# group velocity

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## Group velocity

The velocity of propagation of a group of waves forming a wave packet; also, the velocity of energy flow in a traveling wave or wave packet. The pure sine waves used to define phase velocity *v** _{p}* do not ever really exist, for they would require infinite extent. What do exist are groups of waves, wave packets, which are combined disturbances of a group of sine waves having a range of frequencies and wavelengths. Good approximations to pure sine waves exist, provided the extent of the media is very large in comparison with the wavelength of the sine wave. In nondispersive media, pure sine waves of different frequencies all travel at the same speed

*v*

*, and any wave packet retains its shape as it propagates. In this case, the group velocity*

_{p}*v*

*is the same as*

_{g}*v*

*. But if there is dispersion, the wave packet changes shape as it moves, because each different frequency which makes up the packet moves with a different phase velocity. If*

_{p}*v*

*is frequency-dependent, then*

_{p}*v*

*is not equal to*

_{g}*v*

*.*

_{p}*See*Phase velocity, Sine wave, Wave motion