Final answer:
To discern which TE modes would propagate in the given rectangular waveguide, one must calculate the cutoff frequencies for different modes and compare them to the driving frequency of 1.70×10¹⁰ Hz.
Step-by-step explanation:
To determine which TE modes will propagate in a rectangular waveguide, you need to consider the waveguide's dimensions and the frequency of the electromagnetic wave. The cutoff frequency for any TEmn mode in a rectangular waveguide is given by:
fc = (1/2) √{ (m/a)^2 + (n/b)^2 } × (c/√{εr})
where:
- m and n are the mode numbers,
- a and b are the waveguide dimensions,
- c is the speed of light in vacuum,
- εr is the relative permittivity of the material inside the waveguide (assuming it's air, εr is approximately 1).
Given a rectangular waveguide with dimensions a = 2.28 cm and b = 1.01 cm and a driving frequency of f = 1.70×1010 Hz, you calculate the cutoff frequency for different modes and observe if they are lower than the driving frequency. If the cutoff frequency of a mode is lower than the driving frequency, the mode will propagate.
Using the formulae and dimensions provided, you can calculate the cutoff frequency for the fundamental TE10 mode and find out which higher modes, such as TE01, TE11, etc., can also propagate at the given frequency.