2D Fourier Series Normal modes of a Rectangular Membrane.

Cuthbert Nyack
Waves on a rectangular membrane can be described by the wave equation written with rectangular coordinates in 2 dimensions as shown below.
Solutions which satisfy the boundary conditions (displacement = 0 at the edges) are given below
where k is given by the following relation and c is the wave velocity on the membrane. The time dependence can be a cos or a sin cos is used here to give maximum displacement at t = 0.0.
The applet below show the vibrational modes as a function of n and m. These are called normal modes.

When activated, the following gif image show how the applet should appear.

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COPYRIGHT © 2007 Cuthbert A. Nyack.