**Solution:**

A resonator is a device that exhibits resonance at a particular frequency called resonance frequency. Cavity resonators are constructed by sharing both ends of a guide.

When the canty is excited through probes, with a signal frequency equal to the resonant frequency decided by waveguide dimensions, a resonance is created.

The resonant frequency is expressed as for TE

$$
\begin{aligned}
& a=22.86 \mathrm{~mm} \\
& b=10.16 \mathrm{~mm} \\
& d=15 \mathrm{~mm}
\end{aligned}
$$

$\begin{aligned} f_{\text {or }} & =f_{101}=\frac{v_p}{2} \sqrt{\left(\frac{m}{a}\right)^2+\left(\frac{n}\\{b}\right)^2+\left(\frac{p}{d}\right)^2} \\ f_e & \left.=\frac{1}{2 \pi \sqrt{\mu_0 \varepsilon_0}}-\sqrt{\left(\frac{m \pi}\\{a}\right)^2+\left(\frac{n \pi}{b}\right)^2+\left(\frac{p \pi}{d}\right)^2}\right] \\ & =11.96\mathrm{CH}_2\end{aligned}$