Resonances, bandwidths and acoustical impedance spectra of vocal tract and trachea

This page gives a simplified introduction to measurements, with links to scientific papers.

  • Measurements under near ecological conditions; formants
  • Measurements of the vocal tract resonances and antiresonances
  • Acoustic losses
  • The zeroth resonance
  • The effect of the trachea
  • Limitations

    Measurements under near ecological conditions; formants

      The resonances determine formants in speech (see What is a formant?). Using the formants, the resonance frequencies can be estimated, with limited precision, from the sound of voiced speech. The resonant frequencies can be measured with reasonable precision under nearly ecological conditions using broadband excitation at the open mouth. We describe that technique on a separate page. The present page, showing results from the thesis of Noel Hanna, describes precise measurements of acoustical impedance spectra made under laboratory conditions.

    Measurements of the vocal tract resonances and antiresonances

      The three graphs below, from Hanna et al (2016), show acoustic impedance magnitude |Z|, bandwidth B and quality factor Q for each of the resonances (Ri, dark ellipses) and antiresonances (pale ellipses). The semiaxes show one standard deviation. In the top graph, the quasi-continuous superposed line is an example of one measurement of the |Z| spectrum. All measurements were made on men with their lips sealed around an impedance head (described here). More results (including results on women) are given by Hanna et al, 2016.

      graph showing Z, resonances and antiresonances .

    Acoustic losses

      The top graph above shows that Z(f) is qualitatively somewhat similar to that of a closed duct of the same length. However, the measured bandwidth is larger and the Q smaller; the measurements are more comparable with a closed duct having acoustic losses about five times greater than the visco-thermal losses of a dry, rigid, smooth, closed duct.

    The zeroth resonance

      The lowest resonance (R0 ~ 20 Hz) is due to the inertance Lt of the mass of the tissue surrounding the tract in series with its own compliance Ct and loss b (the tissue vibrates on its own elasticity). The antiresonance (~ 200 Hz) is due to that circuit in parallel with the compliance C of the air in the tract (the tissue vibrates on the 'spring' of the air). (These may influence plosives: Wakita and Fant, 1978. STL-QPSR.(1):9-29.). For further details, again, see Hanna et al (2016).

    The effect of the trachea

      The graphs below shows |Z|(f) measured as the subject moved slowly from closed glottis to inspiration position. When the glottis is closed, the trachea does not interact with the vocal tract and, seen from the lips, the tract looks like a closed duct (as we saw above). As the glottis opens, the effective length of the duct is increased. The number of resonances and antiresonances in a given frequency range increases and their magnitudes decrease. A very simple model can be used:

      For DC flow, the trachea leads to a termination closed at the alveoli. However, a few tens of cm below the glottis, the successive branching of the trachea gives a cross section that increases rapidly with distance from the glottis. In a very simple model, this can be approximated for AC currents as an open duct with an effective length of roughly 20 cm. So opening the glottis transforms the duct from a closed, 17 cm duct to an open 37 cm duct, roughly halving the frequency gap between resonances. The behaviour of this very simple model is shown in the other series of graphs shown below. Both figures are from Hanna et al (2018).

      graph of Z(f) for different glottis openings   cartoon of different glottis openings and corresponding graphs of Z(f).


      For some applications, these measurements are 'from the wrong end' it would be good to know the impedance spectrum seen from the glottis. This is not directly available for human subjects, but can be modelled.

    Papers from this team using Z(f) measurements

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