How long is a vocal tract? Comparison of acoustic impedance spectrometry with magnetic resonance imaging

The acoustic impedance spectrum of the vocal tract, measured during phonation (Hanna et al., 2016. JASA, 139, 2924–2936), shows qualitative and semi-quantitative similarity to that of a simple cylindrical duct of length l. But how does l compare with geometrical length(s) measured from a magnetic resonance imaging (MRI) scan. One male subject (age 34, height 184 cm) (1) performed a neutral /з/ vowel during impedance measurement; (2) was MRI scanned for the same gesture with his lips around a plastic tube with the same dimensions as the impedance head; and (3) was scanned during closed mouth nasal breathing. For the neutral vowel, the effective acoustic length is a weakly increasing function of frequency: the first four acoustic tract resonances give lengths rising from 155 to 195 mm; i.e. the higher resonances occur at slightly lower frequencies than the expected 1:3:5:7 ratios for cylindrical geometry. One factor is that the tract cross-section is on average greater near the lips than near the glottis. In spite of these complications, there is surprisingly good agreement between the acoustic length derived from the first resonance (here 158 mm with glottis closed) and the smoothed airway centroid length in the MRI (156 mm).