that is equal
to the phase velocity when all components have the same speed.
Depending on the range of frequencies and
velocities, the
pulse can produce the illusion of moving faster or slower than the
individual waves and even it can appear to go backwards.
In the
example above, the pulse is
generated by superposition of two waves of equal amplitude, with phase
velocity equal to 1 and two frequencies (and two wavelengths)
very
close to each other, so that the total wave can be written as:
2 A
cos (K_{1}x
- ω_{1}t)
cos [ (K_{2}
- K_{1}) x
- (ω_{2}
- ω_{1})
t ]