The difference between wave propagation in dispersive and non-dispersive media can be effectively demonstrated by observing the wave patterns invoked by uniformly moving surface disturbances. Although the dispersion relation of surface waves on water is complicated, there are some frequency intervals where the phase velocity of the waves reduces to the simple power law behavior cpωκ. Among these cases are gravity waves short compared to the depth of the water (κ=1), short capillary waves (κ=1/3), and long waves in shallow water (κ0). Making use of this power-law behavior, we vary the exponent and visualize the smooth transition from a non-dispersive to a dispersive medium.

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