Abstract
In voice research, analytically-based models are efficient tools to investigate the basic physical mechanisms of phonation. Calculations based on lumped element models describe the effects of the air in the vocal tract upon threshold pressure (Pth) by its inertance. The latter depends on the geometrical boundary conditions prescribed by the vocal tract length (directly) and its cross-sectional area (inversely). Using Titze’s surface wave model (SWM) to account for the properties of the vocal folds, the influence of the vocal tract inertia is examined by two sets of calculations in combination with experiments that apply silicone-based vocal folds. In the first set, a vocal tract is constructed whose cross-sectional area is adjustable from 2.7 cm2 to 11.7 cm2. In the second set, the length of the vocal tract is varied from 4.0 cm to 59.0 cm. For both sets, the pressure and frequency data are collected and compared with calculations based on the SWM. In most cases, the measurements support the calculations; hence, the model is suited to describe and predict basic mechanisms of phonation and the inertial effects caused by a vocal tract.
Highlights
Phonation begins with a flow of air from the lungs that transfers energy to the motion of the vocal folds
By examining a vocal tract of uniform cross-sectional area AVT and length LVT, one can use Newton’s second law to derive the following formula for the pressure required to accelerate the air within the vocal tract: PVT = IVT dU g /dt, (1)
Ishizaka and Flanagan [1] used this formula in their classic paper that developed the two-mass model of the vocal folds
Summary
Phonation begins with a flow of air from the lungs that transfers energy to the motion of the vocal folds. After this airflow leaves the larynx, it encounters a mass of air in the vocal tract with inertial properties. By examining a vocal tract of uniform cross-sectional area AVT and length LVT , one can use Newton’s second law to derive the following formula for the pressure required to accelerate the air within the vocal tract: PVT = IVT dU g /dt, (1). Where the quantity dUg /dt is the time derivative of the glottal flow rate Ug , and IVT is the inertance of the air in the vocal tract. Titze [2] used this formula in his paper dealing with small amplitude
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