Wavenumber

Wavenumber measures spatial frequency: the number of wave cycles per unit distance or, in angular form, the phase change in radians per unit distance.

Wavelength: The distance over which a wave repeats one full cycle. Wavenumber is the reciprocal of wavelength when measured in cycles per unit distance.
Angular wavenumber: The spatial rate of phase change, usually measured in radians per unit distance. It is the angular convention, equal to 2π times cycles per unit distance.
Infrared spectroscopy: A method that identifies molecular vibrations by measuring absorption of infrared radiation. Spectral positions are commonly reported in reciprocal centimeters.
Spectroscopic wavenumber: The reciprocal of wavelength, commonly expressed in reciprocal centimeters in spectroscopy. This convention counts cycles per distance rather than radians per distance.
Spatial frequency: The rate at which a pattern repeats across space, measured in cycles per unit distance. Wavenumber is a standard way to quantify spatial frequency.
Wave vector: A vector whose direction gives a wave's propagation direction and whose magnitude is its angular wavenumber. It extends scalar wavenumber to waves varying across multiple spatial dimensions.
Raman spectroscopy: A spectroscopy method that probes molecular vibrations through inelastic scattering of light. Raman shifts are conventionally expressed as wavenumbers in reciprocal centimeters.
Angular frequency: The rate of phase change with time, measured in radians per unit time. It is the temporal counterpart of angular wavenumber, not a spatial rate.
Phase: A quantity describing a position within a repeating cycle, often expressed as an angle. Angular wavenumber measures how rapidly wave phase changes with position.
Fourier transform: A mathematical transformation that represents a signal as a combination of spatial or temporal frequencies. Its spatial-frequency variable is often expressed as wavenumber.

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