The dominant TE10 cutoff is $c/(2a)=6.56168$ GHz. The next cutoffs TE20≈13.123 GHz and TE01≈14.764 GHz exceed 10 GHz, so TE10 is the only propagating mode.
Its phase constant is $\beta=\sqrt{(2\pi f/c)^2-(\pi/a)^2}$ with a=0.02286 m.
Using c=$3\times10^8$ m/s gives **β≈158.24 rad/m**, in the official 155–162 interval.
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