In physics, a plane wave is a special case of wave or field: a physical quantity whose value, at any moment, is constant through any plane that is perpendicular to a fixed direction in space.[1]
For any position in space and any time , the value of such a field can be written as
where is a unit-length vector, and is a function that gives the field's value as dependent on only two real parameters: the time , and the scalar-valued displacement of the point along the direction . The displacement is constant over each plane perpendicular to .
The values of the field may be scalars, vectors, or any other physical or mathematical quantity. They can be complex numbers, as in a complex exponential plane wave.
When the values of are vectors, the wave is said to be a longitudinal wave if the vectors are always collinear with the vector , and a transverse wave if they are always orthogonal (perpendicular) to it.
^Brekhovskikh, L. (1980). Waves in Layered Media (2 ed.). New York: Academic Press. pp. 1–3. ISBN 9780323161626.
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