Ultrasonic wave transport in a system of disordered resonant scatterers: Propagating resonant modes and hybridization gaps

We present the results of ultrasonic pulse propagation experiments on suspensions of plastic spherical scatterers immersed in water. This system was selected to study the effects of scattering resonances on wave transport. By separating the coherent ballistic component from the multiply scattered wave field, both the dispersion relations and the diffusive propagation of ultrasound were investigated. We show that the dispersion relation is marked by a series of hybridization gaps due to the coupling between the propagating modes of surrounding fluid and the scattering resonances. Effects of dissipation on the formation of the gaps were investigated. We find evidence in our ultrasonic data for the existence of a (slowly propagating) second longitudinal mode, also seen in Brillouin scattering experiments, that arises from the coupling between the resonant scatterers. These results are interpreted with an effective medium model based on the spectral function approach, which gives an excellent description of the dispersion relations in this system. Measurements of the multiply scattered ultrasound allow both the diffusion coefficient and the absorption time to be measured as a function of frequency. The relationship between the diffusion coefficient and the ballistic data is discussed, while the measurement of the absorption time from the decay of the multiply scattered coda enables the absorption and scattering lengths to be separated. These ultrasonic measurements and their interpretation based on the spectral function approach give a very complete picture of wave transport in this strongly scattering resonant system.