  The confinement of high frequency phonons approaching 1 GHz is demonstrated
in phonon-trapping acoustic cavities at cryogenic temperatures using a
low-coupled network approach. The frequency range is extended by nearly an
order of magnitude, with excitation at greater than the 200$^{\text{th}}$
overtone achieved for the first time. Such high frequency operation reveals
Rayleigh-type phonon scattering losses due to highly diluted lattice impurities
and corresponding glass-like behaviour, with a maximum $Q_L\times f$ product of
$8.6\times 10^{17}$ at 3.8K and $4\times10^{17}$ at 15mK. This suggests a limit
on the $Q\times f$ product due to unavoidable crystal disorder. Operation at 15
mK is high enough in frequency that the average phonon occupation number is
less than unity, with a loaded quality factor above half a billion. This work
represents significant progress towards the utilisation of such acoustic
cavities for hybrid quantum systems.
