Topic: Electromagnetics
At cut-off frequency, the phase velocity of a waveguide is
- A. zero
- B. infinite
- C. finite
- D. none of the above
Answer: B. infinite
Explanation: Phase velocity $v_{p} = \frac{c}{\sqrt{1-(f_{c}/f_{o})^{2}}}$. As the wave frequency $f_{o}$ approaches the cut-off frequency $f_{c}$, then $f_{c}/f_{o}$ reaches 1. Therefore $1-(f_{c}/f_{o})^{2} \approx 0$, so $v_{p} = \frac{c}{0} \rightarrow \infty$.