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 ϑ(M_*) where M_* is the reference Mach number even if the initial data are well-prepared and contain only pressure fluctuations of order ϑ(M²_*) We then propose to modify the fluxes computed by Godunov type schemes by solving a preconditioned Riemann problem instead of the original one. We show that this strategy allows to recover a correct scaling of the pressure fluctuations. Numerical experiments confirm these theoretical results.