![Figure 5](PhaseGroupVelocity-SignalFrontVelocity.png)
Figure 5: Difference between phase, group, signal and front velocities. At
, the phase
and group velocities are represented on the left and given respectively by
and
(in the limit
.) The signal and front velocity represented on the right are
given by
(where
is the point where at least half the intensity of the original
signal is reached.) The front velocity is given by
.
![t = δt](article2061x.gif)
![v = δx ∕δt phase P](article2062x.gif)
![vgroup = δxG ∕δt](article2063x.gif)
![δt → 0](article2064x.gif)
![vsignal = δxS ∕δt](article2065x.gif)
![δxS](article2066x.gif)
![vfront = δxF∕δt](article2067x.gif)