Pure tone modes for an elliptic 5:3 drum

This paper shows how to draw the Chladni figures and contour plots for the mode shapes of a vibrating elliptical drum. A Chladni figure is named for a German physicist who found that sprinkling sand on a metal plate held fixed at the center and then vibrating the plate using a violinist's bow would produce patterns shown by the sand collecting on the lines where the plate was relatively motionless. This paper uses Mathieu functions to model what would happen if the plate were elliptical and held fixed at the edges.