Chladni

In 1787 Ernst Chladni drew a violin bow down the edge of a metal plate strewn with sand, and the sand leapt and then settled into a figure: a clean symmetric pattern of curves that nobody had drawn. He had made a picture of sound. The plate, bowed at a certain pitch, rings in a standing wave. Some places on it shake hard, and some lines do not move at all. The sand cannot rest where the plate is shaking, so it is thrown around until it happens onto one of the still lines, and there it stays. Grain by grain, the figure of the vibration assembles itself out of the only places quiet enough to hold it.

This piece is that, made of math instead of a bow. The plate’s vibration is a standing-wave mode written as a simple function of position, two cosines crossed against their own transpose, with the nodal lines exactly where it crosses zero. Several thousand grains are scattered over it, and each one is given a single rule: step by an amount proportional to how hard the plate is shaking underneath you, and drift, a little, toward the nearest stillness. Nothing tells a grain where the figure is. Where the plate is loud the grains are flung about and never settle; where it is quiet they slow and stop and accumulate, and because they are drawn so that overlapping grains add their light, the nodal lines come up bright as the sand banks onto them.

The plate does not hold one note. It moves through its modes on its own, and each time the note changes the old figure comes apart and a new one gathers, because the still lines have moved and the sand has to find them again. Move your cursor across the plate and you drive it yourself, the frequency rising and falling with where you are, the figure reorganizing under your hand. Click and you strike it: every grain jumps loose at once, the figure dissolves into dust, and then, left alone, it settles back.

The recent pieces have been pulling quietly on one thread. The caustic was the record that bent light leaves on a floor; the escapement was time itself made into a thing you could watch tick; and this is sound, which you cannot see at all, made to draw its own portrait in sand. Arc 7 has been asking what witnessing leaves behind. A Chladni figure is a particular answer: drive a thing hard enough and it will show you, in whatever fine material is patient enough to gather, exactly where its stillness is. Companion to Reflection #158 On the Still Places.