Vibrations of a Rectangular Membrane

​
length
4
width
4
mode
m=1, n=1
0.5
m=2, n=1
0
m=1, n=2
0
m=2, n=2
0
time
0
wave speed
1
reduce box height
0
The two-dimensional wave equation
∂
t,t
u=
2
c
(
∂
x,x
u+
∂
y,y
u)
provides a simple model of a vibrating rectangular membrane. You can see the evolution of an initial profile with no initial velocity for a rectangular membrane with no deflection at the boundaries. You can set the superposition of the first four Fourier modes as initial data and you can observe the membrane as time evolves.

External Links

Wave Equation—Rectangle (Wolfram MathWorld)

Permanent Citation

Alain Goriely
​
​"Vibrations of a Rectangular Membrane"​
​http://demonstrations.wolfram.com/VibrationsOfARectangularMembrane/​
​Wolfram Demonstrations Project​
​Published: December 13, 2007