# Conductivity of Waveguides

1. Dec 7, 2008

### unstoppable

1. The problem statement, all variables and given/known data
At frequency f1=9 GHz, the guide wavelength along a certain dielectric-filled conducting waveguide is found to be Lambda1=3.456 cm, for a particular mode. At frequency f2=10GHz, the wavelength is Lambda2=2.345 cm, for the same mode.

(a) What is the cutoff frequency Fo of that mode?

(b) What is the relative permitttivity epsilon of the dielectric

2. Relevant equations

Lambdag=Vp/f where Lambdag is the wavelength along the waveguide.

Vp=omega/Beta=c/n*[1-(omegac/omega)^2]^-1/2 where Vp is the phase velocity.

3. The attempt at a solution

I first solved for Vp using Lambdag=Vp/f and then I plugged in the numerical value for Vp=Lambdag*f and then I solved for Omegac which is the cutoff frequency from the above equation Vp=c/n*[1-omegac/omega^2]^-1/2. However, I am not getting the correct answer. Any ideas on what I should do?

2. Dec 8, 2008

### turin

Is this problem for a physics course or an engineering course? If engineering, do you have Paul and Nasar, Introduction to Electromagnetic Fields?

Does the "g" in "Lambdag" denote "guide" or "group"? (It should denote "guide".)

Hint 1a: How do you know n?
Hint 1b: You are given two sets of f and lambda. Why do you suppose that is?
Hint 2: f is not the same thing as omega.

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