Finding group velocity and Phase velocity

In summary, the conversation discusses finding the group velocity and phase velocity for a given wave packet in a dispersive medium, as well as plotting the w-k variation. It is mentioned that the formula for the group velocity is Vg = dw/dk and the formula for the phase velocity is Vp = w/k. The person asking the question is unsure how to proceed and asks for clarification on the role of the cosine term with the lowest 'w'.
  • #1
vivekrai
72
0

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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  • #2
Bump Please!
 

1. What is group velocity and phase velocity?

Group velocity and phase velocity are two important concepts in wave physics. Group velocity refers to the speed at which the overall energy of a wave packet or group of waves is moving. On the other hand, phase velocity refers to the speed at which the individual peaks or crests of a wave are propagating.

2. How are group velocity and phase velocity related?

Group velocity and phase velocity are related through the dispersion relation, which describes the relationship between a wave's frequency and wavelength. In general, the group velocity is equal to the phase velocity multiplied by the wave's group velocity factor, which takes into account the wave's frequency and wavelength.

3. How do you calculate group velocity and phase velocity?

The group velocity and phase velocity can be calculated using the wave's dispersion relation. This typically involves taking the derivative of the dispersion relation with respect to frequency or wavelength. Alternatively, group velocity and phase velocity can also be measured experimentally through various techniques such as interferometry.

4. What is the significance of group velocity and phase velocity?

Group velocity and phase velocity are important in understanding the behavior of waves in different mediums. They can help determine how a wave will propagate, how it will interact with other waves, and how it may be affected by external factors such as boundaries or obstacles.

5. Can group velocity be greater than the speed of light?

No, according to the laws of physics, it is impossible for the group velocity of a wave to exceed the speed of light. However, there are certain cases where the phase velocity may appear to be greater than the speed of light, but this is due to the wave's energy being transferred to the group velocity rather than the phase velocity.

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