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phase velocity and group velocity of the deep water wave

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For deep water waves the angular frequency is related to the angular wave number by the following relation:
w^2 = gk g=9.8 m/s2

Such a relationship is called a dispersion relation.
a) Use the fact that the Phase Velocity is defined as v_p = w/k to show that for deep water waves the Phase Velocity is
v_p = sqrt(g/k)

b) Use the dispersion relation and the definition of Group Velocity, v_g = dw/dk , to show that the Group Velocity of deep water waves is

v_g = 1/2*sqrt(g/k) = 1/2v_p

https://brainmass.com/physics/velocity/phase-velocity-group-velocity-deep-water-wave-210407

Solution Preview

For deep water waves the angular frequency is related to the angular wave number by the following relation:

g=9.8 m/s2

Such a relationship is ...

Solution Summary

The solution investigates the phase velocity and group velocity of the deep water wave.

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