Propagating waves

A vibrating plate in contact with a fluid at rest may radiate sound by producing acoustic plane waves that travel away from the plate. In the case of an infinite plate, this only happens if the wavelength of the bending waves in the plate is larger than the acoustic wavelength. This occurs when the travelling wave speed of the plate is higher than the wave speed in the fluid. This case is illustrated by the animation below:

The animation below shows the particle displacement induced by a vibrating panel radiating sound in the fluid medium. By concentrating on the red dots, one can see that the particles are oscillating back and forth through an equilibrium position.

Evanescent waves

If the wavelength of the bending waves in the plate is shorter than the acoustic wavelength, then the acoustic waves do not propagate into the fluid. We are left with what are called 'evanescent' waves where the pressure amplitude decreases exponentially with distance from the plate.

The animation below shows the particle displacement induced by a vibrating panel when the travelling wave speed in the panel is less than the wave speed in the fluid. The amplitude of the particle motion decreases exponentially with increasing distance from the boundary. By concentrating on the red dots, you can just see that the particles move in an ellipse.