Finding group velocity and Phase velocity

AI Thread Summary
The discussion centers on calculating the group velocity (Vg) and phase velocity (Vp) of a wave packet represented by a product of cosine functions. The formulas Vg = dw/dk and Vp = w/k are noted, but the user expresses uncertainty about how to apply them to the given wave packet. There is a question regarding whether the cosine term with the lowest angular frequency (w) serves as the modulating component. The user seeks guidance on the correct approach to solve the problem independently. Clarification on these concepts and their application is requested to aid in understanding.
vivekrai
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Homework Statement



A wave packet in a dispersive medium is given as :
y(t) =cos(x-5t)cos(.2x-.4t)cos(.1x-.2t)
Find group velocity and phase velocity for the wave packet. Hence plot w-k variation for the calculated values.

2. The attempt at a solution

We know that for the wave, Vg = dw/dk and Vp=w/k.

I am clueless on how to proceed from here. Does the cosine term with lowest 'w' acts as the the modulating part? Please enlighten me with the correct information. It's not homework question, I'm trying this on myself so I may miss some critical information on how to approach it. Thanks! :)
 
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