# phase velocity question.

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i was intrigued by how to solve this.

the phase velocity of ocean waves is sqrt(g*lambda/2*pi) where g - acceleration due to gravity, lambda is the wavelength of the wave. The question is find the group velocity.

I tried many things but was not able to get to a proper answer. Any help?

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Can you write down the equation for the phase velocity and the equation for the group velocity?

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vp -> phase velocity

vg -> group velocity

generally vp ->c^2(speed of light squared)/vg

Doing that and substituting does not give me a satisfactory answer.

On a more conceptual note -> group velocity is the rate of change of angular velocity('delta'omega) with the change in wave number('delta'k). Phase velocity is omega/k , that is at any particular instant. So to get the group velocity I could also differentiate omega with respect to k, but I do not know anything about them either.

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Your second part is correct. The first is a special case.

$v_g = \frac {d \omega} {dk}$

$v_p = \frac { \omega} {k} = \frac {\lambda} {T}$

$v_p = \sqrt{g*\lambda/2*pi}$

From that you can make some substitutions and find vg

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