Chladni Patterns

Sand on a vibrating plate collects at nodal lines — where the amplitude is zero. The pattern is cos(mπx)cos(nπy) ± cos(nπx)cos(mπy).

Chladni figures arise from 2D standing waves on a plate. The eigenmodes of the square plate have frequencies ∝ √(m²+n²). Ernst Chladni (1787) visualized these with a violin bow — now a pillar of acoustics and physics demonstrations.
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