The velocity that wave energy—comprised of a wave group, train or packet of individual wave phases or components—travels through a medium. The wave energy may be grouped into an envelope that is shrink-wrapped around it. The shape of the envelope around the wave-energy group changes with distance because the individual wave phases move apart from one another.
vg = vp − λ (∂vp/∂λ) = vp + f (∂vp/∂f)
Relation of group velocity to phase velocity. As a wave travels through a medium, its energy moves at the group velocity (vg) and its individual phases, or components, move at their phase velocity (vp). The wave changes shape with distance as each frequency (f), or wavelength (λ), component moves at its separate phase velocity through the phenomenon of dispersion. Relative to the group velocity, each component moves with faster or slower phase velocity, depending on how phase velocity changes with wavelength or frequency.