Wave Equation—Triangle

Author

Eric W. Weisstein
April 30, 2004

This notebook downloaded from http://mathworld.wolfram.com/notebooks/DifferentialEquations/WaveEquationTriangle.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/WaveEquationTriangle.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Square Membrane

MakeBoxes[label[m_,n_],TraditionalForm]:=SubscriptBox["ψ",RowBox[{MakeBoxes[m,TraditionalForm]," ",MakeBoxes[n,TraditionalForm]}]]

Show[GraphicsArray[Block[{$DisplayFunction=Identity},Table[
Plot3D[If[y<x,0,Sin[m Pi x]Sin[n Pi y]-Sin[n Pi x]Sin[m Pi y]],{x,0,1},{y,0,1},PlotRange->All,
PlotLabel->TraditionalForm[label[m,n]],
Mesh->False,PlotPoints->75,Boxed->False,Axes->False],{m,2,4},{n,m-1}]
]],GraphicsSpacing->{-.1,.05}]

Simplify[Table[Sin[m Pi x]Sin[n Pi y]-Sin[n Pi x]Sin[m Pi y],{m,2,4},{n,m-1}],x==y]