The accurate simulation of polydisperse sprays strongly coupled to unsteady gaseous flows is a major issue for solid rocket motor optimization and a challenge for both modeling and scientific computing. The Eulerian Multi-Fluid method (MF) has proven to account for polydispersity efficiently, considering conservation equations for moments of the spray integrated on droplet size intervals. This describes droplet size sorted "fluids" which are all coupled to the gas through drag and heat transfer source terms. The potential of this model to deal with polydisperse acoustics has not been addressed, which is an issue regarding both physics and code quality evaluation. The resulting system is indeed strongly coupled and requires dedicated numerical methods which one wants to control as regards cost and accuracy. In this paper, we define the key issues of polydisperse acoustics and the ability of MF systems to tackle them. We then describe the numerical difficulties of strong coupling. The case of small droplets is particularly harsh and carefully studied. We finally introduce, study and adapt to an industrial-oriented code a numerical strategy for polydisperse moderately dense sprays that can be adapted to accuracy needs. The method is tested on an unsteady polydisperse solid rocket motor case to prove the feasibility of the approach.