History

In 1787 Ernst Chladni drew a violin bow across the edge of a sanded metal plate and published the figures the grains made — the first pictures of vibration. Demonstrating them in Paris in 1809 he so struck Napoleon that a prize was posted for their theory. Sophie Germain, working outside an Academy that would not admit her, submitted three times and took the prize in 1816; Kirchhoff settled the free-edge boundary conditions in 1850. The figures themselves resisted calculation until 1909, when Walther Ritz solved this exact plate — square, free at every edge — with the variational method that now carries his name. That computation is what this page performs, in your browser, at load.

Method

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Certificates of this run

Owned approximations

The exciter is a point that prescribes motion, so the three rigid-body modes are excluded and the real centre post's mass and stiffening are not modelled. Damping is a uniform modal ζ, chosen for legible resonance, not measured steel. The sand is an Itô random walk — step variance proportional to local mean-square plate velocity, plus a first-order drift down the amplitude gradient — standing in for ballistic bounces; rim losses are real, and the corners of the twist figure shed first. Faraday (1831) showed fine powders ride air currents to the antinodes; coarse sand seeks nodes, and this sand is coarse. The tone is the drive sine at true frequency and relative level, not the plate's radiated sound.

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