for {{name}} — after Ernst Chladni, 1787
drag on the plate to bow it — the harder you bow, the harder the sand jumps.
every pair (m, n) has its own nodal geometry. compound mode sounds two at once.
the experiment. Ernst Chladni, physicist, Wittenberg, 1787: cover a square brass plate with fine sand; draw a violin bow across the edge until a standing wave forms; the sand jumps and comes to rest along the *nodes* — the curves along which the plate is not moving — and abandons the *anti-nodes* entirely. Every (m, n) integer pair produces its own figure. Chladni published a hundred of them in *Entdeckungen über die Theorie des Klanges,* Leipzig, 1787. Napoleon saw them demonstrated in Paris in 1808 and reportedly said, quite accurately, that this was the first genuinely new thing in acoustics since Pythagoras.
the math. For a square plate with free edges, the closed-form standing wave is u(x, y) = cos(mπx/L)·cos(nπy/L) − cos(nπx/L)·cos(mπy/L). Sand collects where |u| is near zero. The plate resonates at a frequency proportional to √(m² + n²). No simulation is running — the pattern is Chladni's own analytic solution, applied per grain, at sixty frames per second.
the index. Every pair from (1, 1) to (8, 8) is cataloged below as its own thumbnail — sixty-four figures, the way Chladni numbered his own plates in the 1787 book. Click any figure to load it onto the plate.
compound mode. A real plate can be driven at two frequencies at once, and the sand settles into the sum of both mode shapes — this is how later acousticians (and modern cymatics demonstrations) got the more intricate, flower-like figures Chladni's single-tone bow couldn't produce alone. Turn compound on, pick a second pair (m₂, n₂), and drag the mix slider to blend between them. The plate sings both pitches together.
keyboard. ←/→ change m. ↑/↓ change n. space bow. s toggle sound. r re-scatter. c toggle compound mode.