# Normal Modes of a Circular Drum Head

Normal Modes of a Circular Drum Head

This Demonstration illustrates the normal vibrational modes of a drum head fixed along a circular edge. Each mode with elongation (in polar coordinates) is related to Bessel functions of the first kind, r, where is the radial coordinate, the polar angle, and the time. Selecting the order, , determines the angular periodicity of the drum head. Selecting the zero of (x) determines the number of antinodes along a radial line connecting the center and outer edge.

ψ(t;r,φ)∼costcos(nφ)r

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