Topic: Electromagnetics
Which of the following is True for signal travelling through a Wave-Guide?
- A. Guide wavelength is longer than free space wavelength
- B. Guide wavelength is equal to free space wavelength
- C. Guide wavelength is shorter than free space wavelength
- D. None of the above
Answer: A. Guide wavelength is longer than free space wavelength
Explanation: The relationship between guide wavelength ($\lambda_g$), free-space wavelength ($\lambda_0$), and cutoff wavelength ($\lambda_c$) is given by $\frac{1}{\lambda_g^2} = \frac{1}{\lambda_0^2} - \frac{1}{\lambda_c^2}$. Solving for $\lambda_g$, we get $\lambda_g = \frac{\lambda_0}{\sqrt{1 - (\lambda_0 / \lambda_c)^2}}$. Because the term in the denominator is always less than 1 (for frequencies above cutoff), the guide wavelength $\lambda_g$ is always greater (longer) than the free space wavelength $\lambda_0$.