Rectangular waveguide — identify the dominant (lowest-cutoff) mode Which mode is the dominant mode in a standard rectangular metallic waveguide (i.e., has the lowest cutoff frequency)?

Introduction / Context:
Rectangular waveguides support discrete TE and TM modes. The dominant mode is the one with the lowest cutoff frequency and thus the first to propagate as frequency increases. Correctly identifying the dominant mode is fundamental for design and interpretation of waveguide behavior.

Given Data / Assumptions:

• Rectangular guide with broad dimension a and narrow dimension b.
• Perfectly conducting walls (idealized).

Concept / Approach:
Cutoff frequencies are proportional to mode indices: for TE_mn, f_c ∝ sqrt((m/a)^2 + (n/b)^2). The TE10 mode sets m = 1, n = 0, producing the smallest cutoff because it leverages the largest dimension a and requires no field variation along b. Hence TE10 is dominant in rectangular waveguides.

Step-by-Step Reasoning:

Verification / Alternative check:
Standard waveguide charts list TE10 as the dominant mode; practical guides are sized such that operating frequency is above TE10 cutoff and below the next higher-order mode to avoid multimoding.

Why Other Options Are Wrong:

• TE01/TE02/TM11: all have higher cutoff than TE10 in a rectangular guide of the same dimensions.

Common Pitfalls:
Confusing circular (TE11 dominant) with rectangular (TE10 dominant) guides; misreading indices.

Final Answer:
TE10