Chladni figures – sound that draws forms
Scatter sand on a vibrating plate and it gathers into symmetrical patterns. In 1787 Ernst Chladni made sound visible, and the patterns follow whole numbers.
In 1787 the physicist and musician Ernst Florens Friedrich Chladni published a book in Leipzig titled Entdeckungen über die Theorie des Klanges (“Discoveries on the theory of sound”). He had clamped a thin metal plate at its centre, scattered sand on it and stroked its edge with a violin bow. The plate began to ring, and the sand jumped away from the vibrating parts and gathered on the lines that stayed at rest. Depending on the tone, different, often astonishingly regular figures appeared.
Nodal lines
A vibrating plate does not move the same everywhere. It divides into fields that swing up and down in turn, and between them lie nodal lines on which it rests. For a square plate the vibration shapes can be described approximately by two whole numbers n and m, which count how often the wave repeats in each direction. The higher the numbers, the higher the tone and the finer the pattern.
Chladni figures of a square plate in the classical approximation. The sliders choose the two whole numbers n and m. The sand gathers on the nodal lines where the plate is at rest.
The figures were a sensation. Chladni demonstrated them at the courts of Europe, including before Napoleon, who in 1809 offered a prize for their mathematical explanation. It was won in 1816 by the mathematician Sophie Germain, with a theory of elastic plates that remains the foundation to this day.
From Chladni to cymatics
In the 20th century the Swiss physician Hans Jenny continued the experiments with liquids, pastes and powders and called the field cymatics, the study of waves. His pictures, and the later water sound images of Alexander Lauterwasser (see Links), show how vibration brings forth form, often in patterns reminiscent of flowers, mandalas and stars.
Physically there is nothing mysterious about it, and that is precisely what makes it remarkable. Where a sound meets a bounded body, standing waves arise, and their shapes are determined by whole numbers, like the string lengths on the monochord (see The monochord). Chladni’s plate shows in two dimensions what the Pythagoreans heard on the string: number becomes sound, and sound becomes form.