Editing Group velocity (section)

==Dispersion==
{{main|Group velocity dispersion}}
[[File:Wave disp.gif|thumb|388px|right|Distortion of wave groups by higher-order dispersion effects, for [[surface gravity wave]]s on deep water (with {{math|''v''<sub>g</sub> {{=}} {{sfrac|1|2}}''v''<sub>p</sub>}}).{{paragraph}}
This shows the superposition of three wave components—with respectively 22, 25 and 29 wavelengths fitting in a [[periodic function|periodic]] horizontal domain of 2&nbsp;km length. The wave [[amplitude]]s of the components are respectively 1, 2 and 1 meter.]]
Part of the previous derivation is the [[Taylor series|Taylor series approximation]] that:
:<math>\omega(k) \approx \omega_0 + (k - k_0)\omega'_0(k_0)</math>

If the wavepacket has a relatively large frequency spread, or if the dispersion {{math|''ω(k)''}} has sharp variations (such as due to a [[resonance]]), or if the packet travels over very long distances, this assumption is not valid, and higher-order terms in the Taylor expansion become important.<ref name="Jackson_1999">{{Citation |last=Jackson  |first= John David |year= 1999 |title= Classical Electrodynamics |edition= 3rd |publisher= John-Wiley |isbn= 047130932X |doi=}}</ref>{{rp|324-325}}

As a result, the envelope of the wave packet not only moves, but also ''distorts,'' in a manner that can be described by the material's [[group velocity dispersion]]. Loosely speaking, different frequency-components of the wavepacket travel at different speeds, with the faster components moving towards the front of the wavepacket and the slower moving towards the back. Eventually, the wave packet gets stretched out. This is an important effect in the propagation of signals through [[optical fiber]]s and in the design of high-power, short-pulse lasers.