The experiment, the physics, and what this site simulates

Chladni’s method needs almost nothing: a flat plate, fine sand, a bow, and a fingertip to hold one point still. The finger forces a node; the bow feeds energy in at the edge. Which figure appears depends on where the plate is held and where it is bowed.

The modern version replaces the bow with a shaker or a screw at the centre, driving one point at a frequency you choose. It trades the bow’s mixture of modes for control, and it makes the frequency of every figure a number you can read off a dial.

Both versions show the same thing. The sand is not drawing the sound; it is drawing the plate’s response to being driven — a different picture, and a more interesting one.

A thin plate is governed by the Kirchhoff–Love equation. Its bending stiffness is D = Eh³ / 12(1 − ν²), where E is Young’s modulus, h the thickness and ν Poisson’s ratio, and its frequencies follow f = C·k² with C = (1/2π)√(D/ρh). Pitch rises with the square of the wavenumber k, where on a stretched membrane it rises in proportion.

For the reference plate used here — aluminium, 240 × 240 × 1 mm — that gives C ≈ 0.246 m²/s. Its first point-driven resonances have been measured at 630, 1023, 1240, 1368 and 1795 Hz. Free-edge square modes are approximated by cos(mπx/a)cos(nπy/a) ± cos(nπx/a)cos(mπy/a).

Circular plates are described by nodal diameters n and nodal circles s, with f ∝ (n + 2s)² — Chladni’s law, explained by Rayleigh and tested by Rossing. Leissa’s NASA compilation remains the standard table of plate eigenvalues.

Grains lift off when the plate’s acceleration passes gravity: Γ = Aω²/g > 1. Each landing is followed by a hop in a random direction, longer where the amplitude is larger and nudged downhill, because the surface under a bouncing grain slopes away from the antinode. The grains therefore spread fastest over the antinodes and come to rest at the nodes.

The sorting is quick — a few seconds for a clear figure — and it is statistical, not deterministic. No grain knows where the nodes are. It is thrown about, leans downhill as it goes, and stops being kicked once it arrives at one.

Below the lift-off threshold the result inverts. Faraday reported in 1831 that fine powders creep toward the antinodes instead, carried by the air the plate stirs above it. Coarse sand draws the nodal figure; light powder draws its negative.

The plate on screen is a point-driven sum of modes. Square modes are built on a cosine basis with free edges; circular modes start from tabulated free-plate eigenvalues and are refined against the exact free-edge conditions. Each mode is weighted by how strongly the driving point excites it, and the weighted modes are summed into the displacement field you see, evaluated every frame.

The sand is modelled, not solved. Grains are bouncing random walkers. Past the acceleration threshold each takes a step whose length grows with the local amplitude and leans down the slope, and the hardest-shaken grains are thrown clear to land anywhere on the plate. Every grain lifts off at a threshold of its own, which stands in for the collisions that give a real ridge its width. This reproduces how the sand settles; how fast it settles is tuned by eye. It does not reproduce any individual grain’s path.

What is left out: the square plate’s true lowest (twisting) mode at λ² ≈ 13.5, air drag and the air layer above the plate, and collisions between grains. The resonances this model predicts for the reference plate sit about ten per cent above the published measurements — a gap that a 0.1 mm tolerance on the plate’s thickness would explain.

Built with Next.js and React. The plate and the sand are rendered with Three.js, the sand as GPU particles — one point per grain, positions advanced on the graphics card. Where a browser has no WebGL 2 (graphics acceleration switched off, for instance), the same grain law runs on the CPU with fewer grains and is drawn in two dimensions; a small “2D” badge in the header says so. Scroll sequencing and transitions use GSAP.

Tones are generated in the browser with the Web Audio API at the frequency shown on screen. Nothing is streamed and no audio file is loaded; the pitch you hear is the number driving the plate.

Reduced-motion preferences are respected: with prefers-reduced-motion set, scroll-driven sequences settle into static states and the plate changes without sweeping transitions. The plate can be paused from the header at any time, the introduction can be skipped, and the Lab is reachable directly.

Every control is keyboard operable, with visible focus and standard arrow-key adjustment on sliders. Sound is opt-in — nothing plays until you choose it, and it can be muted at any time without leaving the page.