# Effect of Subglottic Stenosis on Expiratory Sound Using Direct Noise Calculation
## 3 Results
### Effect of SGS Distance  
When altering the distance of the SGS, similar spectra patterns and SPL to those shown in the previous two sections are observed. For the sake of brevity, the SPL and the spectra of these cases are not displayed. Instead, comparisons are made in a similar way to Figure 8, but for different SGS distances. The location of the SGS affects the length of the extended tract, as well as the travel distance of the SGS jet before impinging on the vocal folds. As a result, it also affects the coupling between the hole tone system and the tract. In Figure 9, the effect of the SGS distance in the neutral glottis cases is demonstrated. Compared to the SGS severity and flowrate, the effect of stenosis distance on the overall SPL is negligible. A slightly higher SPL can be observed when the stenosis is farther from the glottis, but the overall difference is very subtle. The influence of the SGS distance on tonal purity is complex. For 96% severity, the \(d=1.0\) cm cases tend to have significantly lower purity.  
At the highest severity of SGS, tones of lower pitches are generally excited as the stenosis moves away from the glottis with a few exceptions. This is due to two contributing factors: (1) the length of the extended vocal tract increases, leading to decreases in the frequencies of tract harmonics, (2) the longer travel distance of the stenosis jet tends to reduce the hole tone frequency, which is particularly evident in the 700 mL/s cases. As the stenosis distance increases from 1.0 cm to 2.0 cm to 3.0 cm, the sound frequency decreases from about 5400 Hz to about 3300 Hz and then to about 2300 Hz. The pure excitation in these cases allows for a clear view of a standing wave in the vocal tract. Figure 10 illustrates the acoustic mode of the \(d=2.0\) cm case and the \(d=3.0\) cm case. Since the pressure drop along the tract is low, the acoustic pressure can be approximated by the gauge pressure near the wall. The centerline pressure is the superposition of the acoustic pressure and the flow pressure. Compared to the quarter wave plus a 3/2 wave mode observed in the \(d=2.0\) cm case, the \(d=3.0\) cm case has a single wave in the vocal tract, which is the next lower acoustic mode. In both cases, the glottal exit is a pressure node.  
Figure 8: Effect of glottal configuration on the acoustic spectrum. Comparison is made between cases with the neutral and constricted glottis and an SGS distance of 2.0 cm.  
For cases with pure excitations, orderly shedding of vortices can also be observed. The contours in the bottom row of Figure 10 show the spatial oscillation of the axial component of the velocity (the x velocity), which arises due to the coupling of the stenosis jet and the acoustic feedback near the exit of the SGS. Both cases have two vortices between the SGS and the vocal folds. However, the \(d\) = 3.0 cm case has a lower vortex shedding frequency due to the longer distance.  
Figure 11 shows the effect of the SGS distance in the constricted glottis cases. Like in the neutral glottis cases, the SGS distance has a negligible effect on the overall SPL, and its influence on purity is complex. In general, the most dominant tract harmonic is not affected by the stenosis distance until the severity is very high. Similar to the neutral glottis cases, the pitch of the sound tends to be higher when the SGS is closer to the vocal tract.  
Figure 10: Acoustic mode change due to stenosis distance. (**a**) \(d\) = 2.0 cm. 3/2 wave in vocal tract and quarter wave in SGS cavity. (**b**) \(d\) = 3.0 cm. Single wave in vocal tract and quarter wave in SGS cavity.  
Figure 9: Effect of stenosis distance on the expiratory sound. Comparison is made among cases with the neutral glottis but different SGS distances.