In physics, front velocity is the speed at which the first rise of a pulse above zero moves forward.
In mathematics, it is used to describe the velocity of a propagating front in the solution of hyperbolic partial differential equation.
Initially it was thought that the group velocity coincided with the speed at which information traveled.
By definition, a signal involves new information or an element of 'surprise' that cannot be predicted from the wave motion at an earlier time.
Using such a form for a signal, it can be shown, subject to the (expected) condition that the refractive index of any medium tends to one as the frequency tends to infinity,[clarification needed] that the wave discontinuity, called the front, propagates at a speed less than or equal to the speed of light c in any medium.