Topic: Microwave Engineering
A cylindrical waveguide with radius of 3.5 cm has waves travelling in $TM_{12}$ mode. The value of $1^{st}$ zero of $2^{nd}$ order Bessel function is 7. Find the cut-off wavelength for this mode.
- A. $\pi$ cm
- B. $1.5\pi$ cm
- C. $2 \pi$ cm
- D. $\pi/2$ cm
Answer: A. $\pi$ cm
Explanation: For a circular (cylindrical) waveguide operating in the $TM_{np}$ mode, the cutoff wavelength is given by $\lambda_c = \frac{2\pi r}{p_{np}}$, where $r$ is the radius and $p_{np}$ is the corresponding root of the Bessel function. Substituting $r = 3.5$ cm and $p_{12} = 7$, we get $\lambda_c = \frac{2\pi(3.5)}{7} = \frac{7\pi}{7} = \pi$ cm.