We extend a low-cost computational aeroacoustic approach by taking into account temporal effects of the modeled turbulent flow. As the noise production is determined by the turbulent frequency spectrum rather than the wavenumber spectrum, temporal properties of the turbulent flow play a role in many cases. We focus on the most dominant temporal effect, on sweeping, i. e. the advection of inertial range structures by the energy containing large scales. By introducing a feedback-mechanism of the turbulent field onto itself, we are able to incorporate this effect in the fast random particle method, which was successfully applied to different cases such as slat noise, jet noise and others. It is shown that sweeping reproduces important properties of spatio-temporal correlations of the turbulent flow, which are not grasp by most turbulence-models. The influence on the sound generation will be discussed for aeroacoustic simulations of jet and trailing edge noise.