Editing Plane wave (section)

{{Use American English|date=January 2019}}
{{Short description|Type of wave propagating in 3 dimensions}}

In [[physics]], a '''plane wave''' is a special case of a [[wave (physics)|wave]] or [[field (physics)|field]]: a physical quantity whose value, at any given moment, is constant through any plane that is perpendicular to a fixed direction in space.<ref>{{cite book |last=Brekhovskikh |first= L. |author-link= Leonid Brekhovskikh |date=1980 |title=Waves in Layered Media |location=New York |publisher=[[Academic Press]] |isbn= 9780323161626 |edition=2 |pages=1–3}}</ref>

For any position <math>\vec x</math> in space and any time <math>t</math>, the value of such a field can be written as
<math display="block">F(\vec x,t) = G(\vec x \cdot \vec n, t),</math>
where <math>\vec n</math> is a [[unit vector|unit-length vector]], and <math>G(d,t)</math> is a function that gives the field's value as dependent on only two [[real number|real]] parameters: the time <math>t</math>, and the scalar-valued [[Displacement (geometry)|displacement]] <math>d = \vec x \cdot \vec n</math> of the point <math>\vec x</math> along the direction <math>\vec n</math>. The displacement is constant over each plane perpendicular to <math>\vec n</math>.

The values of the field <math>F</math> may be scalars, vectors, or any other physical or mathematical quantity.  They can be [[complex numbers]], as in a [[Sinusoidal plane wave#Complex exponential form|complex exponential plane wave]].  

When the values of <math>F</math> are vectors, the wave is said to be a [[longitudinal wave]] if the vectors are always  collinear with the vector <math>\vec n</math>, and a [[transverse wave]] if they are always orthogonal (perpendicular) to it.