The effect of acoustical feedback on buzzing. From lips to vocal folds ? A. Van Hirtum1, I. Lopez1, M.H. Schellekens1, X. Pelorson2, N. Driessen1, A. Hirschberg1 1TU/e, Eindhoven, The Netherlands 2ICP, UMR CNRS 5009, Grenoble, France
Introduction
Fig1: oscillatory behaviour of lips and vocal folds
A particularity of the sound production system consists in the présence of resonators upstream and downstream from the lips and the vocal folds (trachea, vocal fold…etc). These resonators have a great influence on the lips vibration and on the vocal folds vibration. The objectives of this study are to understand phonation, voice disorders through physical modelling. Here are presented the effect of acoustical feedback and measures on lip/vocal folds replica. 1) Experimental study The used replica stands for artificial vocal folds or artificial lips (figure 2). It is constituted by 2 latex cylinders inflated by water under an imposed pressure Pin.
Depending on Pin the opening h between the two tubes of the replica will vary. The airflow coming from the lungs is simulated with a source of pressure Pl.
Fig2: Experimental `in-vitro' set-up
• Experiment 1 : mechanical resonances of the lips/vocal folds replica
[Cullen et al., 2000] Fig3: set-up of the first experiment
We measured the replica’s response to white noise, by acoustical excitation while the internal pressure in the replica is fixed. We observed 3 resonance frequencies around respectively 100, 160 et 230 Hz as illustrated in Figure 4.
Fig4: Example of measured mechanical resonances for Pin=9.1kPa
• Experiment 2 : acoustical feedback
Fig5: set-up of the seond experiment
To study the effect of acoustical feedback a pipe with length Ld is added to the downstream end of the replica. This is depicted in Figure 5. We measure the oscillation behaviour of the replica in function of Pin, Pl and Ld. From this experiments with obtain information on the minimum upstream pressure pressure Pl,thres necessary to sustain oscillation.
Fig6: Measured threshold pressure for oscillation (Pl,th)
When there is a strong acoustical coupling between the internal pressure of the replica and the again the threshold (external) pressure for it oscillation, we observe - self sustained oscillations for Pl =O(1000 Pa) - a small variability for internal pressure Pin up to 10kPa. - the minimum Pl,th coincides with Pin=9.1kPa for which h=0. But in case of a weak acoustical coupling, we notice too that these self sustained oscillations are only possible using very high [O(3000 Pa)] pressures Pl,th whatever Pin, that is totally unrealistic for speech !
Fig7: Example measured oscillation frequency (fres) as function of Pl and Ld
As concerns the measured oscillation frequency (fres) as function of Pl and Ld, we find that oscillation frequency is determined by downstream acoustics in the case of a strong acoustical coupling (second mechanical resonance). When ther is a small acoustical coupling, the oscillation frequency corresponds to the third mechanical resonance, but the frequency jumps to the second mechanical resonance when Pl increases. 2) Theoretical analysis
Fig8: The one mass model compared to the two mass model with a delayed mass
Fig9: Physical description of the one mass model
We simulated two models : the one mass model and the two mass model with a delayed mass. From these models, we observe the threshold pressure for oscillation, as a function of the replica’s pressure. The obtained results are very close to the “invitro” measures on the replica, excepted between 6000 and 8000 Hz.
Fig10: Modelled threshold pressure (Pl,th) as function of Pin preliminary results
Fig11: Model parameter (fL)
Fig12: Modelled threshold pressure (fres) as function of Pin
Fig13: Modelled oscillation frequency (fres) as function of Pl
Conclusions We have presented here an experimental set-up for the validation of a theoretical model. We have observed some fundamental differences between weak (vocal tract) and strong (brass instrument) acoustical coupling. •
In the case of strong acoustical coupling, Pl,th(Pin), fres(Pin) and fres(Pl) are well predicted by theoretical model. Further validation is needed (oscillation amplitude, onset and offset of oscillation, mechanical boundary conditions ...).
•
in the case of weak acoustical coupling , no oscillations are possible for the one mass model.
However , the threshold pressure measured on the replica are quite weak compared to those measured on real vocal folds. It would be usefull to build a new replica.
