Examples of Two Dimensional Nodal Patterns on a Square Chladni Plate

Examples of exquisite nodal patterns on a square Chladni plate at resonant frequencies between 932 Hz and 1459 Hz are displayed.

Discussion

A Chladni plate (named after Ernst Chladni, 1756-1827, a German physicist known as the father of acoustics) is simply a thin sheet or plate of wood, metal, or other stiff material that can be made to vibrate in one way or another. In these movies, square and round plates of metal are mounted on a wave driver. To begin an experiment, sand is sprinkled on the plate. When the frequency of the wave driver matches a resonant frequency of the metal plate, three things happen: the sound level rises dramatically from that at off-resonant frequencies (energy transfer to the plate is much greater at resonant frequencies), two dimensional standing waves are established, and sand particles dance away from regions where wave displacements are large to collect in nodal regions, where there is little or no movement of the plate. Sand-covered nodal curves enclose bare antinodal regions of the plate in patterns that become more complex and intricate as the driving frequency increases. Because a sheet of metal lacks the uniformity of, for example, a string or pool of water of constant depth, there is no simple relationship between driving frequency and the number of nodal regions, such as those we found for waves on strings or in ripple tanks, other than the increasing complexity observed with increasing frequency. This is reflected in the table below, which lists results for a set of successive resonant frequencies for a square Chladni plate.

In this movie, the driving frequency is increased from 932 Hz to 1459 Hz, and passes through three resonances (955 Hz, 1055 Hz and 1377 Hz) of the square plate. As a resonant frequency is reached, the sound level increases and a new nodal pattern forms.