# 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.