Resonances and wave propagation velocity in the subglottal airways

Abstract

Previous studies of subglottal resonances have reported findings based on relatively few subjects, and the relations between these resonances, subglottal anatomy, and models of subglottal acoustics are not well understood. In this study, accelerometer signals of subglottal acoustics recorded during sustained [a:] vowels of 50 adult native speakers (25 males, 25 females) of American English were analyzed. The study confirms that a simple uniform tube model of subglottal airways, closed at the glottis and open at the inferior end, is appropriate for describing subglottal resonances. The main findings of the study are (1) whereas the walls may be considered rigid in the frequency range of Sg2 and Sg3, they are yielding and resonant in the frequency range of Sg1, with a resulting ~4/3 increase in wave propagation velocity and, consequently, in the frequency of Sg1; (2) the "acoustic length" of the equivalent uniform tube varies between 18 and 23.5 cm, and is approximately equal to the height of the speaker divided by an empirically determined scaling factor; (3) trachea length can also be predicted by dividing height by another empirically determined scaling factor; and (4) differences between the subglottal resonances of males and females can be accounted for by height-related differences.

Subglottal resonances of adult male and female native speakers of American English

“…Considered separately for males and females, Sg1 is not strongly correlated with Sg2 or Sg3 (0.27 < r < 0.58), but Sg2 is strongly correlated with Sg3 (r > 0.73). The poor correlations involving Sg1 are presumably due to the effects of the subglottal tissue resonance, which was shown to be in the vicinity of Sg1 (Lulich et al, 2011a) and which may variably affect the Sg1 frequency (without altering the Sg2 and Sg3 frequencies) depending on the mechanical properties of the tissue and the proximity of Sg1 to the tissue resonance. The strong correlation between Sg2 and Sg3 was noted before (Lulich et al, 2011a) and, together with the fact that the mean ratio between Sg3 and Sg2 (1.62) is roughly equal to the expected relation 5/3, is evidence that at frequencies far from the tissue resonance the subglottal system behaves like an equivalent uniform tube closed at the glottal end and open at the distal end.…”

“…For Sg1, the wave propagation velocity is increased to c ¼ c w ¼ 46 586 cm/s as a result of the nearby wall tissue resonance (Lulich et al, 2011a).…”

“…This has been difficult to achieve because typical methods for directly measuring the input impedance are quite invasive and/or technically challenging, requiring access to patients with laryngectomies (Ishizaka et al, 1976), placing miniature pressure transducers below the glottis (Cranen and Boves, 1987), or using an endotracheal tube (Habib et al, 1994). An alternative, noninvasive method is the use of an accelerometer placed against the skin of the neck (Cheyne, 2002;Chi and Sonderegger, 2007;Madsack et al, 2008;Madsack, 2008, 2009;Lulich, 2010;Wokurek and Madsack, 2011;Gr aczi et al, 2011;Lulich et al, 2011a;Lulich et al, 2011b). In this case, the source of sound comes from the phonation volume velocity (as is the case in microphone recordings of vowels), and the motion of the neck tissues (and hence the accelerometer) is related to the pressure at the top of the trachea.…”

“…Few studies have collected information about speaker height in addition to SGRs (Habib et al, 1994;Jung, 2009a;Lulich et al, 2011a), and few have measured SGRs separately in different vowels (Cranen and Boves, 1987;Madsack, 2008, 2011). Of these, Habib et al (1994) and Jung (2009a) measured SGRs in fewer than 10 speakers, and Cranen and Boves (1987) measured SGRs in only two speakers (i.e., the authors themselves).…”

Frequency warping using subglottal resonances: Complementarity with VTLN and robustness to additive noise

“…1) uses a piece-wise linear function to map the first three SGRs -Sg1, Sg2 and Sg3 -of a target speaker (subscript t) to the first three SGRs of a reference speaker (subscript r). Since Sg2 and Sg3 are not necessarily integer multiples of Sg1 [14], SGR warping results in frequency-dependent scaling. As Fant's studies on vowel normalization have shown [15], speaker variability can be best minimized using a combination of frequency-independent and frequency-dependent scaling.…”