Chladni's law

Chladni's law, named after Ernst Chladni, relates the frequency of modes of vibration for flat circular surfaces with fixed center as a function of the numbers m of diametric (linear) nodes and n of radial (circular) nodes. It is stated as the equation

f=C(m+2n)^{p}

where C and p are coefficients which depend on the properties of the plate.^[1]

For flat circular plates, p is roughly 2, but Chladni's law can also be used to describe the vibrations of cymbals, handbells, and church bells in which case p can vary from 1.4 to 2.4.^[2] In fact, p can even vary for a single object, depending on which family of modes is being examined.

[1]
Rossing, Thomas D.; Fletcher, Neville H. (2004), Principles of Vibration and Sound, Springer, pp. 73–74, ISBN 9780387405568.
[2]
Fletcher, Neville Horner; Rossing, Thomas D. (1998), The Physics of Musical Instruments, Springer, p. 680, ISBN 9780387983745.

A Study of Vibrating Plates by Derek Kverno and Jim Nolen (Archived 27 July 2011)

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[1] [1]
Rossing, Thomas D.; Fletcher, Neville H. (2004), Principles of Vibration and Sound, Springer, pp. 73–74, ISBN 9780387405568.

[2] [2]
Fletcher, Neville Horner; Rossing, Thomas D. (1998), The Physics of Musical Instruments, Springer, p. 680, ISBN 9780387983745.

[1]

[2]

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Chladni's law

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