gokul.er137 Posted August 16, 2009 Share Posted August 16, 2009 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? Link to comment Share on other sites More sharing options...
Klaynos Posted August 16, 2009 Share Posted August 16, 2009 Can you write down the equation for the phase velocity and the equation for the group velocity? Link to comment Share on other sites More sharing options...
gokul.er137 Posted August 16, 2009 Author Share Posted August 16, 2009 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. Link to comment Share on other sites More sharing options...
Klaynos Posted August 16, 2009 Share Posted August 16, 2009 Your second part is correct. The first is a special case. [math] v_g = \frac {d \omega} {dk}[/math] [math] v_p = \frac { \omega} {k} = \frac {\lambda} {T} [/math] [math] v_p = \sqrt{g*\lambda/2*pi} [/math] From that you can make some substitutions and find vg Link to comment Share on other sites More sharing options...
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