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I have been able to confuse myself: I am studying the form of the modes in a rectangular waveguide: enter image description here

I understand that each mode has a different spatial distribution, but what I dont understand is if all the modes have the same frequency?

or each spatial distribution has a different frequency?

I hope you can help me Thank you

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    $\begingroup$ in a longitudinally homogeneous waveguide the mode shapes are frequency independent $\endgroup$
    – hyportnex
    Commented Aug 28, 2020 at 14:28

1 Answer 1

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Your pictures show square waveguides. For this case the frequencies are proportional to $\sqrt{m^2+n^2}$, where m and n are the number of bumps in each direction. For your pictures this gives the frequency ratios $1:\sqrt{2}:1:\sqrt{2}$ and $\sqrt{2}:\sqrt{3}:\sqrt{3}:2$.

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