# Effect of Subglottic Stenosis on Expiratory Sound Using Direct Noise Calculation
## 3 Results
### Constricted Glottis
#### 3.2.2 Sound Spectrum under Constricted Glottis  
Figure 7 displays the spectra for the constricted glottis configuration (\(g=0.4\) cm) at a fixed SGS distance of 2.0 cm using the same layout as Figure 5. The oblique lines indicating constant St are for the SGS jet except in the first subfigure, where they are for the glottal jet. The first observation is that it is mostly the harmonics of the X-O VT that are excited. In the absence of the SGS, the sound comes from the coupling between the vocal tract and the glottal jet (i.e., the pipe tone system). Higher harmonics become more dominant as flowrate increases. The purity of the tones varies with the flowrate. In most cases, clusters of peaks are observed around vocal tract harmonics. At 700 mL/s, a pure tone (1709 Hz) is excited, corresponding to the 2 nd harmonic of the X-O VT. The spatial distribution of the wall pressure shows a 3/4 wavelength standing wave.  
The effect of the SGS on the spectrum appears to be subtle but consistent. While the excited sound are still harmonics of the X-O VT, the dominant harmonics tend to shift toward the preferred St of the SGS jet and the hole tone system. Taking the cases with a 1000 mL/s flowrate as an example, the most dominant harmonic is the third one without SGS. As the severity increases, the second harmonic becomes dominant due to the lower frequency preferred by the SGS jet. This continues up to a severity of 84%. As the severity further increases to 91% and the preferred SGS jet frequency becomes higher, the third harmonic becomes dominant again and the fourth harmonic starts to appear on the spectrum. At 96% severity, the fourth harmonic becomes dominant and even higher harmonics appear on the spectrum. The SGS also affects the purity of the excited tones. Taking 1000 mL/s cases again as an example, for a severity from 51% to 84% the spectra contain a single narrow dominant peak at the second harmonic of the X-O VT. In these cases, the shedding frequency of the SGS jet is locked to the VT harmonics, indicating the hole tone system and the pipe system are coupled into resonance. Indeed, the amplitude of the peaks are slightly higher than when SGS is absent. For severities of 91% and 96%, the  
Figure 6: Overall sound pressure level of parametric cases for the constricted glottis and an SGS distance of 2.0 cm.  
peaks are more distributed, and no resonance is formed. In the 91% severity case, a hump around 2000 Hz can be seen, which is from the hole tone system. The same influence of the SGS can be observed for cases with a different flowrate.  
Secondly, a few special cases are noted. For 91% severity at 100 mL/s, the hole tone mechanism is dominant. For 96% severity at 300 mL/s, a pure tone is excited at the frequency of the third harmonic of the X-O VT (2806 Hz) with a weak subharmonic of about half the frequency (1413 Hz). Inspection of the flow field animation confirms that the frequency of this subharmonic is the same as the vortex shedding frequency of the SGS jet. For 96% severity at 500 mL/s, the peak of the spectrum aligns with none of the X-O tract harmonics. Instead, the frequency is close to the estimated resonance frequency of the Helmholtz resonator formed by the SGS, the glottis, and the cavity in-between (Figure 1c; see Appendix A for the estimation of the Helmholtz resonance frequency). Inspection of the acoustic field shows that the acoustic pressure on the cavity wall oscillates uniformly, and the glottal exit is close to a pressure node.  
Lastly, the spectra show that harmonics of the extended tract are not excited due to it being broken by the constricted glottis.