Relation between group velocity and phase velocity

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Homework Help Overview

The discussion revolves around the relationship between group velocity and phase velocity in wave mechanics. Participants are exploring the implications of their assumptions and the mathematical relationships involved.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants are questioning the validity of their initial assumptions regarding the relationship between group and phase velocities. There is a focus on the terms involved in the equations and how they relate to each other.

Discussion Status

Some participants have provided affirmations regarding the correctness of assumptions, while others are still evaluating the completeness of their reasoning. There is an ongoing examination of the mathematical expressions and their implications.

Contextual Notes

There appears to be some confusion regarding the dependencies of the wave number on frequency and other variables, which is being discussed but not resolved.

unscientific
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Homework Statement



k2mnp1.png



Homework Equations





The Attempt at a Solution


2hg8yt1.png


Is my initial assumption wrong?
 
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unscientific said:

Homework Statement



k2mnp1.png



Homework Equations





The Attempt at a Solution


2hg8yt1.png


Is my initial assumption wrong?

No, it's right.
 
rude man said:
No, it's right.

But I seem to be missing out on a 1/vph term..
 
unscientific said:
But I seem to be missing out on a 1/vph term..

You asked if you initial assumption was right. I did not check all your work. Will try later.
 
You wrote dk/dw = (2pi/0)dn/dw.

However, k depends on more than w:
dk = ∂k/∂w dw + ∂k/∂n dn

So 1/vg = dk/dw = ∂k/∂w + ∂k/∂n dn/dw
= n/c + (w/c) dn/dw
Etc.
 

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