An air filled rectangular waveguide of inside dimensions 7 X 3.5 cm2oprtates in the dominant mode TE10
The cut-off frequency in the dominant mode is
\(f_c=\frac{c}{2a}=\frac{3\times{10}^8}{2\times7\times{10}^{-2}}=2.14\ GHz\)
The guide wavelength is
\(\lambda_g=\frac{\lambda}{\sqrt{1-\left(\frac{f_c}{f}\right)^2}} = \frac{3\times{10}^8/3.5\times{10}^9\ }{\sqrt{1-\left(\frac{2.14}{3.5}\right)^2}} = \frac{0.0857}{0.791}=10.83\) cm
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