- SI Base Unit: Reciprocal metre
- Units: Reciprocal metre
In the physical sciences, the wavenumber is a property of a wave, its spatial frequency, that is equal to the reciprocal of the wavelength. It is also the magnitude of the wave vector. Its usual symbols are , , σ or k, the first three used for one definition, the last for another. The wavenumber has dimensions of reciprocal length, so its SI unit is m and cgs unit cm (in this context formerly called the kayser, after Heinrich Kayser).
It can be defined as either
For electromagnetic radiation in vacuum, wavenumber is proportional to frequency and to photon energy. Because of this, wavenumbers are used as a unit of energy in spectroscopy. In the SI units, wavenumber is expressed in units of reciprocal meters (m), but in spectroscopy it is usual to give wavenumbers in reciprocal centimeters (cm). The angular wavenumber is expressed in radians per meter (rad·m).
In general, the angular wavenumber k, the magnitude of the wave vector, is given by
where ν is the frequency of the wave, λ is the wavelength, ω = 2πν is the angular frequency of the wave, and vp is the phase velocity of the wave.
For the special case of an electromagnetic wave in vacuum, where vp = c, k is given by
where E is