Can the TE01 mode be used in an air-filled rectangular waveguide at 10 GHz?

[faraaa]

Homework Statement

How to solve this problem?

An air-filled waveguide of rectangular cross-section (1 cm x 2 cm) is used to
carry EM waves at a frequency of 10 GHz.
Show that only the TE01 mode can be used?

I tried to find the cut-off frequency ( 7.5GHZ) and is that enough to prove that only TE01 can be used?

 

[rude man]

Homework Statement

How to solve this problem?

An air-filled waveguide of rectangular cross-section (1 cm x 2 cm) is used to
carry EM waves at a frequency of 10 GHz.
Show that only the TE01 mode can be used?

I tried to find the cut-off frequency ( 7.5GHZ) and is that enough to prove that only TE01 can be used?

The answer to your question is no. You haven't justified your answer mathematically.

Use the formula for cutoff frequency f_c(m,n,a,b) where m,n are the mode descriptors T_mn and a and b are the waveguide dimensions. Then show that the only possible mode is TE₀₁. Remember to distinguish between a and b with respect to the cutoff formula.

PS the TM₀₁ mode requires one extra step beyond just using the f_c formula.