Should Equation (30) be Revised to '2πfn=2nc'π/L'?

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The discussion centers on a potential correction to the equation "2πfn=2nπ/L," questioning whether it should include the propagation velocity, suggesting "2πfn=2nc'π/L" instead. Key points include the clarification that fn represents a temporal frequency, while n is the mode number and L is the transmission line length. The context involves photon modes in a one-dimensional transmission line, which has two modes propagating in opposite directions. The importance of including the propagation velocity (c') in the equation is emphasized to ensure dimensional consistency, confirming that the original equation cannot be correct without it. The derivation of Johnson noise, which is referenced, is noted to be extensive and requires consulting the original text for full understanding.
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Just above equation (30), it says "2πfn=2nπ/L". Should it be "2πfn=2nc'π/L" instead?
 
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vaatmoly said:
Just above equation (30), it says "2πfn=2nπ/L". Should it be "2πfn=2nc'π/L" instead?
Is fn a spatial or a temporal frequency?
What is n and L?
Maybe you could make pdf of the section, so one can see the context.
 
You have to get the book and read it. It's part of the derivation of Johnson noise. The derivation is several pages long.
 
vaatmoly said:
You have to get the book and read it. It's part of the derivation of Johnson noise. The derivation is several pages long.
Maybe you could just define the quantities in the equation?
 
Yes, sure.
We are considering photon modes in a transmission line(an electromagnetic system in one dimension). The transmission line has 2 photon modes(one propagating in each direction) of frequency "2πfn=2nπ/L" where L is the transmission line length, c' is the propagation velocity on the line, n is the mode number
 
vaatmoly said:
Yes, sure.
We are considering photon modes in a transmission line(an electromagnetic system in one dimension). The transmission line has 2 photon modes(one propagating in each direction) of frequency "2πfn=2nπ/L" where L is the transmission line length, c' is the propagation velocity on the line, n is the mode number
Then it's pretty clear. The frequency has dimension 1/time so you need the c in the equation to get the dimensions right.
The 2nd equation could be right, the 1st can't be.
 

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