Since a general wave (or wavelike phenomenon) need not embody the causal flow of any physical effects, there is obviously there is no upper limit on the possible phase velocity of a wave. However, even for a “genuine” physical wave, i.e., a chain of sequentially dependent events, the phase velocity does not necessarily correspond to the speed at which energy or information is propagating. This is partly a semantical issue, because in order to actually convey information, a signal cannot be a simple periodic wave, so we must consider non-periodic signals, making the notion of “phase” somewhat ambiguous. If the wave profile never exactly repeats itself, then arguably the “period” of the signal must be the entire signal. On this basis we might say that the velocity of the signal is unambiguously equal to the “phase velocity”, but in this context the phase velocity could only be defined as the speed of the leading (or trailing) edge of the overall signal.

— Phase, Group, and Signal Velocity

— mathpages

2013.07.02 Tuesday ACHK