The acoustic characterization of porous materials is based on models of the dynamic tortuosity and compressibility. These models are obtained by limited Taylor expansion of the relaxation function as a function of frequency, and usually stop at second order. Most acoustic characterization methods are based on these developments. We show in our work that only porous materials having low resistivities are correctly represented by these developments. However, to properly describe and characterize resistive porous materials, it is necessary to go to a higher order. This brings to light new parameters that have been ignored until now in the acoustic characterization of porous materials. Taking these new parameters into consideration modifies the value of the other classical parameters, obtained by inverse characterization.