Williams, S. A. Department of Physics, Iowa State University, Ames, Iowa.
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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 υp 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 υf, and any wave packet retains its shape as it propagates. In this case, the group velocity υg is the same as υp. 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 υp is frequency-dependent, then υg is not equal to υp. See also: Phase velocity; Sine wave; Wave motion
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