WOLFRAM|DEMONSTRATIONS PROJECT

Normal Modes of a Circular Drum Head

show mesh

order n

0

1

2

3

4

5

th

k

zero

1

2

3

4

time

This Demonstration illustrates the normal vibrational modes of a drum head fixed along a circular edge. Each mode with elongation (in polar coordinates)

ψ(t;r,φ)∼cos

ω

n,k

tcos(nφ)

J

n



j

j,k

r

is related to Bessel functions of the first kind,

J

n



j

j,k

r

, where

r

is the radial coordinate,

φ

the polar angle, and

t

the time. Selecting the order,

n

, determines the angular periodicity of the drum head. Selecting the

th

k

zero

j

j,k

of

J

n

(x)

determines the number of antinodes along a radial line connecting the center and outer edge.