What happens when two travelling cosine waves
of the form cos(kx - wt) add
together?
We will vary k and w by small increments dk and dw,
and then add the cosine
functions using the trigonometric identity
cos A + cos B = 2cos((A+B)/2)cos((A-B)/2).
cos((k+dk)x - (w+dw)t) + cos((k-dk)x - (w-dw)t)
= 2cos(kx - wt)cos((dk)x - (dw)t)
Stationary group where the group velocity is zero.
k = 12, w = 2, dk = 1, dw = 0
Moving group where the phase velocity is zero.
k = 12, w = 0, dk = 1, dw = 2
Moving group and phase where both velocities are nonzero.
k = 12, w = 7, dk = 1, dw = 2
