Isospectral Drums

Application ID: 119

Striking a drum excites a spectrum of vibration modes that together make up the instrument’s characteristic sound or acoustic signal. These vibration modes correspond to the eigenmodes, or eigenfunctions, of the drum’s membrane. Thus you can study this problem by solving eigenvalue problems for stretched membranes.

Two different geometric shapes are modeled, with all other parameters being equal. If you can find two differently shaped membranes that have identical eigenvalues—in other words, they are isospectral—then it’s not possible to “hear” the shape of a specific drum.

This model example illustrates applications of this type that would nominally be built using the following products: