Review of Traveling Waves

The phase of the wave goes through
in one wavelength in
.
So the wavelength
satisfies

Similarly the phase goes through
in one period
in time.

is the angular frequency. It changes by
every cycle.
The frequency
increases by 1 every cycle so

There is no reason to memorize these equations. They should be obvious.

Lets see how fast one of the peaks of the wave moves. This is called the phase velocity.
At time
, there is a peak at
. This is the peak for which the argument of cosine is 0.
At time
, the argument is zero when
or at
.
If we compute the phase velocity by taking
, we get

That is, one of the peaks of this wave travels with a velocity of .

In non-relativistic QM, we have
,
, and
, so

You may remember that a pulse will move at the group velocity which is given by

(The phase velocity for the non-relativistic case is .)

Jim Branson 2013-04-22