Discussion
The modes in a rectangular waveguide are denoted by TEmn/TMmn, where m and n are the Eigen values along the larger and smaller dimensions of the waveguide respectively. Which one of the following statements is true ?
Answer: A
The true statement is that the TM\(_{10}\) mode does not exist.
For TM modes in a rectangular waveguide, the longitudinal electric field is \(E_{z} \propto \sin(m\pi x/a)\sin(n\pi y/b)\). If either m or n is zero, \(E_{z}\) vanishes everywhere and the whole field is zero, so TM\(_{10}\), TM\(_{01}\) and the like cannot exist; the lowest TM mode is TM\(_{11}\).
TE\(_{10}\) certainly exists: it is the dominant mode, with the lowest cut-off frequency. So TE\(_{10}\) and TM\(_{10}\) do not both exist. The cut-off frequency \(f_{c} = \frac{c}{2}\sqrt{(m/a)^{2} + (n/b)^{2}}\) increases, not decreases, as m and n increase.
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