A prominent feature of many practical flows is the hydrodynamic wave system attached to moving bodies or concentrations of vorticity. Sound waves are usually present, and these act as a mechanism for energy and momentum transport. With their source rooted in the unsteadiness of the flow, they can sometimes play an important role in determining the general flow structure, particularly if the flow is unstable. In this thesis we investigate the basic connection between sound, and hydrodynamic waves. By analysing the waves attached to boundaries which are in prescribed unsteady motion, details emerge concerning the linear production of sound from hydrodynamic motions. We show that the abrupt arrest or commencement of a steady hydrodynamic wave causes the production of a quantity of sound energy exactly equalling that of the hydrodynamic wave. For more gentle modulations of the steady state, we identify those aspects of the evolving hydrodynamic field which determine how much sound is produced. These results are used to suggest ways to improve procedures for minimising the noise from vibrating surfaces. According to linear theory, when waves on an infinite fluid boundary travel at sonic speed the fluid response is infinite. We use the ideas developed to cope with the sound generation problem to investigate the effects of unsteady transonic motion. We give a detailed analysis of acoustic 'Cerenkov radiation', which would occur if a body travelled through an inviscid medium supersonically, and decelerated to a subsonic speed. We assess the degree to which non-linear transonic effects are important. Sound waves are known to be a critical factor leading to the destabilisation of line vortices, and we were intrigued to know whether compressibility has a corresponding effect on the stability of a rigid body moving steadily in an irrotational, inviscid flow. Our investigation reveals that the motion is always stable.