A plane wave satisfies the one-dimensional wave equation in Cartesian coordinates.

To obtain plane waves, the position vector must remain perpendicular to a give plane. Pick a point on the plane . In order for the wave to be planar,

(1)

(2)

The wave then satisfies the generalization of the one-dimension equation,

where is the angular frequency, k is the wave vector, r is the radius vector, and is the phase of the wave.

Spherical Wave, Wave