Wavenumber

In the physical sciences, the wavenumber (or wave number), also known as repetency,^[1] is the spatial frequency of a wave. Ordinary wavenumber is defined as the number of wave cycles divided by length; it is a physical quantity with dimension of reciprocal length, expressed in SI units of cycles per metre or reciprocal metre (m⁻¹). Angular wavenumber, defined as the wave phase divided by time, is a quantity with dimension of angle per length and SI units of radians per metre.^[2][3][4] They are analogous to temporal frequency, respectively the ordinary frequency, defined as the number of wave cycles divided by time (in cycles per second or reciprocal seconds), and the angular frequency, defined as the phase angle divided by time (in radians per second).

In multidimensional systems, the wavenumber is the magnitude of the wave vector. The space of wave vectors is called reciprocal space. Wave numbers and wave vectors play an essential role in optics and the physics of wave scattering, such as X-ray diffraction, neutron diffraction, electron diffraction, and elementary particle physics. For quantum mechanical waves, the wavenumber multiplied by the reduced Planck constant is the canonical momentum.

Wavenumber can be used to specify quantities other than spatial frequency. For example, in optical spectroscopy, it is often used as a unit of temporal frequency assuming a certain speed of light.