Finding group velocity and Phase velocity

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SUMMARY

The discussion focuses on calculating the group velocity (Vg) and phase velocity (Vp) of a wave packet represented by the equation y(t) = cos(x - 5t)cos(0.2x - 0.4t)cos(0.1x - 0.2t). The relationship Vg = dw/dk and Vp = w/k is established as the foundation for these calculations. The participant seeks clarification on identifying the modulating term within the cosine functions to proceed with the analysis. The conversation emphasizes the importance of understanding wave packet behavior in dispersive media.

PREREQUISITES
  • Understanding of wave mechanics and wave packets
  • Familiarity with the concepts of group velocity and phase velocity
  • Knowledge of calculus, specifically differentiation
  • Experience with trigonometric functions and their properties
NEXT STEPS
  • Study the derivation of group velocity and phase velocity in wave mechanics
  • Learn about dispersion relations in different media
  • Explore the application of Fourier transforms in wave packet analysis
  • Investigate plotting w-k (angular frequency vs. wave number) variations for wave packets
USEFUL FOR

Students and professionals in physics, particularly those studying wave mechanics, as well as educators looking to enhance their understanding of wave packet behavior in dispersive media.

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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