In a standard hollow rectangular waveguide, which mode has the minimum (lowest) cutoff frequency among all allowed modes?

Introduction / Context:
Rectangular waveguides guide energy as discrete modes. The mode that begins to propagate at the lowest frequency is called the dominant mode. Knowing the dominant mode is essential for sizing the guide and predicting single-mode bandwidth.

Given Data / Assumptions:

• Hollow rectangular waveguide with dimensions a (broad wall) and b (narrow wall).
• Air-filled guide (effective speed ≈ c).
• Comparing cutoff frequencies of several low-order modes.

Concept / Approach:

The cutoff frequency for TEmn is f_c = (c/2) * sqrt((m/a)^2 + (n/b)^2). For TE10 (m=1, n=0), f_c = c/(2a), which is lower than TE20 (m=2), TE01 (n=1), TE11 (m=1, n=1), and any TM mode because additional indices increase f_c.

Step-by-Step Solution:

Verification / Alternative check:

Mode charts and measured transmission show TE10 propagates first; higher modes appear only as frequency increases.

Why Other Options Are Wrong:

• TE11, TE01, TE20, TM11: All have higher cutoffs than TE10 for the same guide.

Common Pitfalls:

Assuming TE01 could be dominant—only true if b were greater than a, which contradicts “broad wall” terminology.

Final Answer:

TE10