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

  • Thread starter Thread starter vaatmoly
  • Start date Start date
AI Thread Summary
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.
vaatmoly
Messages
7
Reaction score
1
Just above equation (30), it says "2πfn=2nπ/L". Should it be "2πfn=2nc'π/L" instead?
 
Physics news on Phys.org
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.
 

Thread 'Hassani's books on Mathematical Physics/Methods'

By looking around, it seems like Dr. Hassani's books are great for studying "mathematical methods for the physicist/engineer." One is for the beginner physicist [Mathematical Methods: For Students of Physics and Related Fields] and the other is [Mathematical Physics: A Modern Introduction to Its Foundations] for the advanced undergraduate / grad student. I'm a sophomore undergrad and I have taken up the standard calculus sequence (~3sems) and ODEs. I want to self study ahead in mathematics...
View full post »

Similar threads

I Adding total time derivative to Lagrangian/Canonical Transformations
Replies
2
Views
306
A The Lagrangian of a free particle ##L=-m \, ds/dt##
Replies
3
Views
518
I A sufficient condition for integrability of equation ##\nabla g=0##
2
Replies
71
Views
1K
A Decomposition of SU(2)-invariant spin network state in 3 dimensions
Replies
0
Views
1K
B Parametric Representation of Lines
Replies
13
Views
3K
EMF induced in moving rod in B-field, why is "L" length of wire frame?
Replies
4
Views
795
A Converting momentum sums to integrals in curved spacetime
Replies
1
Views
2K
I Mathematical proof for the Lagrangian function
Replies
4
Views
1K
I Why do the lines m and l coincide in the proof of the parallelogram rule?
Replies
4
Views
2K
How to solve this driven RLC circuit?
Replies
13
Views
1K

Hot Threads

Recent Insights

Back
Top