Plane Wave

Wave in which the wavefronts are everywhere parallel planes normal to the direction of propagation.

The general solution for the acoustic pressure of a plane wave is:

the wave propagating in the +x direction is given by the term

the wave propagating in the -x direction is given by the term

where

p = acoustic pressure [Pa]

A = magnitude of the positive travelling wave [Pa]

B = magnitude of the negative travelling wave [Pa]

ω = frequency [rad s^-1]

t = time [s]

k = wavenumber of the propagating wave [m^-1]

x = position along the x axis [m]

The acoustic wave propagation in a duct will be plane up to the frequency at which the first sloshing mode occurs. This is given by:

where

a = radius of the pipe [m]

For intake systems the speed of sound is ~343ms^-1 and the internal radius of ducts is ~0.03m. This gives a cut-off of ~3300Hz below which only plane wave propagation needs to be considered. Higher order acoustic modes decay very rapidly with distance.

See also: Longitudinal Wave, Transverse Wave, Wave.