A transfer-matrix approach for estimating the characteristic impedance and wave numbers of limp and rigid porous materials

A method for evaluating the acoustical properties of homogeneous and isotropic porous materials that may be modeled as fluids having complex properties is described here. To implement the procedure, a conventional, two-microphone standing wave tube was modified to include: a new sample holder; a section downstream of the sample holder that accommodated a second pair of microphone holders and an approximately anechoic termination. Sound-pressure measurements at two upstream and two downstream locations were then used to estimate the two-by-two transfer matrix of porous material samples. The experimental transfer matrix method has been most widely used in the past to measure the acoustical properties of silencer system components. That procedure was made more efficient here by taking advantage of the reciprocal nature of sound transmission through homogeneous and isotropic porous layers. The transfer matrix of a homogeneous and isotropic, rigid or limp porous layer can easily be used to identify the material's characteristic impedance and wave number, from which other acoustical quantities of interest can be calculated. The procedure has been used to estimate the acoustical properties of a glass fiber material: good agreement was found between the estimated acoustical properties and those predicted by using the formulas of Delany and Bazley.