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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

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Solution Summary

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

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 ...

Purchase this Solution


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