Wave Equation--Triangle


The equation of motion for a membrane shaped as a right isosceles triangle of length c on a side and with the sides oriented along the positive x and y axes is given by




and p, q integers with p>q. This solution can be obtained by subtracting two wave solutions for a square membrane with the indices reversed. Since points on the diagonal which are equidistant from the center must have the same wave equation solution (by symmetry), this procedure gives a wavefunction which will vanish along the diagonal as long as p and q are both even or odd. We must further restrict the modes since those with p<q give wavefunctions which are just the negative of (q,p) and (p,p) give an identically zero wavefunction.

The plots above show the lowest order spatial modes.

See also

Wave Equation, Wave Equation--1-Dimensional, Wave Equation--Disk, Wave Equation--Rectangle

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Cite this as:

Weisstein, Eric W. "Wave Equation--Triangle." From MathWorld--A Wolfram Web Resource.

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