What's the Difference Between Phrase Velocity and Omega?

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Discussion Overview

The discussion centers around the differences between phase velocity and angular frequency (omega) in the context of wave equations. Participants explore definitions, relationships, and distinctions between phase velocity and group velocity, as well as their implications in specific physical scenarios.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant humorously misinterprets "phase velocity" as "phrase velocity" before clarifying the context relates to wave equations.
  • Another participant explains that omega is the angular frequency related to the usual frequency by the equation ω = 2πf, and describes phase velocity as the speed at which a wave crest travels.
  • A participant questions the difference between phase velocity and group velocity, suggesting they seem similar.
  • In response, another participant provides an animation link illustrating that individual waves move at phase velocity while the group moves at group velocity, noting that phase velocity can appear to move backwards relative to the group.
  • Further clarification is provided that phase velocity is calculated as ω/k, while group velocity is defined as dω/dk, with both derived from the dispersion relation ω(k).
  • A specific example is mentioned regarding nanosized magnetic materials where phase velocity can be opposite in direction to group velocity, highlighting a unique case in the dispersion relation.

Areas of Agreement / Disagreement

Participants express varying levels of understanding and clarification regarding the concepts, but there is no explicit consensus on the implications of phase and group velocities in all contexts. The discussion remains open-ended with multiple viewpoints presented.

Contextual Notes

Participants reference animations to illustrate concepts, indicating a reliance on visual aids for understanding complex relationships. The discussion includes specific examples that may depend on particular physical conditions or definitions.

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phrase velocity and "omega"

what's the difference between phrase velocity and "omega"?
 
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Phrase velocity depends on how fast you can talk. :smile: :smile:

No wait, you're asking about wave equations like this one, right?

y = A \sin (kx - \omega t)

\omega is the angular frequency of the wave, in radians per second. It's related to the usual frequency (cycles per second) by the number of radians per cycle: \omega = 2 \pi f. Both describe the rate at which any particular point on the wave oscillates up and down (or back and forth, or whatever).

Phase velocity (not "phrase velocity") is how fast a "crest" of the wave moves in the direction the the wave is traveling in. You can calculate it either as period/wavelength (think distance/time), or as \omega / k.
 
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i see... then what's the difference between phase velocity and group velocity?
they seem similar~
 
Try this animation:

http://www.phys.virginia.edu/classes/109N/more_stuff/Applets/sines/GroupVelocity.html

The individual waves in the group move at the phase velocity. The shape of the group as a whole (the "envelope" of the individual waves) moves at the group velocity.

In the initial settings for this animation, the phase velocity is smaller than the group velocity, so the individual waves appear to be moving backwards with respect to the groups, although they're actually moving forwards in an absolute sense.
 
Last edited by a moderator:
thank you very much! :)
 
The important difference is that while the phase velocity is given by \omega/k, the group velocity is d \omega /dk. Both are determined from the dispersion relation \omega(k)

To bring out the contrast, in certain nanosized magnetic materials, it is possible to have spin-wave modes (magnons), where the phase velocity is opposite in direction to the group velocity. The dispersion relation is a positive-valued curve with a negative slope.

See this animation (the last of the 6 files) :

http://www.csupomona.edu/~ajm/materials/animations/packets.html
 
Last edited by a moderator:
thanks! :)
 

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