Fig 1.
Schematic (not to scale) of the experimental setup testing a physical model (blue region) in a syrinx or larynx position.
The microphone was placed 10 cm downstream from the opening of the vocal tract. Pressure transducers (P1, P2) were placed below the respective sound sources. A 15l expansion chamber simulated acoustic properties of the lung. Flow rate was measured upstream from the expansion chamber. Trachea length was varied between 0 cm and 248 cm.
Fig 2.
Sound production is more efficient when the sound source is in a syringeal position.
(A) PTP was consistently lower in the syrinx than in the larynx. (B) The syringeal sound source generated higher sound intensities (depicted as Amplitude, relative change in output voltage of microphone signal) than the larynx for most tracheal lengths. (C) The fluctuating fundamental frequency is evidence for the strong interaction between sound source and vocal tract filter. (D) Glottal efficiency of a laryngeal or syringeal sound source at different tracheal lengths. Between 40 and 80 cm tracheal length, the effect is most dramatic. The two vertical dashed lines indicate a tracheal length range (40 cm ± 10 cm), which is most likely to correspond with a sound source of 1 cm vocal fold length used in this study. This tracheal length corresponds to an avian archosaur of approximately 20 to 30 kg body mass [18]. Tracheal lengths much shorter or much longer than this range could correspond to a few extreme exceptions in which the trachea is very short or very long. Numerical data used in this figure is included in S1 Data. PTP, phonation threshold pressure; TE, tracheal elongation.
Fig 3.
The effect of trachea length as studied by computational simulation.
Differences between the syrinx and larynx position in phonation are shown for threshold pressure (A), fundamental frequency (B), power input into trachea (C), glottal power (D), power at the mouth (E), and efficiency (F). Efficiency was computed as the mouth power divided by the input power. The two vertical dashed lines indicate the tracheal length range (40 cm ± 10 cm), which is most likely to correspond with a sound source of 1 cm vocal fold length used in this study (see Fig 2). Numerical data used in this figure is included in S1 Data.
Fig 4.
(A–C) Trachea length was stepwise elongated (to the right of dashed line) or shortened (to the left of dashed line). In chicken and budgerigars, fundamental frequency increases in response to trachea shortening and slightly decreases in response to trachea elongation. In the zebra finch, very small changes were observed in fundamental frequency. However, vocal quality changed sometimes dramatically (e.g., occurrence of nonlinear phenomena). The decrease of fundamental frequency in the inertive reactance region below F1 (primarily in the chicken) is in agreement with theory. Inertance of the vocal tract effectively adds mass to the coupled oscillating system, thereby lowering F0. The closer F0 is to F1, the greater the inertance and hence the greater the F0 drop. Why did the zebra finch apparently exhibit only type 1 coupling throughout shortening and lengthening? There are morphological differences between the structures of the vocal folds of the three bird species that could explain this. The initial length of the trachea is shown by the vertical dashed line. Numerical data used in this figure is included in S1 Data. F1, first formant
Fig 5.
The interaction between sound source and filter is conceptualized as either Level 1 or Level 2 interaction.
Level 1 interactions are characterized by effects on the glottal flow, which will lead to acoustic effects, including changes in harmonic emphasis and/or the occurrence of nonlinear phenomena. Level 2 interactions are characterized by effects on vocal fold vibrations, which will lead to changes in fundamental frequency and/or also the occurrence of nonlinear phenomena.
Fig 6.
Acoustic characteristics of the avian and mammalian trachea.
(A) The relationship between BM and fundamental (or dominant) frequency has been studied many times in birds and in mammals. A summary of model functions is provided in S2 Table. The regression curves for birds (red) and mammals (blue) suggest that the slope of the relationship is similar in both groups. An average regression model (F0 = 450 × BM−0.38) was used to estimate wavelength. Wavelength is the ratio of speed of sound (340 m/s in warm humidified air) and F0. (B) The tracheal length of birds appears to be much closer to the wavelength of F0 than that of mammals. The length and diameter of the mammalian trachea were modeled after data published by Tenney, Bartlett [17], and Moore and colleagues [76] and that of the avian trachea were modeled after data published by Hinds and Calder [18]. For a given body size, the mammalian trachea is acoustically much shorter than the avian trachea. (C, D) The graphs illustrate the relationship between vocal tract reactance and fundamental frequency for a 20-kg bird or mammal, respectively. Frequency range was established from various models listed in S2 Table. In both birds and mammals, the lowest fundamental frequency overlaps with the positive reactance range, i.e., the left side of F1. The close match between tracheal length and quarter wavelength of the fundamental frequency in birds provides the most dramatic supportive interaction. BM, body mass; F0, fundamental frequency; F1, first formant; F2, second tracheal formant.