Bow a metal plate and scatter sand across it: the sand flees the shaking and piles up along the lines that DON'T move — the nodal lines — drawing a figure that belongs to that one note. This is Chladni's own experiment, 1787. Pick a mode, tap PLAY to hear the note that makes it, and watch the sand find the still lines.
A vibrating square plate's modes are the standing waves cos(mπx)cos(nπy) − cos(nπx)cos(mπy); the SAND collects exactly where that function is zero (the nodal lines that never move), which the page samples live to draw the figure. The note's pitch rises with the mode as √(m²+n²) — higher modes, finer figures, higher notes — and PLAY sounds that frequency through Web Audio. The nodal pattern is computed from the real mode shape, not drawn by hand.
The cos-combination is the ideal free-square-plate model; a real plate needs full Kirchhoff–Love elasticity (its exact figures depend on material, thickness and clamping), and the frequency here is a √(m²+n²) scaling, not a plate's true eigenfrequency. The nodal geometry — where the figure comes from — is exact for the model.