Major confusion: harmonic waves

[StephenPrivitera]

"In contrast to the case of a harmonic wave on a string, a harmonic wave in a dispersive medium cannot be regarded as a simple succession of wave pulses because the pulses change their shape, whereas a harmonic wave does not."
Is this self-contradictory or is it just me? A harmonic wave in a dispersive medium has pulses which change shape, but a harmonic wave does not have pulses which change shape. What is the author trying to say?
Next sentence,
"There is then no simple connection between the speed of a wave pulse and the speed of a harmonic wave."
What's the difference?
"We call the speed of the peak of a wave pulse the group velocity."
I looked this up. It is
v=dw/dk where w is the angular frequency and k is the wave number
How would I take this derivative(ie, how do I write w=f(k))?
Why would w and k change?

 

[Aaron Bex]

The group velocity is the speed of the peak of a wave pulse. It is calculated by taking the derivative of the angular frequency (w) with respect to the wave number (k). The angular frequency and wave number can change depending on the dispersive medium and the frequency of the wave.