Question

27. A drumhead is a circular membrane of radius a. When it is struck, waves propagate across the drumhead. The membrane vibrates with displacement 5, where $(1,0,1) = n(r, e)e-lw and n(t,0) satisfies the Helmholtz equation 1 an 1 a rar an ar 1+2 20² +k?n=0 where k= w2/02 and v is the speed with which waves propagate across the drumhead. (The speed v depends on the tension in the drumhead, among other things.) The bound- ary condition is that n=0 at r = a. Separate variables, and find the eigenfunctions. Determine the first three allowable frequencies w in terms of the drum parameters v and a.

Answer 1

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