## 2 Models and Methods
### Larynx Model and Measuring Setup  
The model used for the synthetic larynx and the subglottal system is shown in Figure 3. It is composed of a mass-flow generator [28], which provides the air flow, an acoustic silencer, a subglottal channel, and the mounting device for the synthetic vocal folds. The subglottal channel provides a rectangular flow cross-section, whose dimensions are 1.8 cm by 1.5 cm. The length of the subglottal channel is 19 cm. Thus, the frequency required for it to serve as an acoustic \(\lambda\)/4 resonator is 451 Hz,  
Figure 2: (Color online) Measured and calculated phonation threshold pressures as functions of the glottal half-width with and without a vocal tract. which is at least three times larger than any of the oscillation frequencies for the vocal folds reported below. Two measures were employed to minimize the effects of acoustic perturbations on the entering airflow. Most of the silencer is covered with Sonatech PUR SKIN 30 sound-absorbing foam (SONATECH GmbH + Co. KG, Ungerhausen, Germany) matting, which is very effective at damping acoustic fluctuations. These regions are colored in orange in the silencer depicted in Figure 3. In order to interrupt acoustic standing waves in the axial direction, a core body in the center of the silencer is also covered with PUR SKIN. The silicone-based vocal fold model is shown in Figure 4, and its dimensions are those appropriate for the human scale. The glottal thickness of the human larynx is about 0.35 cm, and its glottal length is near 1.5 cm. Data will be reported below with two single-layer vocal fold models fabricated from mixtures of two-component Smooth-On EcoFlex 30 (Smooth-On, Inc., Macungie, PA, USA) and Smooth-On Silicone Thinner flexibilizer [17]. The first of these, Model 113, contains a smaller amount of silicone thinner than the second, Model 114. Accordingly, the [PERSON]'s modulus for Model 113 is 4.4 kPa, and that for Model 114 is 2.5 kPa. These values are in the range of those for which [PERSON], [PERSON], and [PERSON] [15] observed oscillations driven by aerodynamic forces. These [PERSON]'s moduli were determined with a hybrid experimental-numerical technique described in the papers of [PERSON] et al. [29] and [PERSON] et al. [30]. The geometry of the vocal folds shown in Figure 4 was chosen to closely approximate the model developed by [PERSON], [PERSON], and [PERSON] [31; 32]. [PERSON] et al. used the scaled-up rigid model M5 developed by [PERSON] et al. [33] as their guide. The larynx model shown in Figures 3 and 4 readily developed oscillations whose frequencies ranged from about 110 Hz to 150 Hz when the flow rates were set in the range from 60 to 120 L/min. The supraglottal channel with a variable lateral displacement \(D\) is shown [17] in Figure 5. It is bounded by two large glass plates that define the extent of one of the directions perpendicular to the direction of airflow and by two smaller aluminum plates that define the extent of the other direction perpendicular to the direction of airflow. The displacement \(D\) varied from 1.8 to 7.8 cm in the course of the experiments. Since the other perpendicular direction remains constant at 1.5 cm, the area of the  
Figure 4: (Color online) Schematic diagram and photograph of the synthetic silicone model of one of the vocal folds (distances are in millimeters). R1: radius 1 mm; R2: radius 2 mm. Figure 3: (Color online) (A) Schematic diagram of the synthetic larynx model including the mass flow generator, silencer, subglottal channel, and mounting device for the synthetic vocal folds (distances are in millimeters). vocal tract varies from 2.7 cm\({}^{2}\) to 11.7 cm\({}^{2}\) in the course of the experiments. The length of the vocal tract is 19.0 cm. The supraglottal channel used for the variable length measurements [18] is shown in Figure 6. The vocal tract is now composed of sections. The first of these is 4.0 cm long, and each of the other sections is 5.0 cm long.