Standing waves in a drum membrane are complicated and satisfactory analysis requires knowledge of Bessel functions. In contrast to standing waves in one dimensional media such as waves in a string, sound waves in a pipe, etc., the resonance frequencies of membrane standing waves are not integer multiples of the lowest order mode. Consider a circular membrane of radiusStanding Waves in a Drum Membrane

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`> `**with(plots):**
**animate3d([r,theta,BesselJ(0,2.40483*r)*sin(2*Pi*t)],r=0..1,theta=0..2*Pi,t=0..0.95,frames=20,coords=cylindrical);**

`> `**with(plots):**
**animate3d([r,theta,.5*BesselJ(0,5.52008*r)*sin(2*Pi*t)],r=0..1,theta=0..2*Pi,t=0..0.95,frames=20,coords=cylindrical);**

`> `**with(plots):**
**animate3d([r,theta,BesselJ(1,3.8317*r)*sin(theta)*sin(2*Pi*t)],r=0..1,theta=0..2*Pi,t=0..0.95,frames=20,coords=cylindrical);**

`> `**with(plots):**
**plot(BesselJ(0,x),x=0..10,color=red);**

`> `**plot(BesselJ(1,x),x=0..10,color=blue);**

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