Question

A section of rectangular waveguide of cross section $3cm\times 1.5cm$ is to be used as a delay line in a radar at $10GHz$ What should be the length (in meter) of the section to realize a delay of $10nsec$. (assume the waveguide is operating in the dominator mode).

• A. 1.45
• B. 1.11
• C. 2.60
• D. 3.21

Answer 1

The correct option is C 2.60

The length of the waveguide $L=V_{g}t$.

Here $t=10msec$ and $v_g=c\sqrt{1-{\left(\frac{f_{c_{10}}}{f}\right)}^2}$

$\therefore f_{c_{10}}=\frac{c}{2a}=\frac{3\times {10}^{10}}{2\times 3}=0.5\times {10}^{10}=5GHz$

$\therefore v_g=3\times {10}^8\sqrt{1-{\left(\frac{5\times {10}^9}{10\times {10}^9}\right)}^2}=2.6\times {10}^{8}m/sec$

$\therefore L=v_{g}t=2.6\times {10}^8\times 10\times {10}^{-9}=2.6m$