This study investigates the influence of pore size polydispersity on the acoustic behavior of high-porosity solid foams using numerical simulations. The effect of the size of the periodic unit cell (PUC) on the transport parameters is first examined. It is found that the size of the PUC required for properly estimating the acoustic properties of random foams depends on both the analyzed transport parameter(s) and level of polydispersity. Assuming identical and constant aperture ratio of membranes, the results indicate that (i) the viscous permeability is a reliable indicator regarding the size of the PUC (a more constraining property than the other transport parameters), and (ii) high-polydispersity foams require a larger number of pores in the PUC to achieve convergence with respect to morphological characteristics and acoustic properties. The influence of polydispersity on dimensionless transport parameters is then analyzed. It is found that polydispersity has a negligible effect on the high-frequency tortuosity but induces substantial variations in the remaining macroscopic parameters. Simulations further show that the ratio of the dimensionless transport parameters does not depend on membrane aperture ratio. This important result allows us to propose a fast method to estimate the acoustic properties of a random foam from the transport parameters of monodisperse foams with different pore sizes, for each studied transport parameter. The proposed method is finally employed to characterize the pore size and polydispersity in two real foams (with and without membranes), solving an inverse problem.