GATE 2021 EC – Question 64
A standard air-filled rectangular waveguide with dimensions $a=8$ cm, $b=4$ cm, operates at 3.4 GHz. For the dominant mode of wave propagation, the phase velocity of the signal is $v_p$. The value (rounded off to two decimal places) of $v_p/c$, where $c$ denotes the velocity of light, is ________.
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Correct answer: 1.19 to 1.21
Explanation
The dominant mode is TE$_{10}$ with cutoff $f_c=\frac{c}{2a}=\frac{3\times10^8}{0.16}=1.875$ GHz. The phase velocity is $\frac{v_p}{c}=\frac{1}{\sqrt{1-(f_c/f)^2}}=\frac{1}{\sqrt{1-(1.875/3.4)^2}}=\frac{1}{\sqrt{0.696}}\approx1.20$.