For an air-filled rectangular cavity made of copper ($\delta_c = 5.8 \times 10^7$ S/m) with dimensions $a = 5$ cm, $b = 4$ cm, $d = 10$ cm and is operating at 3.45 GHz. Determine:
(a) The lowest five order resonant modes,
(b) The cavity quality factor,
(c) The cavity bandwidth.
Hints:
\begin{itemize}
\item For TM modes: $m = 1, 2, 3...$, $n = 1, 2, 3...$ and $p = 0, 1, 2, 3...$
\item For TE modes: $m = 0, 1, 2, 3...$, $n = 0, 1, 2, 3...$ and $p = 1, 2, 3...$
\end{itemize}
Find out the dominant mode and the next mode resonant frequencies first.
