The accurate simulation of polydisperse sprays strongly coupled to unsteady gaseous flows is a major issue, e.g. for solid rocket motor optimization. The Eulerian Multi-Fluid method (MF) has proven to account for polydispersity efficiently by describing continuously droplet sizes, that are sorted into "fluids" which are coupled to the gas through drag and heat source terms. The potential of this model to capture polydisperse two-way interactions has not been addressed. Such an interaction is described through two strongly coupled systems of equations, which involve a large spectrum of scales in both time and space and require specific numerical methods to reach accuracy and predictability with an acceptable computational cost. In this paper, we define the physics and key issues of polydisperse spray-acoustics, identify physically relevant test cases and investigate the abilities of MF systems. We also describe the numerical peculiarities related to strong coupling, at high mass loading, of polydisperse sprays in unsteady gaseous flow fields. The case of small droplets, i.e. with relaxation time scales that are shorter than the gas flow scales, is carefully studied. We finally introduce, thoroughly study, and adapt to an industrial-oriented code a new numerical strategy with a high level of flexibility, which can be adapted to accuracy needs. The method is tested on an unsteady polydisperse solid rocket motor to prove its feasibility and efficiency for two-way coupling in a supersonic nozzle, which is representative of the difficulties encountered in a wide range of unsteady flows.