Chladni's law, named after

Ernst Chladni Ernst Florens Friedrich Chladni (, , ; 30 November 1756 – 3 April 1827) was a German physicist and musician. His most important work, for which he is sometimes labeled the father of acoustics, included research on vibrating plates and th ...

, relates the

frequency Frequency is the number of occurrences of a repeating event per unit of time. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio ...

modes of vibration A normal mode of a dynamical system is a pattern of motion in which all parts of the system move sinusoidally with the same frequency and with a fixed phase relation. The free motion described by the normal modes takes place at fixed frequencies. ...

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 In mathematics, a coefficient is a multiplicative factor involved in some term of a polynomial, a series, or any other type of expression. It may be a number without units, in which case it is known as a numerical factor. It may also be a ...

which depend on the properties of the plate. Chladni plate 10

For flat circular plates, ''p'' is roughly 2, but Chladni's law can also be used to describe the vibrations of

cymbal A cymbal is a common percussion instrument. Often used in pairs, cymbals consist of thin, normally round plates of various alloys. The majority of cymbals are of indefinite pitch, although small disc-shaped cymbals based on ancient designs sou ...

handbells A handbell is a bell designed to be rung by hand. To ring a handbell, a ringer grasps the bell by its slightly flexible handle – traditionally made of leather, but often now made of plastic – and moves the arm to make the hinged cla ...

, and

church bells A church bell is a bell in a church building designed to be heard outside the building. It can be a single bell, or part of a set of bells. Their main function is to call worshippers to the church for a service of worship, but are also rung o ...

in which case ''p'' can vary from 1.4 to 2.4.. In fact, ''p'' can even vary for a single object, depending on which family of modes is being examined.

References

External links

A Study of Vibrating Plates
by Derek Kverno and Jim Nolen (Archived 27 July 2011) Waves Quantum mechanics {{applied-math-stub