A rectangular waveguide with dimensions a $=9\mathrm{.}0$ cm$,$ b $=4\mathrm{.}5$ cm; contains air inside. It is satisfied that a $>$ b$.$

Determine:

$($a$)10\%$ The frequency range for which the guide propagates only one ET mode, state which.

$($b$)10\%$ The frecquency range for which the guide propagates only three ET modes, indicate which.

For the solution vary m from $0$ to $2,$ and vary n from $0$ to $2,$ generationg all possibilities

f$\_($cET$\_($mn$))=($u$^(\text{'}))/(2)*\backslash$sqrt$(($m$^(2))/($a$^(2))+($n$^(2))/($b$^(2)))$