Understanding the Three Velocities of Light: Phase, Group, and Signal

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SUMMARY

The discussion confirms the existence of three velocities of light: Phase, Group, and Signal. It clarifies that these velocities apply to traveling waves, not standing waves, which have a Phase velocity of zero. The group velocity is defined mathematically as v_G = ∂ω/∂k, where ω is a slowly varying function of k. The group velocity typically represents the signal velocity and is considered the velocity of transport for the dominant frequency component, as noted in Jackson's second edition on page 319.

PREREQUISITES
  • Understanding of wave mechanics and terminology
  • Familiarity with the mathematical representation of wave functions
  • Knowledge of the concepts of Phase, Group, and Signal velocities
  • Basic grasp of Taylor series expansions in physics
NEXT STEPS
  • Study the mathematical derivation of Group velocity in wave mechanics
  • Explore the implications of Phase velocity in standing waves
  • Investigate the relationship between Group velocity and information transfer
  • Read Jackson's "Classical Electrodynamics" for deeper insights on wave propagation
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Physicists, students of wave mechanics, and anyone interested in the properties of light and wave propagation will benefit from this discussion.

LarryS
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I believe there are three possible velocities of light: Phase, Group and Signal? Is that correct? Does a standing wave have a Phase velocity of zero? What is an example in which the Signal and Group velocities would be different? Obviously, I need clarification on this whole subject. Thanks in advance.
 
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The P, G, and S velocities are defined for a traveling wave, and do not apply for a standing wave.
v_G=\frac{\partial\omega}{\partial k} is the signal velocity if the higher terms in a Taylor expansion of \omega(k) are negligible. That is when
\omega is a slowly varying function of k.
 
From Jackson (page 319 in the second edition):

"The general usage is to take the group velocity of the dominant frequency component as the signal velocity and velocity of transport. This suffices in most circumstances, but with sensitive enough detectors the signal velocity can evidently be pushed close to the velocity of light in vacuum, independent of the medium."
 

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