Question

The modes in a rectangular waveguide are denoted by TE_mn/TM_mn where m and n are the eigen numbers along the larger and smaller dimensions of the waveguide respectively. Which one of the following statements is TRUE?
1. The TM₁₀ mode of the waveguide does not exist
2. The TE₁₀ mode of the waveguide does not exist
3. The TM₁₀ and the TE₁₀ modes both exist and have the same cut-off frequencies
4. The TM₁₀ and the TM₀₁ modes both exist and have the same cut-off frequencies

Answer 1

Correct Answer - Option 1 : The TM₁₀ mode of the waveguide does not exist

For a TE_mn mode to exist, We need to have  m,n = 0,1,2,......

but does not exist for m = n = 0. For all other combinations TE_mn exists.

For a TM_mn mode to exist, We need to have m,n = 1,2,3, ....... i.e m & n both must be non-zero

⇒ TM₀₁, TM₁₀ modes do not exist

 Waveguides only allow frequencies above the cut-off frequency to pass through. It blocks or attenuates the frequencies below the cut-off frequencies.

The cut off frequency is mathematically calculated as:

\({{f}_{c\left( min \right)}}=\frac{c}{2}\sqrt{{{\left( \frac{m}{a} \right)}^{2}}+{{\left( \frac{n}{b} \right)}^{2}}}\)

Where a and b are the dimensions of the waveguide

m and n are mode numbers TEmn.