2D Fourier Series Normal modes
of a Rectangular Membrane.
Waves on a rectangular membrane can be described by the wave
equation written with rectangular coordinates in 2 dimensions as
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
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COPYRIGHT © 2007 Cuthbert A. Nyack.