The Singing Plate

A vibrating plate, driven at a resonant frequency, makes scattered sand flee the antinodes and pile on the nodal lines — the Chladni figures. This bench doesn't replay a stored pattern: it discretizes the operator −Δ on the plate's shape and numerically solves the eigenproblem −Δu = λu for the standing modes, then proves the eigenfrequencies match the closed forms.

Shape

Boundary

Mode eigenpair

#1 f ≈ — · λ = —

The bars are the solved eigenfrequencies √λ. The lit bar is the current mode.

Find resonance

Drive frequency —

Sweep the drive; the plate rings only at an eigenfrequency.

Sand

Grains 2200

Amplitude 1.00

Skin

Pick a shape + boundary, then step the mode — each is a true eigenvector of the discrete Laplacian. The sand drifts off the shaking antinodes and settles on the still nodal lines. Find resonance sweeps a drive frequency that snaps to the nearest solved eigenfrequency. Skins change only colour — the geometry, the spectrum, and the figures are identical. Distinct from the Garden's watch-only Chladni animation: this one solves the eigenproblem.