Wave vector

In physics, a wave vector (or wavevector) is a vector used in describing a wave, with a typical unit being cycle per metre. It has a magnitude and direction. Its magnitude is the wavenumber of the wave (inversely proportional to the wavelength), and its direction is perpendicular to the wavefront. In isotropic media, this is also the direction of wave propagation.

A closely related vector is the angular wave vector (or angular wavevector), with a typical unit being radian per metre. The wave vector and angular wave vector are related by a fixed constant of proportionality, 2 $π$ radians per cycle.

It is common in several fields of physics to refer to the angular wave vector simply as the wave vector, in contrast to, for example, crystallography.^[1]^[2] It is also common to use the symbol $k$ for whichever is in use.

In the context of special relativity, a wave four-vector can be defined, combining the (angular) wave vector and (angular) frequency.

^ Physics example: Harris, Benenson, Stöcker (2002). Handbook of Physics. p. 288. ISBN 978-0-387-95269-7.{{cite book}}: CS1 maint: multiple names: authors list (link)
^ Crystallography example: Vaĭnshteĭn (1994). Modern Crystallography. p. 259. ISBN 978-3-540-56558-1.

[1] Physics example: Harris, Benenson, Stöcker (2002). Handbook of Physics. p. 288. ISBN 978-0-387-95269-7.{{cite book}}: CS1 maint: multiple names: authors list (link)

[2] Crystallography example: Vaĭnshteĭn (1994). Modern Crystallography. p. 259. ISBN 978-3-540-56558-1.

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