These analysis uses cylindrical coordinates.
In circular waveguide TE11 mode has the lowest cut off frequency and is the dominant mode.
If D is diameter of waveguide
?c = 1.706 D for TE11 mode
?c = 1.029 D for TE21 mode
?c = 0.82 D for TE01 mode
?c = 1.306 D for TM01 mode.
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