Major confusion: harmonic waves

  1. "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?
  2. jcsd
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