Investigation of the ballistic propagation of acoustic waves through a resonantly scattering, Inhomogeneous medium indicates that although the ballistic signal remains coherent with the incident pulse, it is nevertheless strongly affected by scattering resonances. These resonances cause considerable frequency dispersion and substantially reduce the phase and group velocities. The experimental data are quantitatively described by a theoretical model that correctly accounts for the coupling between the resonant scatterers, leading to an effective renormalization of the scattering within the medium. This approach; resolves a long-standing problem in the definition of the group velocity in strongly scattering materials.