Sand on a Singing Plate

Bow the edge of a thin plate covered in sand, and the sand leaves the parts that shake and gathers on the lines that stay still. The Public Domain Review's essay on 19th-century sound books starts with this experiment. Here is a plate you can play with, and a correction to the date.

The pattern is the old textbook approximation: two simple wave patterns across a square, cos(nπx)·cos(mπy) and the same with n and m swapped, added or subtracted. The sand follows the places where the result is zero. A real plate with free edges, held at the centre, makes patterns close to these but not identical.

The date

The essay opens: "In 1777, the German physicist Ernst Chladni … designed an experiment that revolutionized our understanding of sound." In 1777 Chladni was twenty. He took his law degree in Leipzig in 1782 and only then turned to physics in earnest. His sand figures were first published in 1787, in Entdeckungen über die Theorie des Klanges.

1777 is the year his later doctoral adviser, Georg Christoph Lichtenberg, published the electrical figures that carry his name: dust settling into patterns on a charged plate. That may be where the date came from.

The experiment itself is older than both. Robert Hooke ran a violin bow along a glass plate covered with flour on 8 July 1680 and saw the nodal patterns appear. He had seen them already in 1671. Chladni made them systematic and famous.

What stands on what