A mathematical description of an experimentally-verified scheme leading to a phase-locked stimulated Brillouin scattering (SBS) is presented. It is shown that this phase-locking of the SBS process may have its origin in a transient acoustic standing wave initiated by an arising optical interference field, eventually leading to a stationary density modulation of the medium. An appropriate solution was obtained by solving the acoustic wave-equation with electrostriction as a driving force. As a consequence of the damping term being included in this equation, the acoustic standing wave becomes gradually attenuated and, contrary to the undamped solution published earlier, thus constitutes a truly transient phenomenon.