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
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.
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?