The Chladni plate demonstrates modes of vibration. A metallic plate with tiny grains of sand on its surface is vibrated causing the sand to gently move along the surface. Where the sand is not moving corresponds to nodal curves of the vibration. Some experimentalists vibrate the plate from the side using a bow. Here we attached the plate to a mechanical vibrator that we control with a function generator (causing a node at the center where the plate is attached).
Here is a fun video produced by NPR’s Science Friday on the Chladni Plate demo:
Here is an example with a guitar-shaped plate:
Here is a beautiful video demonstrating modes (and transitions between modes) for a rectangular plate from the UCLA Physics department:
Using Fourier Series we can understand general vibrations of the surface as temporal superpositions of these fundamental modes (e.g., found using separation of variables).