# Homework Help: Microwaves in waveguides

1. Jun 24, 2012

### 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.

2. Relevant 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?

3. 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!

Last edited: Jun 24, 2012
2. Jun 24, 2012

### Dickfore

Do you know what a wavevector is?

3. Jun 24, 2012

### Roodles01

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

4. Jun 24, 2012

### Dickfore

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

5. Jun 24, 2012

### 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.

Last edited: Jun 24, 2012
6. Jun 24, 2012

### Dickfore

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

7. Jun 24, 2012

### Roodles01

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

8. Jun 24, 2012

### Dickfore

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

9. Jun 24, 2012

### rude man

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.

10. Jun 25, 2012

### Roodles01

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