Topic: Electromagnetics
The true statement for wave propagation in rectangular wave guides filled with air is
- A. The phase velocity is equal to velocity of light in air
- B. The phase velocity is always more than the velocity of light in air
- C. The phase velocity is always less than the velocity of light in air
- D. The phase velocity is undefined.
Answer: B. The phase velocity is always more than the velocity of light in air
Explanation: Let the velocity of light in air is c, $c=\frac{1}{\sqrt{\mu_{0}\epsilon_{0}}}$. Let $v_{p}$ is the phase velocity of light which is propagated down the guide and is given by $v_{p}=\frac{c}{\cos \theta}=\frac{c}{\sqrt{1-(\frac{f_{c}}{f_{0}})^{2}}}$. Since $\cos\theta \le 1$, so $v_{p} \ge c$. Also from the equation, when the wave can propagate in waveguide when $f_{c}>f_{0}$, so since $\frac{f_{c}}{f_{0}}<1$, $v_{p}>c$. Phase velocity is always greater than velocity of light in air.