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Waveguides and Cavity resonator Equation confusion

  1. Mar 13, 2015 #1
    1. The problem statement, all variables and given/known data
    This is not a homework question and I am asking this question out of curiosity. We have been taught rectangular wave guides and cavity resonator recently and I don't want to gulp the wave equations as it is, so the problem that I am facing ( I have written it on paper and uploaded the photo) . Don't know if my question is stupid but it really confuses me .

    2. Relevant equations

    3. The attempt at a solution

    Attached Files:

  2. jcsd
  3. Mar 16, 2015 #2
    I don't know exactly what is your problem but I assume you confuse why in rectangular wave guide we set d^2/dz^2=Gama^2 but in cavity d^2/dz^2=-Kz^2?
    As you know in the wave guide we transfer a wave in Z direction and it goes through wave guide with it's wave coefficient (Beta) but in cavity a wave repeat simultaneously in the cavity in +Z and -Z direction to create a fix resonator so it should be in sinusoidal form
  4. Mar 16, 2015 #3
    Yes this is what I am confused about. Thank you for reply :) , it helped a lot . So this means I am making changes in equation because I know that in resonator my wave has to be a standing wave rather being a propagating one in +z or -z direction.
  5. Mar 16, 2015 #4
    Yes of course ,However you can try to solve wave equation in cavity and use separation variables to obtain it's answers after that you should add two new boundary condition ( E tangential in EZ(0)=EZ(d)=0 )that only a sinusoidal form can prove that.
  6. Mar 16, 2015 #5
    Thank you :)
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