A YIG disk with parallel and polished surfaces was bonded onto a quartz rod with a transducer attached to it. The YIG sample was placed in a microwave cavity in a parallel-pumping configuration. For microwave power several decibels above the threshold for spin-wave instability, parametric generation of low-frequency acoustic waves was observed, and was accompanied by the simultaneous appearance of low-frequency modulation of the microwave reflected power. The effects were attributed to the beating of spin-wave side bands with the central band. The existence of side bands was confirmed by measuring the spin-wave spectrum. In the mode-locking experiment, a low-frequency acoustic wave was sent into the YIG sample through the transducer. Experimental evidences show that the acoustic wave, through magnetoelastic coupling, not only locks the phase but also enhances the amplitude of the sidebands relative to the central band.