We propose to extend the fix of Roe's approximate Riemann solver developed for the Barotropic Euler equations in [2] to the full Euler equations. This scheme is built mainly to handle low Mach acoustic waves. Moreover, compared to pressure-centered type schemes, this numerical fix has the advantage of improving the numerical solution in the sense that the oscillating modes are reduced. The theoretical study is based on a two-time scales asymptotic analysis. It is proved that the Euler system equipped with a general equation of state is consistent with a first-order wave system in a low Mach number regime. Similar analysis is performed at the discrete level on the Roe scheme to derive the new fix. Numerical tests confirm the results obtained for the Barotropic case about the ability of this fix to deal with both steady and low Mach acoustic computations also in the case of full Euler equations.