Chladni's plates

In 1787 Chladni engraved the figures that sand made on his ringing plates, and sand on the computed plate finds them again.

A square plate seen from above, sand lying along Chladni's figure 127: a star of eight lines with four rounded arcs at its edges, his engraving under it. The sand is shaken loose, the plate tilts up and ripples as it rings, the sand runs off the moving parts onto the still lines, and the plate lies flat again under his lines.

His 60 figures are measured, as printed in 1787. The plate and the sand are a model: a free, even square plate by Ritz's 1909 method, its grains stepping only as far as it moves. It rings slowed, one pace for every pitch, and far taller than a plate moves. The sand lands on his lines on 44 figures. Of the other 16, seven need two close pitches at once, two are his hand and seven are unsettled.

Figures: Chladni 1787, Entdeckungen über die Theorie des Klanges, Tab. VIII to X (public domain). Plate: Ritz's 1909 method.

Read the paper: Gander & Kwok 2012