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In physics, a plane wave is a special case of wave or field: a physical quantity whose value, at any moment, is constant over 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 from only two real parameters: the time

where is a unit-length vector, and is a function that gives the field's value as from only two real parameters: the time , and the displacement of the point along the direction . The latter 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 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.

Often the term "plane wave" refers specifically to a traveling plane wave, whose evolution in time can be described as simple translation of the field at a constant wave speed along the direction perpendicular to the wavefronts. Such a field can be written as

where is now a function of a single real parameter

Sinusoidal plane wave

The term is also used, even more specifically, to mean a "monochromatic" or sinusoidal plane wave: a travelling plane wave whose profile is a sinusoidal function. That is,

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