The effect of acoustic oscillations of the alpha-quartz crystalline la
ttice on the behaviour of muonium polarization has been studied experi
mentally. It is shown that when the frequency of the standing ultrasou
nd wave coincides with one of the muonium quadrupole interaction frequ
encies a specific broadening of the muonium line occurs; that is a muo
nium acoustic resonance is observed. The possibilities of using this e
ffect for investigating properties of solids by the muSR method are di
scussed.