Dispersion
Dispersion occurs when pure plane waves of different wavelengths have different propagation velocities, so that a wave packet of mixed wavelengths tends to spread out in space. The speed of a plane wave, v, is a function of the wave's wavelength :
The wave's speed, wavelength, and frequency, f, are related by the dispersion relation
Dispersion relations are more commonly expressed in terms of the angular frequency and wavenumber . Rewriting the relation above in these variables gives
The use of ω(k) to describe the dispersion relation is standard because both the phase velocity ω/k and the group velocity dω/dk have convenient representations via this function.
The elementary sorts of waves being considered can be described by
where
- A is the amplitude of the wave,
- A0 = A(0,0),
- x is a position along the wave's direction of travel, and
- t is the time at which the wave is described.
Read more about this topic: Dispersion Relation
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