The Vibrating Ellipse-Shaped Drum

Volume 6, Issue 4
Fall 1996

The Laplace equation for an ellipse is solved by the method of separation of variables. The resulting one-dimensional differential equations are solved with Mathieu functions. The eigenvalues are calculated numerically and the various kinds of eigenmodes are visualized with 3D and contour plots. Some degenerate eigenmodes are explicitly calculated.