Editing Wave (section)

=== Wave velocity ===
{{further|Phase velocity|Group velocity|Signal velocity}}
[[Image:Seismic wave prop mine.gif|thumb|upright=1.4|[[Seismic wave]] propagation in 2D modelled using [[FDTD]] method in the presence of a landmine]]

Wave velocity is a general concept, of various kinds of wave velocities, for a wave's [[phase (waves)|phase]] and [[speed]] concerning energy (and information) propagation. The [[phase velocity]] is given as:
<math display="block">v_{\rm p} = \frac{\omega}{k},</math>
where:
* ''v''<sub>p</sub> is the phase velocity (with SI unit m/s),
* ''ω'' is the [[angular frequency]] (with SI unit rad/s),
* ''k'' is the [[wavenumber]] (with SI unit rad/m).

The phase speed gives you the speed at which a point of constant [[phase (waves)|phase]] of the wave will travel for a discrete frequency. The angular frequency ''ω'' cannot be chosen independently from the wavenumber ''k'', but both are related through the [[dispersion relation]]ship:
<math display="block">\omega = \Omega(k).</math>

In the special case {{math|1=Ω(''k'') = ''ck''}}, with ''c'' a constant, the waves are called non-dispersive, since all frequencies travel at the same phase speed ''c''. For instance [[electromagnetic wave]]s in [[vacuum]] are non-dispersive. In case of other forms of the dispersion relation, we have dispersive waves. The dispersion relationship depends on the medium through which the waves propagate and on the type of waves (for instance [[electromagnetic wave|electromagnetic]], [[sound wave|sound]] or [[ocean surface wave|water]] waves).

The speed at which a resultant [[wave packet]] from a narrow range of frequencies will travel is called the [[group velocity]] and is determined from the [[gradient]] of the [[dispersion relation]]:
<math display="block">v_{\rm g} = \frac{\partial \omega}{\partial k}</math>

In almost all cases, a wave is mainly a movement of energy through a medium. Most often, the group velocity is the velocity at which the energy moves through this medium.

[[File:Light dispersion of a mercury-vapor lamp with a flint glass prism IPNr°0125.jpg|thumb|right|upright|Light beam exhibiting reflection, refraction, transmission and dispersion when encountering a prism]]

Waves exhibit common behaviors under a number of standard situations, for example: