Editing Dispersion relation (section)

{{Short description|Relation of wavelength/wavenumber as a function of a wave's frequency}}
[[Image:Prism-rainbow.svg|frame|right|
In a prism, [[Dispersion (optics)|dispersion]] causes different colors to [[refraction|refract]] at different angles, splitting white light into a rainbow of colors.]]

In the [[physical science]]s and [[electrical engineering]], '''dispersion relations''' describe the effect of [[#Dispersion|dispersion]] on the properties of waves in a medium. A dispersion relation relates the [[wavelength]] or [[wavenumber]] of a wave to its [[frequency]]. Given the dispersion relation, one can calculate the frequency-dependent [[phase velocity]] and [[group velocity]] of each sinusoidal component of a wave in the medium, as a function of frequency. In addition to the geometry-dependent and material-dependent dispersion relations, the overarching [[Kramers–Kronig relations]] describe the frequency-dependence of [[wave propagation]] and [[attenuation]].

Dispersion may be caused either by geometric boundary conditions ([[waveguide]]s, shallow water) or by interaction of the waves with the transmitting medium. [[Elementary particle]]s, considered as [[matter wave]]s, have a nontrivial dispersion relation, even in the absence of geometric constraints and other media.

In the presence of dispersion, a wave does not propagate with an unchanging waveform, giving rise to the distinct frequency-dependent [[phase velocity]] and [[group velocity]].