Large amplitude oscillations have been observed in pre-mixed combustion systems, where the flame is stabilized in the recirculation zone behind an obstacle or a sudden expansion (a dump), and have been related to coupling between the combustion dynamics and the acoustics of the system. We have constructed a model, which includes an intake duct connected to a large upstream reservoir at a fixed pressure, a compact combustor with a sudden expansion followed by a sudden contraction (a cavity), and a long exhaust duct connecting the combustor to the atmosphere, to describe a system typical of a pre-mixed dump combustor. The upstream and downstream components are modeled as ID non-reacting flow systems, while the combustor is modeled using a vortex simulation of the 2D Navier-Stokes equations with a low-Mach number, thin flame combustion model. Results indicate that the system dynamics is comprised of the combustor wake-mode, ƒD/U=O(0.l, and several other modes characteristic of the acoustics of the overall system, with the former being one of the lowest subharmonic of the latter. This subharmonic selection mechanism, manifesting the coupling between the convective dynamics in the combustor and the acoustics of the system, is consistent with the fact that although several experiments and numerical simulations exhibit the same low frequency instability, the high frequency contents are different since they are dependent on the system configuration. The origin of the low frequency is the coalescence of a group of eddies, which are shed from the separating shear layer, as they move into the recirculation zone.