What is the relationship between frequency and cross section in a waveguide?

[Roodles01]

I have a question relating to waveguides. Fine, but having looked at what TE TM modes are I don't really see how I can find the frequency of the μwave with the information I have.

Homework Equations

A waveguide with dimensions a & b (short & long sides respetively) propogates in the TM₁₀ mode.

What is the frequency of the μwave?

Now, I have as a clue "the possible modes for f can be found from the guide dimension & wavelength λ. Where λ= c/f

Lovely, but what is the relationsip of f & cross section to λ?

The Attempt at a Solution

Surely this is simple enough NOT to have to go into Maxwell's curl equations!

I just don't have enough information!
Confused, simple!

 

[Dickfore]

Do you know what a wavevector is?

 

[Roodles01]

I have some idea, yes.
A vector in 3 dimensions with magnitude & direction which helps to describe a wave.

 

[Dickfore]

OK, now if you know the wavevector, can you calculate the frequency of the wave?

 

[Roodles01]

No. I don't think i have enough information.
I don't know which equation to use.
I also don't have a wave number, k, etc. which I need for k = (2*pi)/λ
Sorry.

 

[Dickfore]

$$\omega = 2 \pi f = \frac{2 \pi}{\lambda} c = c k$$

 

[Roodles01]

again I'm back to λ= c/f without 2 variables.

 

[Dickfore]

The point is, the transversal components of the wave vector $\vec{k}$ can only get discrete values.

 

[rude man]

I have a question relating to waveguides. Fine, but having looked at what TE TM modes are I don't really see how I can find the frequency of the μwave with the information I have.

Homework Equations

A waveguide with dimensions a & b (short & long sides respetively) propogates in the TM₁₀ mode.

What is the frequency of the μwave?

Now, I have as a clue "the possible modes for f can be found from the guide dimension & wavelength λ. Where λ= c/f

Lovely, but what is the relationsip of f & cross section to λ?

The Attempt at a Solution

Surely this is simple enough NOT to have to go into Maxwell's curl equations!

I just don't have enough information!
Confused, simple!

Not enough info.

Any frequency higher than the cutoff frequency can propagate, limited only by the finite conductivity of the waveguide.

The cutoff freq. for your waveguide is √{(1/4πε)(1/a²)} SI.

 

[Roodles01]

OK. I have, as dimensions short side a = 4cm & long side b = 5cm
I'm still working at it.