Singing sand

In 1787 Ernst Chladni sprinkled sand on a metal plate, clamped it at the centre, and drew a violin bow along its edge. The plate rang, and the sand ran off the parts that were shaking and piled up on the lines that weren't. Each note left a different figure.

This plate is idealised. Each pattern is a pair of standing waves, cos(nπx)·cos(mπy) ± cos(mπx)·cos(nπy), and its pitch grows with n² + m², as a real square plate's does. Only the modes that are still at the centre are kept, since that's where the plate is bolted. Every mode answers the drive with a resonance peak, so between peaks the plate barely moves, and the sand stops where it is.

The sand follows two rules. Each grain gets a random kick in proportion to how hard its spot is shaking, and it drifts a little downhill toward stiller plate. Nobody tells it where the lines are; it finds them.

Sing to it asks for your microphone. Your voice stays in the browser: the page finds its pitch by autocorrelation, matching the wave against itself to measure one period, and drives the plate at that frequency. The plate only moves while it hears a steady note. Use the arrows to jump straight to the next resonance, or press on the plate to pour more sand.