# 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

141 views
in General
closed
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

by (60.0k points)
selected

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
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}