Numerical models consisting of two-dimensional (2D) and three-dimensional (3D) uniform grid meshes for the transmission line matrix method (TLM) currently use and , 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 one-section 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 one-section 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 two-tube 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.