WOLFRAM|DEMONSTRATIONS PROJECT

Normal Modes of a Circular Drum Head

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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.