# Dictionary:Group velocity

**1**. The velocity with which the energy in a wavetrain travels. In dispersive media where velocity varies with frequency, the wavetrain changes shape as it progresses so that individual wave crests travel at different velocities (phase velocities, *V*) than does the envelope of the wavetrain. The velocity of the envelope is the group velocity *U*:

where λ=wavelength and *f*=frequency. *Normal mode propagation* (q.v.) results in dispersion and thus different values for group and phase velocities. See also Figure D-16 and compare *phase velocity*.

**2**. Angular dispersion; in anisotropic media, group velocity is the velocity of energy transport radially outward from a point source. Also called **ray velocity**; see Figure A-14.

**3**. When frequency dispersion and angular dispersion occur together, the velocity of the wave envelope (group velocity) and energy velocity (the ratio of the time-average Poynting vector to the time-average stored energy density) are not the same.

## References

- ↑ Balch, A. H. and Smolka, F. R., 1970, Plane and spherical Voigt waves: Geophysics, 35, 745–761.