This paper presents an analysis of Godunov scheme in the low Mach number regime. We study the Riemann problem and show that the interface pressure contains acoustic waves of order Mach even if the initial data are well prepared and contain only pressure fluctuations of order Mach squared. We then propose to modify the fluxes computed by Godunov type schemes by solving a preconditioned Riemann problem instead of the original one. This strategy is applied to VFRoe solvers where we show that it allows to recover a correct scaling of the pressure fluctuations. Numerical experimen- ts confirm these theoretical results.