Vibrations of a Rectangular Membrane

Manipulate[Plot3D[B[1,1] Cos[(Sqrt[(1/(a^2))+(1/(b^2))]) c π t] Sin[((π x)/a)] Sin[((π y)/b)]+B[2,1] Cos[(Sqrt[(4/(a^2))+(1/(b^2))]) c π t] Sin[((2 π x)/a)] Sin[((π y)/b)]+B[1,2] Cos[(Sqrt[(1/(a^2))+(4/(b^2))]) c π t] Sin[((π x)/a)] Sin[((2 π y)/b)]+B[2,2] Cos[(Sqrt[(4/(a^2))+(4/(b^2))]) c π t] Sin[((2 π x)/a)] Sin[((2 π y)/b)],{x,0,a},{y,-b,b},ColorFunction->Function[{x,y,z},Hue[z/(Abs[B[1,1]]+Abs[B[2,1]]+Abs[B[1,2]]+Abs[B[2,2]])]],ColorFunctionScaling->False,PlotRange->{{0,a},{-b,b},{-(Abs[B[1,1]]+Abs[B[2,1]]+Abs[B[1,2]]+Abs[B[2,2]])+zrange,Abs[B[1,1]]+Abs[B[2,1]]+Abs[B[1,2]]+Abs[B[2,2]]-zrange}},ClippingStyle->None,ImageSize->{390,350},BoxRatios->Automatic],
{{a,4,"length"},1,10,.01,Appearance->"Labeled",ImageSize->Tiny},
{{b,4,"width"},1,10,.01,Appearance->"Labeled",ImageSize->Tiny},
Delimiter,
"   mode",
{{B[1,1],0.5,"m=1, n=1"},-2,2,.01,Appearance->"Labeled",ImageSize->Tiny},
{{B[2,1],0,"m=2, n=1"},-2,2,.01,Appearance->"Labeled",ImageSize->Tiny},
{{B[1,2],0,"m=1, n=2"},-2,2,.01,Appearance->"Labeled",ImageSize->Tiny},
{{B[2,2],0,"m=2, n=2"},-2,2,.01,Appearance->"Labeled",ImageSize->Tiny},
Delimiter,
{{t,0,"time"},0,10,.01,Appearance->"Labeled",ImageSize->Tiny},{{c,1,"wave speed"},0,2,.01,Appearance->"Labeled",ImageSize->Tiny},
Delimiter,
{{zrange,0,"reduce box height"},0,2,0.1,Appearance->"Labeled",ImageSize->Tiny},
ControlPlacement->Left,AutorunSequencing->{1,2,3,5,7}]

THIS NOTEBOOK IS THE SOURCE CODE FROM

"Vibrations of a Rectangular Membrane" from The Wolfram Demonstrations Project
 http://demonstrations.wolfram.com/VibrationsOfARectangularMembrane/

Contributed by: Alain Goriely

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