Spin waves are a promising prospect for the development of microwave information processing devices. A major obstacle in the study of spin waves is the large intrinsic spin-wave damping in most known magnetic materials. Viable spin-wave amplification techniques are thus required to make further progress in the development of spin-wave-based logic devices. In this paper, we investigate a novel technique of parametric modulation of spin waves using bulk acoustic waves. Although it is not a conclusive proof of parametric amplification, we show that bulk acoustic waves at twice the frequency of the propagating spin waves on coupling into an yttrium iron garnet film can modulate the amplitude of the spin wave. This paper provides insight into magnon-phonon interactions, and suggests a new mechanism to compensate for inherent losses in spin-wave propagation in spin-wave-based logic devices.