Chladni's Law

Description

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 shown here.

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. In fact, p can even vary for a single object, depending on which family of modes is being examined.

Related formulas

Variables

ffrequency of modes of vibration for flat circular surfaces with fixed center (dimensionless)
Ccoefficient which depends on the properties of the plate (dimensionless)
mnumber of diametric (linear) nodes (dimensionless)
nnumbers of radial (circular) nodes (dimensionless)
pcoefficient which depends on the properties of the plate (dimensionless)