Theoretical modeling of the driving processes of solar-like oscillations is a powerful way of understanding the properties of the convective zones of solar-type stars. In this framework, the description of the temporal correlation between turbulent eddies is an essential ingredient to model mode amplitudes. However, there is a debate between a Gaussian or Lorentzian description of the eddy-time correlation function (Samadi et al. 2003b, A&A, 403, 303; Chaplin et al. 2005, MNRAS, 360, 859). Indeed, a Gaussian description reproduces the low-frequency shape of the mode amplitude for the Sun, but is unsatisfactory from a theoretical point of view (Houdek 2010, Ap&SS, 328, 237) and leads to other disagreements with observations (Samadi et al. 2007, A&A, 463, 297). These are solved by using a Lorentzian description, but there the low-frequency shape of the solar observations is not correctly reproduced. We reconcile the two descriptions by adopting the sweeping approximation, which consists in assuming that the eddy-time-correlation function is dominated by the advection of eddies, in the inertial range, by energy-bearing eddies. Using a Lorentzian function together with a cut-off frequency derived from the sweeping assumption allows us to reproduce the low-frequency shape of the observations. This result also constitutes a validation of the sweeping assumption for highly turbulent flows as in the solar case.