# Effect of Subglottic Stenosis on Expiratory Sound Using Direct Noise Calculation
## 3 Results
### Neutral Glottis
#### 3.1.2 Sound Spectrum under Neutral Glottis  
Figure 5 depicts the spectra for the neutral glottis with a fixed SGS distance of 2.0 cm. The spectra are divided into subfigures, each containing five cases that share the same SGS severity but have increasing flowrates (shown at the top). Each black curve in the subfigures represents the spectrum of the acoustic pressure of a single case. The amplitude of the spectra is normalized with respect to the highest peak of each case. The spectrum is shown up to 4000 Hz, beyond which the amplitude is almost zero. To aid in the interpretation of the spectra, shaded bands are included to represent estimated frequencies of various sources of acoustic resonance, including the harmonics of the vocal tract (VT) from the glottis to the mouth and the harmonics of the extended tract (XT) from the SGS to the mouth (see Figure 1c). Note that, depending on the size of the SGS and the glottis, the vocal tract and extended tract can be considered as having an open-open (O-O) or a closed-open  
(X-O) end condition. The frequencies of the harmonics are estimated using the formulas for straight tubes with ideal O-O or X-O end conditions, and the specific acoustic modes are annotated to the right. The bands are thickened to suggest a larger error in the estimated frequencies for higher harmonics [55]. A detailed explanation of the frequency estimates is provided in Appendix A. The characterization of the tonal sound is based on the matching between the spectrum and these frequency source estimates. Two oblique lines in the subfigures indicate a constant Strouhal number (St) of 0.1 (blue line) and 0.5 (orange line), which are calculated based on the size of the smaller orifice in the system and its average jet velocity. Figure 4: Overall sound pressure level of parametric cases for the neutral glottis and an SGS distance of 2.0 cm. Figure 5: Spectra of acoustic pressure for cases with an SGS distance of 2.0 cm and the neutral glottis. The amplitude (acoustic pressure in Pa) is normalized to [0, 1] in the spectrum plot with maximum peak marked for each case at the bottom axis. The blue oblique line represents a constant St = 0.1 and the orange line St = 0.5, calculated for the glottal jet in the first two subfigures and the SGS jet in the rest. When there is no SGS present (a 0% blockage), the spectra show a hump around a low frequency that increases with flowrate. This frequency originates from the instability of the glottal jet, corresponding to a constant Strouhal number (St) of 0.1 (blue line). The tones are classified as the jet tone from the glottis. For the cases with a blockage of 51%, the effect of the SGS is almost negligible, and the spectra are similar to those of 0% blockage cases. At an SGS blockage of 75%, the low frequency peak resulting from the glottal jet can also be observed for most cases, yet it is less dominant. A single narrow frequency peak appears at flowrates of 300 mL/s and 500 mL/s, which is found to match the vortex shedding frequency of the SGS jet, indicating that it is a hole tone of the SGS jet. As the flowrate increases, the first acoustic harmonic of the open-open XT begins to appear at 700 mL/s and becomes dominant at 1000 mL/s. At an SGS blockage of 84%, most spectra become noisy with peaks of tapering amplitude around tract harmonics. At an SGS blockage of 91%, a pure SGS hole tone of 265 Hz is excited under a flowrate of 100 mL/s. As the flowrate increases to 300 mL/s and beyond, the spectra become cluttered with peaks around tract harmonics. The disappearance of the pure hole tones at 300 and 500 mL/s seen in 75% severity could be related to the relative size of the obstacle hole (the glottal opening) and the orifice (the stenotic opening). The diameter ratio of the hole to the orifice is 1.4 at 84% severity and 1.8 at 91% severity compared to 1.1 at 75% severity. [PERSON] and [PERSON] [14] demonstrated that when the hole diameter was increased to twice the size of the orifice, the sound pressure became barely measurable.