    $\begingroup$ From a non-math standpoint, if you are just trying to make the sound of drums, you can look into so-called "physical modeling" software from the music world. madronalabs.com/products/kaivo : "Kaivo brings some of the latest academic research in physical modeling to a patchable package for the first time. Mathematically speaking, its finite difference time domain (FDTD) models let the player reach inside the instrument and affect the internal vibrations at any point. This allows for a fine degree of realistic detail, like the bridge rattles on a 'gut string' model, for example." $\endgroup$
    – sfscs
    Commented Jul 16 at 6:38
  • $\begingroup$ interesting, but it seems you cannot choose the shape of the drum with that software. $\endgroup$
    – Carlo Beenakker
    Commented Jul 16 at 8:33

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