Named for Ernst Chladni, these figures represent nodal patterns formed by vibrating surfaces. Traditionally, these are formed placing fine particles on a surface, like a sheet of metal that is set vibrating (a violin bow against an edge of the metal plate is one popular method). The particles settle in the areas of the surface that have the least motion - the nodes. At resonant frequencies, a characteristic pattern emerges.

You can add and modify the vibrations applied to the simulated surface below. Unlike actual physical systems, the simulation allows you to superimpose vibrations that would occur on a fixed edge surface along with those that would occur on surface whose edges are allowed to freely vibrate.

The first button set (grey) will modify the frequency of the wave. The second button (blue) allows you to change the wave between one that form on a fixed edge surface to one that forms on a surface that can vibrate freely. The red button will remove the wave from the surface. When normalized, the overall result is kept in the range between 0 and 1.

Add Vibration

The displacement of particles on the surface is modeled by the (unsipmlified) equation below, where x and y range from zero to 2pi.