Chladni Plate

What it is

A Chladni plate is a metal sheet dusted with sand and bowed at its edge: at certain pitches the sand skitters away from the vibrating regions and settles along the still lines, drawing the plate's standing wave as a figure. This is that experiment as a simulation, with about 40,000 grains finding the nodal lines in real time.

The figures are the closed-form eigenmodes of a square plate rather than a recorded animation, so every pitch between two named modes is a real blend you can hold and scrub through.

Ernst Chladni demonstrated this with a violin bow in 1787, and the figures did more than look good: they were the first clear evidence that a vibrating surface has discrete modes, and Napoleon put up a prize for the mathematics that would explain them. Sophie Germain won it. The grains here are integrated individually against the gradient of the plate's displacement, so they crowd into the nodal lines from both sides the way real sand does — each grain taking a random step scaled by how hard the plate is moving under it, plus a slide down that gradient, which is why the figure keeps shimmering instead of freezing once it forms.

Scrubbing the pitch is the part worth doing slowly. Between two named modes the plate is genuinely in both, and the sand strands itself along lines that belong to neither before collapsing onto the next figure — the pattern that appears at a clean mode is a resting place, not a frame of an animation. Turning Bow on plays the tone that figure belongs to, so the pitch you are looking at and the pitch you are hearing are the same number.

How to use it

• Scrub the pitch dial to move between modes.
• Tap to pour more sand onto the plate.
• Drag to sweep the grains around.
• Turn Bow on to hear the tone the pattern belongs to.

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