Titze (1988) used the surface wave model to derive an analytical expression for threshold pressure in terms of the glottal geometry and biomechanical parameters of the larynx. This formula was tested in a series of experiments in 1995 and 1997. Since the membrane of the physical model used in the experiments becomes rounded when a fluid flows beneath it, the effects of glottal curvature were investigated. Because physical model used for the experiments could be adjusted to give a divergent prephonatory glottal geometry, an angle θ was also introduced in addition to the curvature correction. Including the curvature coefficient b and the prephonatory glottal angle θ do not seem likely candidates for discrepancies observed in the experiments because such effects are hard to distinguish from changes in the effective values of the glottal halfwidth and the damping coefficient.
Nardone’s mathematical model was built from the classic, lumped element, two-mass model of Ishizaka and Flanagan. The mathematical model is based on ten, second-order, nonlinear, coupled, ordinary differential equations that are solved simultaneously using the software Mathematica. Nardone’s model was employed to study the role of vocal tract parameters and viscous damping constants in determining the threshold pressure. Calculated results were compared with Chan and Titze’s (2006) experimental data. The results indicate that the threshold pressure is consistently lowered when the vocal tract is included, which follows the same trend as the experimental results of Chan and Titze (2006). Increasing the vocal tract area in the mathematical model achieved a larger difference between the calculated results with vocal tract and with a larger vocal tract area. We have also shown that an increased viscous damping constant leads to a bigger threshold pressure differences. Comparison of the calculated results with Chan and Titze’s (2006) experiments were not able to generate a consistent fit over the entire range of glottal widths studied. Successes were recorded over parts of the range with different sets of parameters.