A Note on the Physical Interpretation of Frequency Dependent Boundary Conditions in a Digital Waveguide Mesh

Digital Waveguide Mesh (DWM) is a popular method for time domain modelling of sound fields. DWM consists of a recursive digital filter structure where a D'Alembert solution of the wave equation is propagated. One of the attractive characteristics of this method is related to the simplicity of incorporating frequency dependent boundary conditions. The impedance of the boundaries can be simulated by means of digital filtering. So far such digital filters have been designed to provide reflection factors corresponding to the impedance of the boundaries for normal sound incidence. However, the resulting model of the boundary does not agree with the behaviour of a locally reacting surface, and this can give rise to contradictions in the physical interpretation of the reflected sound field. This paper analyses the behaviour of frequency dependent boundary conditions in DWM in order to obtain a physical interpretation of the simulated impedance surfaces. The interpretation is validated by several examples.