Physical Modeling with the 2-D Digital Waveguide Mesh
Scott A. Van Duyne, Julius O. Smith · 1993
An extremely efficient method for modeling wave propagation in a membrane is provided by the multidimensional extension of the digital waveguide. The 2-D digital waveguide mesh is constructed out of bidirectional delay units and scattering junctions. We show that it coincides with the standard finite difference approximation scheme for the 2-D wave equation, and we derive the dispersion error. Applications may be found in physical models of drums, soundboards, cymbals, gongs, small-box reverberators, and other acoustic constructs where a one-dimensional model is less desirable. 1 Background Theory There are many musical applications of the onedimensional digital waveguide ranging from the generation of wind and string instrument tones, to flanging effects [Van Duyne and Smith, 1992], to reverberation [Smith, 1987]. We review the theoretical derivation of one-dimensional traveling waves as a basis for development of the twodimensional digital waveguide mesh. 1.1 The 1-D Wave Equation...