Computational aeroacoustics methods and parallel computers are used to study the phenomenon of flow-induced noise from two-dimensional cavities. The Navier-Stokes equations are solved in two-dimensions. In previous studies, the laminar cavity flow acoustics were solved using a higher-order dual time stepping approach with a Runge-Kutta explicit steady state solver. In the current study, the Crank- Nicholson implicit scheme is used as the steady state solver in a dual time stepping method and cavity flows with turbulent upstream boundary layers are considered. The one equation Spalart-Allmaras turbulence model is used to describe the evolution of the turbulent eddy viscosity. In the present study, flows over two-dimensional cavities for different length to depth ratios, flow speeds and types of incoming boundary layers are examined. It is observed that as the length to depth ratio increases for the two-dimensional cavity, the cavity flow starts to oscillate in a wake mode. As the depth of the cavity is reduced, the large vortical structures found in deeper cavities collapse and the pressure distribution becomes unsteady, with discrete fluctuation frequencies. The mean and fluctuating quantities are examined and the noise generation mechanisms are identified. To avoid the use of a full turbulent grid, simple wall functions are used upstream of the cavity.