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Homework Help: Microwaves in waveguides

  1. Jun 24, 2012 #1
    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. jcsd
  3. Jun 24, 2012 #2
    Do you know what a wavevector is?
  4. Jun 24, 2012 #3
    I have some idea, yes.
    A vector in 3 dimensions with magnitude & direction which helps to describe a wave.
  5. Jun 24, 2012 #4
    OK, now if you know the wavevector, can you calculate the frequency of the wave?
  6. Jun 24, 2012 #5
    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
    Last edited: Jun 24, 2012
  7. Jun 24, 2012 #6
    \omega = 2 \pi f = \frac{2 \pi}{\lambda} c = c k
  8. Jun 24, 2012 #7
    again I'm back to λ= c/f without 2 variables.
  9. Jun 24, 2012 #8
    The point is, the transversal components of the wave vector [itex]\vec{k}[/itex] can only get discrete values.
  10. Jun 24, 2012 #9

    rude man

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    Homework Helper
    Gold Member

    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.
  11. Jun 25, 2012 #10
    OK. I have, as dimensions short side a = 4cm & long side b = 5cm
    I'm still working at it.
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