Modelling the sound of a drum head.

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Please excuse me if this is not the most appropriate subforum for this question and please move it if necessary.

I am trying to make a numerical model with Mathematica to synthesize the sound of a struck drum head (circular membrane).

I solve the wave equation for a circular membrane to get a numerical function for amplitude u(time,position) which depends on some striking function f. But now I don't know how to convert the information to obtain a 1-dimensional time series that can be listened to with the speakers. I feel I am missing something fundamental here.

In the case of a string, one can pick any point on it x0 , and then the function u(t,x0) can be sent straight to the speakers provided x0 is not on a node of the string. I am guessing this is kind of the same way a guitar pick up works (?) . However in the case I of the drum, isolating an arbitrary point on the surface does not feel it should be physically accurate representation of the sound.

Looking forward to hear your opinion,

Arthur

edit: here is a java application that can produce a drum head sound http://www.falstad.com/circosc/
 
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