From absorption to impedance: Enhancing boundary conditions in room acoustic simulations

In room acoustic simulations the surface materials are commonly represented with energy parameters, such as the absorption and scattering coefficients, which do not carry phase information. This paper presents a method to transform statistical absorption coefficients into complex surface impedances which are needed for phased or time-domain calculation methods. Two 5-parameter impedance models based on fractional calculus are suggested to achieve a general model for common acoustic materials, thereby ensuring that the impedance found has a physical meaning. The five parameters for the general models are determined by solving an inverse problem with an optimization method. Due to the non-uniqueness of retrieving complex-valued impedances from real-valued absorption coefficients, prior information about the absorber of interest can be used as constraints, which is shown to help determine the impedance more correctly. Known material models, such as Miki’s and Maa’s models, are taken as references to assess the validity of the suggested model. Further stability and sensitivity investigations indicate that the method presented constitutes an efficient solution to convert sound absorption coefficients back to their original complex surface impedances.