Solution:

$\lambda_c=\frac{2 a b}{\sqrt{m 2 b 2+n 2 a 2}}\\$ Here, $a=2 \times 10^{-2} \mathrm{~m} ; \quad b=5 \times 10^{-2} \mathrm{~m}\$

Thus, Cutoff Wave length $\lambda_{\mathrm{c}}=9.285 \mathrm{~cm}$ and $\mathrm{f}_{\mathrm{c}}=\frac{c}{\lambda c}=3.23 \mathrm{GHz}\\$. Wave impedance for TM mode $=\eta \sqrt{1-\left(\frac{f c}{f}\right)^2}\$

$=377 \sqrt{1-\left(\frac{3.23}{9}\right)^2}\\$ $=351.8$ ohms