Cymatics
Drive a vibrating plate at different frequencies and watch standing wave patterns emerge. Nodal lines — where the plate stays still — appear dark, while antinodes glow gold. A genuine wave simulation, not pre-computed eigenmodes.
About this lab
In the late 18th century, the German physicist Ernst Chladni discovered that when a metal plate is bowed with a violin bow, sand sprinkled on its surface migrates to the nodal lines — the curves where the plate remains stationary — revealing intricate geometric patterns. These "Chladni figures" caused a sensation when demonstrated to Napoleon in 1809, and the French Academy offered a prize for their mathematical explanation. Sophie Germain eventually derived the correct plate equation, showing that a thin elastic plate resists bending through a biharmonic term involving the fourth spatial derivative of displacement.
The patterns arise from the interference of waves reflecting off the plate boundaries. At most frequencies, the reflections are incoherent and the plate vibrates chaotically with no clear pattern. But at resonant frequencies, standing waves form: the plate divides into regions vibrating in phase and out of phase, separated by nodal lines where displacement is zero. Sand collects along these nodal lines because particles are pushed away from vibrating regions toward stationary ones. The shape of the nodal pattern depends on the frequency, the plate geometry, and where the plate is driven or held.
The mathematics connects directly to quantum mechanics. The Chladni patterns on a square plate correspond to products of sine functions, identical in form to the wavefunctions of a particle in a two-dimensional box. The nodal lines of the plate are analogous to the nodes of electron orbitals. For circular plates, the eigenmodes involve Bessel functions, the same special functions that appear in the hydrogen atom's radial wavefunctions. This is not a coincidence: both systems are governed by eigenvalue problems for second-order partial differential equations on bounded domains.
Modern cymatics has practical applications in engineering and acoustics. Vibration testing of aircraft panels and spacecraft components uses exactly these patterns to identify structural resonances and potential fatigue points. Musical instrument makers have long used Chladni-like patterns to tune the top plates of violins and guitars, adjusting wood thickness to shift resonant frequencies. The patterns are also beautiful, which is why cymatics demonstrations — using a speaker, a metal plate, and salt or sand — remain one of the most visually striking experiments in all of physics.