On the Apparent Propagation Speed in Transmission Line Matrix Uniform Grid Meshes

Abstract

Numerical models consisting of twodimensional (2D) and threedimensional (3D) uniform grid meshes for the transmission line matrix method (TLM) currently use 2 and 3, respectively, to compensate for the apparent sound speed. In this paper, new compensation factors are determined from a priori simulations, performed without compensation, in 2D and 3D TLM onesection tube models. The frequency values of the first mistuned resonance peaks, obtained from these simulations, are substituted in the corresponding equations for the resonance frequencies in onesection tubes to find the apparent sound propagation speed in the mesh environment and, thus, the necessary compensation. The new factors have been tested in more complex models like a twotube concatenation model and a realistic magnetic resonance imaging (MRI)reconstructed human vocal tract (VT) model. Important VT modeling results confirm the improvement over the conventional compensation factors, particularly for frequencies above 4 kHz. Among these results are the identification of the spectral trough at about 5200 Hz caused by the piriform fossa and the application of a pitch extraction algorithm to the 3D TLM output signal, finding a difference smaller than 0.66% relatively to human voice pitch.