The Sound Attenuation Coefficient Optimization in Case of a Three Parameter Impedance Model for a Rectangular 3D Straight Lined Duct of Finite Dimensions

A method for the minimization of the ratio of the sound pressure level at the exit to that at the entrance is presented for a rectangular 3D straight lined duct carrying a uniform gas flow. The duct dimensions, the incident sound wave as well as the frequency of the sound wave propagation are assumed to be known. It is assumed also that the liner impedance model is the mass-spring–damper model. The idea is to compute the considered ratio for a large number of combinations of the values of the inertance, resistance and stiffness of the liner and, by fitting the obtained data, to establish a formula for the dependence of the ratio in discussion on these three parameters of the liner. Using the obtained formula, the minimum value of the ratio, as well as the values of the inertance, resistance and stiffness, for which the minimum is obtained, are found.