Editing Group velocity (section)

{{Short description|Velocity at which the overall shape of a wave's amplitudes propagates}}
[[Image:Wave group.gif|frame|[[Dispersion (water waves)|Frequency dispersion]] in groups of [[gravity wave]]s on the surface of deep water. The {{colorbox|red}} red square moves with the [[phase velocity]], and the <span style="border-radius: 25px; background-color:#77ac30; border:1px solid;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span> green circles propagate with the group velocity. In this deep-water case, ''the phase velocity is twice the group velocity''. The red square overtakes two green circles when moving from the left to the right of the figure.{{paragraph}}
New waves seem to emerge at the back of a wave group, grow in amplitude until they are at the center of the group, and vanish at the wave group front.{{paragraph}}
For surface gravity waves, the water particle velocities are much smaller than the phase velocity, in most cases.]]
[[File:Wave packet propagation (phase faster than group, nondispersive).gif|thumb|Propagation of a wave packet demonstrating a phase velocity greater than the group velocity.]]
[[Image:Wave opposite-group-phase-velocity.gif|thumb|right|This shows a wave with the group velocity and phase velocity going in different directions.<ref name=nemirovsky2012negative>{{cite journal
 | last=Nemirovsky
 | first=Jonathan
 | author2=Rechtsman, Mikael C
 | author3=Segev, Mordechai
 | title=Negative radiation pressure and negative effective refractive index via dielectric birefringence
 | journal=Optics Express
 | date=9 April 2012
 | volume=20
 | issue=8
 | pages=8907–8914
 | doi=10.1364/OE.20.008907
 | bibcode=2012OExpr..20.8907N
 | pmid=22513601
 | doi-access=free
 }}</ref> The group velocity is positive (i.e., the [[envelope (waves)|envelope]] of the wave moves rightward), while the phase velocity is negative (i.e., the peaks and troughs move leftward).]]

The '''group velocity''' of a [[wave]] is the [[velocity]] with which the overall envelope shape of the wave's [[amplitude]]s—known as the ''modulation'' or ''[[envelope (waves)|envelope]]'' of the wave—propagates through space.

For example, if a stone is thrown into the middle of a very still pond, a circular pattern of waves with a quiescent center appears in the water, also known as a [[capillary wave]]. The expanding ring of waves is the '''wave group''' or [[wave packet]], within which one can discern individual waves that travel faster than the group as a whole. The amplitudes of the individual waves grow as they emerge from the [[trailing edge]] of the group and diminish as they approach the leading edge of the group.