Through a linear analysis of a perturbed wave equation, we show how to modify Godunov type schemes applied to the compressible Euler system to make them accurate at any Mach number. This allows to propose a family of all Mach Godunov type schemes and to justify existing all Mach schemes. In the non-linear barotropic case and when the Godunov type scheme is a Roe scheme, a linear stability result is proposed and a formal asymptotic analysis justifies the construction by showing how it is related with the linear analysis of a perturbed wave equation. All the studied numerical results show that the all Mach Godunov scheme is both accurate and stable for all Mach flows.