An integrated hybrid approach for the numerical simulation of aeroacoustics at low Mach numbers is presented. The method is based on a viscous/acoustic splitting. The turbulent incompressible background flow is computed with large eddy simulation, based on the incompressible Navier-Stokes equations, whereas the acoustics are computed from linearized Euler equations with a high-resolution scheme. The focus is on the numerical efficiency of the approach. To accelerate the computations, hierarchical grids and a frozen fluid approach for the acoustics are employed and investigated. For validation and the investigation of the numerical efficiency and accuracy the sound emission of a plate in the turbulent wake of a circular cylinder is employed as a test case.