# What is the value of the major cross-sectional dimension(width) of a rectangular waveguide with dominant TE10 mode propagation, if its cut off frequen

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What is the value of the major cross-sectional dimension(width) of a rectangular waveguide with dominant TE10 mode propagation, if its cut off frequency is 10 GHz?
1. 15 mm
2. 30 mm
3. 7.5 mm
4. 45 mm

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Correct Answer - Option 1 : 15 mm

Concept:

The dominant mode in a particular waveguide is the mode having the lowest cut-off frequency.

The cut-off frequency for a rectangular waveguide with dimension ‘a (length)’ and ‘b (width)’ is given as:

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

'm' and 'n' represents the possible modes.

c = speed of light = 3 × 1010 cm/s

Calculation:

TE10 mode means m = 1, n = 0

The cut - off frequency of the dominant mode TE10 of the rectangular waveguide is:

${f_c} = \frac{c}{{2a}}$

Where a is the dimension of the inner broad wall

$\begin{array}{l} a = 3 \times \frac{{{{10}^{10}}}}{{2 \times 10 \times {{10}^9}}}\\ a = 1.5\;cm \end{array}$

= 15 mm