# Solved Problems-9

Problem-9
The cross section of a rectangular waveguide is 20 cm Ã— 5 cm. If it is filled with air, find the first six lowest order modes which will propagate through the waveguide and their cut-off frequencies.
Solution
Here, a = 20 cm, b = 5 cm.

The cut-off frequency is given as,

We know that for TEmnp modes, any two indices have to be nonzero; whereas for TMmnp modes, all the indices have to be nonzero. Since a > b, the lowest-order mode will be TE10. Next higher order modes will be TE20TE30TE40TE01TE11 and TM11.

The corresponding cut-off frequencies are given as follows.

Hence, the first six lowest-order modes with their cut-off frequencies are given in this table.

 Mode Resonant Frequency (GHz) TE10 0.75 TE20 1.5 TE30 2.25 TE40 3 TE01 3 TE11 and TM11 3.092