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Concept# Wavenumber

Summary

In the physical sciences, the wavenumber (or wave number), also known as repetency, is the spatial frequency of a wave, measured in cycles per unit distance (ordinary wavenumber) or radians per unit distance (angular wavenumber). It is analogous to temporal frequency, which is defined as the number of wave cycles per unit time (ordinary frequency) or radians per unit time (angular frequency).
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's 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.
Wavenumber, as used in spectroscopy and most chemistry fields, is defined as the number of wavelengths per unit distance, typically centimeters (cm−1):
where λ is the wavelength. It is sometimes called the "spectroscopic wavenumber". It equals the spatial frequency.
For example, a wavenumber in inverse centimeters can be converted to a frequency in gigahertz by multiplying by 29.9792458 cm/ns (the speed of light, in centimeters per nanosecond); conversely, an electromagnetic wave at 29.9792458 GHz has a wavelength of 1 cm in free space.
In theoretical physics, a wave number, defined as the number of radians per unit distance, sometimes called "angular wavenumber", is more often used:
When wavenumber is represented by the symbol ν, a frequency is still being represented, albeit indirectly. As described in the spectroscopy section, this is done through the relationship , where νs is a frequency in hertz. This is done for convenience as frequencies tend to be very large.

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