Question

The EM wave which does not propagate through a rectangular waveguide with a = 30 mm & b = 15 mm is:
1. EM wave of frequency 4.5 GHz
2. EM wave of frequency 5.5 GHz
3. EM wave of frequency 50 GHz
4. EM wave of frequency 300 GHz

Answer 1

Correct Answer - Option 1 : EM wave of frequency 4.5 GHz

Concept:

Dominant Mode: 

1. The dominant mode in a particular waveguide is the mode having the lowest cutoff frequency.

2. For rectangular waveguide, this is the TE₁₀ mode.

3. The critical frequency for the dominant mode is given as:

\({f_c} = \frac{c}{2}\sqrt {{{\left( {\frac{m}{a}} \right)}^2} + {{\left( {\frac{n}{b}} \right)}^2}} \;\)

Where a and b are sides of the rectangle in cm,

m and n describe the mode.

For TE₁₀ mode:

\(f_c=\frac{c}{2a}\)

Calculation:

Given:

a = 30 mm  

b = 15 mm

For TE₁₀ mode,

\(f_c \ = \ \frac{3 \ \times \ 10^8}{2 \ \times \ 30 \ \times \ 10^-3}\)

\(f_c \ = \ 5 \ GHz\)

So, the waves having the frequency above cutoff frequency (f_c) will only pass.

Hence from the options given 4.5 GHz will not pass.

Hence the solution is a option (1).