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.
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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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