Rectangular waveguide — frequency window for single-mode TE10 operation To ensure that only the dominant TE10 mode propagates in a rectangular waveguide, the operating frequency must…

Introduction / Context:
Rectangular waveguides support discrete TE/TM modes, each with a cutoff frequency. For clean, single-mode transmission, designers operate the guide between the cutoff of the dominant mode (TE10) and the cutoff of the next higher mode (often TE20 for typical aspect ratios). This question asks for the correct condition to guarantee only TE10 propagates.

Given Data / Assumptions:

• Rectangular guide of broad dimension a and narrow dimension b.
• Dominant mode: TE10 (lowest cutoff).
• Next relevant higher mode: TE20 for many standard guides.

Concept / Approach:
Guided modes propagate only when the operating frequency f exceeds their cutoff frequency f_c. For single-mode TE10 operation, we must have f above f_c(TE10) so that TE10 propagates, and simultaneously below f_c of all higher modes to keep them evanescent. In standard rectangular guides, f_c(TE20) is the next threshold to avoid. Therefore:

Step-by-Step Solution:

Verification / Alternative check:
Textbook mode charts show TE10 cutoff f_c = c/(2a) and TE20 cutoff f_c = c/a. Practical bands are chosen well within this window to allow manufacturing tolerances.

Why Other Options Are Wrong:

• A: True but incomplete; does not prevent higher modes.
• B: True but incomplete; does not guarantee TE10 is above cutoff.
• D: Would block TE10 entirely, so no propagation.

Common Pitfalls:
Operating too close to either cutoff (excess dispersion/loss near f_c) or forgetting about the next higher cutoff in multimode avoidance.

Final Answer:
must be more than cutoff frequency of TE10 mode and less than cutoff frequency of TE20 mode