Technique · Fields

Chladni plate

Sand on a vibrating metal plate, gathered along the lines where the plate stays still; the figure re-forms as the pitch is swept.

Chladni plate is a field drawn for every pixel by the graphics chip. Every piece on Synapse Drip is made from a recipe that layers techniques like this one, and you can change any of it in the Studio.

Good to know

  • Napoleon saw Chladni demonstrate his figures in Paris in 1809, and the French Academy of Sciences then set a prize for a mathematical theory of vibrating plates; Sophie Germain won it in 1816 on her third attempt.
  • The Swiss physician Hans Jenny coined the word cymatics in the 1960s and photographed such patterns in sand, powders and liquids.
  • Sand gathers on the nodal lines because the rest of the plate moves up and down and throws it off; the lines are the only places that stay still.
  • Ernst Chladni, a German physicist, published his sand figures in 1787 by drawing a violin bow across the edge of a plate sprinkled with sand.
  • Violin makers have used Chladni patterns to tune the top and back plates of an instrument, tapping the wood and watching where the sand gathers.

The mathematics

  • The height of a square plate in this mode is cos(3.00 pi x) cos(5.00 pi y) minus a weight times the same with n and m swapped; the sand lies where that sum is zero, so a mode with higher n and m has more nodal lines and a finer pattern.
  • A plate bends rather than stretches, so the frequency of a mode grows with the square of its wave number, roughly with n squared plus m squared; doubling the pitch more than doubles the detail.
  • The figures are standing waves, the eigenmodes of a drum or plate; the same patterns, in the language of quantum mechanics, describe the allowed states of a particle in a box.

In art

  • Cymatic images, with their fine symmetric lines, are often paired with music, from album covers to installations in which a speaker shakes a plate of sand.
  • The patterns look designed but are found: nothing draws a line, and the symmetries come from the shape of the plate and the frequency alone.

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