A new impedance-based approach to analysis and control of sound scattering

A new theoretical solution to the problem of scattering sound by arbitrary obstacles in a fluid medium is presented. The scattering matrices are expressed in terms of three input impedance matrices defined with respect to the fluid–scatterer interface: one impedance matrix describes the scatterer and two matrices characterize the fluid. General properties of the scattering matrices are studied. Some useful representations of the scattered field are proposed. The general solution is applied to three well-known practical problems for which some new results are obtained or the existing results are generalized. For the first problem (of the most efficient passive sound absorber), an equation that determines its surface impedances is derived. A similar result is obtained for the second problem (of the best scatterer). For the third problem (of how to make a body to be acoustically transparent), “active” solutions that can be realized as smart coatings are proposed. Computer simulations illustrate the results.