= Solution
An empty perfectly conducting rectangular <electromagnetic waveguide> has
$$
\omega^2=c^2\left[k_z^2+\pi^2\left(\frac{m^2}{a^2}+\frac{n^2}{b^2}\right)\right].
$$
The lowest <transverse electric mode> has indices $(1,0)$ or $(0,1)$. A simply connected hollow metallic guide has no <transverse electromagnetic mode>. With $a=b=10^{-2}\,\mathrm m$, the two lowest modes are degenerate and their <cutoff frequency> is
$$
\boxed{f_c=\frac{c}{2a}\simeq15.0\,\mathrm{GHz}.}
$$
Propagation with nonzero axial energy transport requires $f>f_c$; the equality is the lower limiting frequency, with zero axial <group velocity>. A filling medium would replace $c$ by $1/\sqrt{\mu\epsilon}$.
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