Group velocity

A quantity describing the rate of propagation of a wave process in dispersing media. Let the wave process be described by the wave equation with variable coefficients:

The solutions sought satisfy the conditions

and have the form

The function should be a non-zero solution of the one-dimensional boundary value problem

If, in a certain range of variation of , there exists a finite number of for which this problem has a non-zero solution , then the quantities and are said to be, respectively, the phase and group velocities of the wave

The two velocities are related by the Rayleigh formula:

where is the wave-length.

References

[1]	L.I. Mandel'shtam, , Complete works , 5 , Leningrad (1950) pp. 315–319; 419–425; 439–467 (In Russian)
[2]	G.S. Gorelik, "Oscillations and waves" , Moscow-Leningrad (1950) (In Russian)

References

[a1]	L. Brillouin, "Les tenseur en mécanique et en élasticité" , Masson (1949)