EXPERIMENTAL INVESTIGATION OF THE INFLUENCE OF THE MECHANICAL CHARACTERISTICS OF THE LIP ON THE VIBRATIONS OF THE SINGLE REED

Transcription

1 EXPERIMENTAL INVESTIGATION OF THE INFLUENCE OF THE MECHANICAL CHARACTERISTICS OF THE LIP ON THE VIBRATIONS OF THE SINGLE REED B Gazengel, T Guimezanes, J P Dalmont Jean Baptiste Doc, Sylvain Fagart, Y Léveillé. Laboratoire d'acoustique de l'université du Maine, UMR CNRS 6613 Av. Olivier Messiaen, Le Mans Cedex 9 bruno.gazengel@univ lemans.fr Abstract The effect of lip on the response of single cane reed is studied. In a first part, the real human lip is characterized using a shaker and a impedance head. The measurement is conducted for different lip configuration. Then artificial lips are built and their mechanical impedance are measured. An artificial lip is retained for making experiments conducted on single reeds. The mechanical response of a a reed mounted on a mouthpiece and excited with a loudspeaker is measured using an artificial lip pressed against the reed. The measured transfer functions show a two degree of freedom response which resonance characteristics depend on the lip pressure. For a high lip pressure, the first resonance shows a high damped resonance around 1200 Hz and the second resonance is located around 4000 Hz. INTRODUCTION The characteristics of single cane reed are important for clarinet or saxophone players. Indeed, it is well known that the stiffness of the reed is the first criteria for the choice of a reed. Resonance characteristics are also certainly important for the spectrum [Guillemain, 2005]. This is why the reed is classically modeled as a single degree of freedom oscillator. Such a model can be a powerful tool to predict the functioning of the clarinet or even to synthesize a realistic sound of clarinet [Guillemain, 2005; Dalmont, 2005]. However, this is only a first order approach and an accurate modeling of the clarinet needs more investigation. Some authors have studied the modes of the free reed in forced oscillations [Fachinetti, 2003; Pinard, 2003]. However, it is not straightforward how these modes might have an influence on the functioning or the timbre of the instrument. It is rather intuitive that in practice the lip might have a great importance on the vibrations of the reed and this is the aim of the present paper to investigate how the lip modifies these vibrations. The goal of the present work is to determine experimentally the equivalent mechanical parameters of the lip and reed system in forced oscillations assuming a

2 linear response of the system (small amplitude oscillations). In the first part, the mechanical response of human lips are measured. Considering that these responses can be modeled as those of a single degree of freedom system, equivalent parameters are derived. Different artificial lips are then built and their mechanical responses are measured. The artificial lip whose impedance is the closest to that of the human lips is retained for the study. In a second part, the artificial lip is used on an experimental system which enables to measure the mechanical response (velocity/pressure) of a single cane reed mounted on a mouthpiece and pressed by an artificial lip. EXPERIMENTAL STUDY OF LIPS This part aims at designing an artificial lip which mechanical characteristics are close to that of a human lip. The characteristics of human lip are first measured. Natural lip In a first step, the natural lip mechanical impedance is characterized using an impedance head driven by a shaker (Fig 1). This impedance head is connected to a small plate which is pressed against the natural lip. The experiment is conducted using three different lip s (high, medium and low). The high case corresponds to a very tight embouchure whereas the low corresponds to a very loose embouchure. These two extreme cases are probably not used in a musical performance. tooth Lip plate Impedance head shaker Figure 1: Natural lip mechanical impedance measurement (left : principle, right : view of the measurement) Different measured admittance (velocity / force) curves are presented in Fig. 2. Results show that the lip and plate system resonance frequency is between 50 to 300 Hz with a mechanical compliance of 11 to 300 µm/n and a quality factor of about 1.5 (Table 1). Assuming that the plate mass Mp connected to the impedance head is known, a first simple approach consists in assuming that the lip mass M L can be estimated using the lumped constant model shown in Fig. 3. In this case, the lip mass can be estimated by subtracting the plate mass to the estimated mass. Results are given in Table 1.

3 Figure 2: Real lip mechanical response (velocity / force) for three embouchure sl Mp ML RL Figure 3: Lumped modeling of the lip the plate used for the impedance measurement Artificial lip In a second step, different artificial lips are realized using a rubber balloon filled with water or glycerin (Fig. 4) and foam. The mechanical admittance of these artificial lips are measured using a shaker and an impedance head for different static load (which are not measured). Results (Fig. 5) show that the artificial lip filled with water has a larger quality factor than that of with the lip filled with glycerin, both being larger than that of the human lip.

4 balloon liquid foam Figure 4: Artificial lip mechanical (left : principle, right : view of the sample) Figure 5: Real and artificial (water and glycerin) lip mechanical response obtained for medium The equivalent parameters of the natural lip and artificial lip (filled with glycerin) connected with the measurement mass (plate) are given in Table 1. These are obtained by assuming a single degree of freedom system.

5 Natural lip Artifical lip (glycerin) LIP AND PLATE Small Medium High Small Medium High Resonance frequency (Hz) 56, ,5 82,7 Quality factor 1,61 1,45 1,55 5,8 6,3 4,35 Mechanical compliance x10 6 (m/n) LIP Small Medium High Small Medium High Mass (g) 6, ,8 2,8 2,6 Damping (Nm 1s) 5, ,7 1,15 2,7 Mechanical compliance x10 6 (m/n) Table 1: Equivalent parameters of natural and artificial lip (glycerin) with plate and without plate These results show that the natural lip should better be replaced by an artificial lip filled with glycerin in order to obtain mechanical characteristics which represent at best the functioning of the real lip. However, the damping of the artificial lip is too low compared with the damping of the natural lip and the artificial compliance is too large compared with the natural compliance. VIBRATIONS OF REED WITH A LIP The aim of this section is to measure the mechanical response (velocity/pressure) of the reed mounted on the mouthpiece and pressed by an artificial lip. Experimental system The experiment setup is presented in Fig. 6. In this experiment, the mouthpiece cavity is excited with a loudspeaker. The pressure inside the mouthpiece, assumed to be uniform in the mouthpiece cavity, is measured with an electret microphone. The velocity of a point of the reed tip is measured with a laser vibrometer. The artificial lip is pressed against the reed with different static pressure (which are not measured). The transfer function is measured by means of a HP analyser connected to a PC with a HPIB connection. Results The measured transfer functions are presented in Fig. 7 for the artificial lip filled with glycerin and in Fig. 8 for the artificial lip filled with water.

6 microphone Laser vibrometer conditionning Lip conditionning Velocity out ampli. Loudspeaker analyzer source 1 HP-IB PC 2 Figure 6: View of the experimental setup In the absence of lip the measurement of the tip vibrations emphasizes 4 or five modes between 0 and 8 khz. This is in agreement with other studies. The results with the lip made with a balloon filled with water emphasize peculiar results : first mode is split into 3 to five modes which can be interpreted as modes of the balloon itself. Results with the lip filled with glycerin are probably more realistic. When the lip is pressed against the reed, higher modes seems to disappear. For a small lip pressure the first reed resonance frequency is shifted to the low frequency range which can be interpreted as an added mass effect. When the lip pressure increases the first resonance tends to disappear which can be explained by the large damping introduced by the lip and a second peak appear which can be interpreted as the first flexural mode of the reed pinched at the lip position. Generally speaking, the reed and lip system shows a two degree of freedom response with resonance frequencies located around 1200 Hz and 4000 Hz. This suggests that the reed mechanical response could be modeled as a two degree of freedom.

7 Figure 7: Transfer functions of the reed + lip system obtained for different lip pressure Left : lip filled with glycerin. Figure 8: Transfer functions of the reed + lip system obtained for different lip pressure Left : lip filled with glycerin. Right : lip filled with water.

8 CONCLUSION AND PERSPECTIVES The mechanical response of a cane clarinet reed has been studied experimentally, the reed being mounted on a mouthpiece and pressed by an artificial lip. In order to design the artificial lip, the mechanical admittance of the human lip has been measured and equivalent parameters (mass, compliance, damping) have been identified. Two artificial lip (filled with water and glycerin) have been built and characterized experimentally. The glycerin lip shows characteristics which represent at best the real lip. The mechanical response of the reed has been measured using the glycerin artificial lip for different lip pressures. Results show that the mechanical response of the reed depends highly on the lip pressure. However the reed and lip system can be viewed as a two degree of freedom system for low level excitation levels. This shows that modal analysis of the free reed has to be interpreted with discretion. This work is a first approach of the subject and further work need to be done. First concerns the estimation of the mechanical parameters characterizing the real human lip for different embouchure and different musicians. Second work will consists in designing artificial lip which characteristics are nearer from those of the real lip. Finally a physical model of the reed and lip system similar to the one developed in [Avanzini, 2004] but based on experimental results will be developed in order to better understand the effect of the lip on the reed vibration. REFERENCES Guillemain Ph., Helland R. T., Kronland Martinet R.,Ystad S. (2005) The Clarinet Timbre as an Attribute of Expressiveness, Lecture Notes in Computer Science, LNCS 3310, Springer Verlag, pp Dalmont J. P.,Gilbert J., Kergomard J., Ollivier S. (2005) An analytical prediction of the oscillation and extinction thresholds of a clarinet, J. Acoust. Soc. Am. 118, pp Fachinetti, M.L., Boutillon, X., Constantinescu, A. (2003), Numerical and experimental modal analysis of the reed and pipe clarinet, J. Acoust. Soc. Am. America 113(5), pp Pinard, F., Laine, B., Vach, H. (2003), Musical quality assessment of clarinet reeds using optical holography, J. Acoust. Soc. Am. America 113(3), pp Avanzini, F., van Walstijn., M. (2004) Modelling the Mechanical Response of the Reedmouthpiece lip System of a Clarinet. Part I. A One Dimensional Distributed Model. Acta Acustica united with Acustica, 90(3), pp