# How the Chladni Plate works

A black square plate, strewn with sand, with a frequency knob. Turn the knob onto a resonance, or draw a bow along an edge, and the sand runs off the parts that move and piles up on the lines that stand still, so the plate draws its own figure. I didn't draw any of the figures. This page is how the plate finds them.

Guide · With a Pass · https://tactileui.dev/docs/how-the-chladni-plate-works

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The physics is DOM-free, so the tests run it in Node.

## The plate's modes

A square plate with free edges has natural shapes it likes to vibrate in, its modes. I use the classical approximation for a free square plate, with u and v running from 0 to 1 across it: