What you are looking at
In 1787 Ernst Chladni sprinkled sand on a metal plate clamped at its centre and drew a violin bow along the edge. The plate rang a note and the sand jumped into sharp figures. Each figure belongs to one of the plate's natural ways of vibrating, called a mode. The sand gets bounced off the parts that move and comes to rest on the nodal lines, where the plate stays still.
Every shape has its own set of modes, and each mode rings at its own pitch. That's why the outline matters so much. A circle gives rings and spokes, a square gives the classic crossed figures, and a star's inside corners pinch the vibration so its arms ring on their own. On this page the modes are computed for whatever outline you choose, including one you draw.
Two kinds of grain
Chladni noticed that very fine powder misbehaves: it collects in little heaps where the plate moves the most. In 1831 Michael Faraday explained why. The vibrating plate stirs the air just above it into small circulating currents. Heavy sand ignores the air and gets bounced to the still lines, while light dust is carried along and dropped at the antinodes. Give the two grain types different weights and colours, and one plate shows both pictures at once.
Rich sounds
The plate responds to each frequency in a sound separately and adds the results. The sand doesn't follow individual wiggles; it reacts to how much each spot shakes on average. So a sound with several notes in it only leaves sand where all of them are quiet. A sawtooth's overtones rarely line up with the plate's resonances, so tiny pitch changes make the figure jump. Two notes a hair apart make the figure pulse, and a short loop makes the sand twitch in rhythm.
Two mounts, in and out of sync
With two shakers placed symmetrically, moving them together pushes only the symmetric modes. The others get pushed in opposite directions at once and cancel. Moving them in opposite directions picks the other half. At the same pitch, flipping the sync can swap one figure for a completely different one. A quarter-cycle apart, no spot is ever fully still, so the wave travels around. On a circle it rotates, and the sand blurs into rings. A small drift makes the phase roll slowly, so the plate breathes between figures.
Keys: Space pause · M sound · R re-scatter sand · ←/→ previous/next resonance · H heat map. Drag the markers on the plate: A/B mounts, clamps (bolts), the contact mic, and the bow. Double-click a clamp to remove it.
What is computed and what is approximated
- Computed: the natural modes of a thin elastic (Kirchhoff) plate with free edges, solved on a grid of up to 96×96 points for your exact outline, clamps and mounts. They match textbook values for a free strip and a free square within 1%, and a free circle within about 1.5% (checked in the tests).
- Computed: the plate's motion over time at the audio sample rate, mode by mode, for any signal. Mount phases are applied with a true Hilbert-transform phase shift, so "90° apart" means the same thing for a drum loop as for a sine.
- Computed: the average shaking at every point, including how different modes reinforce or cancel each other. This is what the sand reacts to.
- Computed: pitches in hertz, from the plate's size, thickness and material. Wood is treated as isotropic, which real spruce is not.
- Approximated: the sand. Grains hop when the local acceleration exceeds about 1 g, scatter randomly, and drift toward calmer spots. It's a rule of thumb, not a simulation of bouncing grains.
- Approximated: the powder. Faraday's air currents are stood in for by a drift toward the strongest shaking. Air flow itself isn't simulated.
- Approximated: the edges and the damping. A curved outline becomes a staircase on the grid. Damping is one number for every mode, or a simple power of the pitch (Physics, "Damping rise"). The bow uses a textbook stick-slip friction curve.
- Approximated: the sound. You hear a contact microphone at the mic marker, not the sound the plate radiates into the room. Above about 2–5 kHz (depending on grid size) there are no modes, so the plate falls silent there.