THE DISPERSION OF WAVES

In a non-dispersive medium, the velocity of a wave is independent of the wavenumber k, i.e. v = ω/k = constant, and
ω = constant × k.
In a dispersive medium the velocity v = ω/k does depend on the wavenumber k, and so also will the frequency ω = vk. The relationship between the frequency ω and the wavenumber k is called the dispersion relation of the medium. The dispersion relation is determined by the physical properties of the medium. Different media will, in general, have different dispersion relations and these will lead to different wave behaviours. behaviour. Here we want to discuss the general case and in particular to illustrate the difference between phase velocity and group velocity. For this it will suffice to note that in a dispersive medium the frequency ω is a function of the wavenumber k: ω = ω(k).