Phase velocity, Group velocity

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SUMMARY

Phase velocity and group velocity are critical concepts in wave mechanics, particularly when analyzing signal propagation through media such as crystals. The phase velocity refers to the speed at which a wave phase propagates, while group velocity is the speed at which the overall envelope of the wave packet travels. For a Gaussian-shaped signal, the maximum intensity can be determined using the formula t = z/(group velocity), evaluated at the frequency of largest intensity. Understanding these definitions is essential for accurately describing wave behavior in various physical contexts.

PREREQUISITES
  • Understanding of wave mechanics
  • Familiarity with Gaussian functions in the frequency domain
  • Knowledge of signal propagation in different media
  • Basic mathematical skills for evaluating wave equations
NEXT STEPS
  • Study the mathematical derivation of phase and group velocity
  • Explore the implications of dispersion in wave propagation
  • Learn about the applications of group velocity in optics and telecommunications
  • Investigate the relationship between wave packets and signal integrity
USEFUL FOR

Physicists, engineers, and students studying wave mechanics, optics, and signal processing will benefit from this discussion, particularly those looking to deepen their understanding of wave propagation phenomena.

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Would someone be kind enough to please give physical meanings to these two terms? I have never fully understood their meaning and difference (although I know how to express them mathematically).

If, say, I have a Gaussian-shaped signal in the frequency domain that I am sending through a medium (such as a crystal) in the direction z say and I want to specify where the maximum intensity is as a function of t (it is at z=0 when t=0), am I right in saying that I would use:

t= z/(group velocity)

where the group velocity is obviously evaluated at the frequency of largest intensity.

Any help on this fairly basic matter would be much appreciated.
 
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Thank you, I shall have a look but I actually think that I have a good enough understanding now having read a few relevant sections in the Feynman Lectures (sorry, this is what I should have done first).
 

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