Page 58 - Spring 2018

Woodwind Acoustics
inputs more acoustic power than the bore loses. The result is that a small signal at the fundamental frequency increases exponentially until the small signal approximation is no lon- ger valid (Li et al., 2016). (This argument treats the inertia of the reed as negligible, which ceases to be even approximately true for high notes.) This simple model also explains the fi- nal transient. For example, if the reed is abruptly stopped by the tongue, the fastest possible decay rate is determined by the quality factor of the operating resonance.
Qualitatively, the double reeds of oboe, bassoon, and others share the same principles, although the geometry of the reed and its motion are both more complicated. The compliance and inertia of the reeds, the acoustic resistance in the narrow passage between them, and the Bernoulli force on the reed play larger roles, and the difference between the quasi-static and oscillating regimes is greater (Almeida et al., 2007).
Controlling the Output Sound
In Sound Production with an Air Jet, I mentioned some of the jet control parameters used by flutists. The argument immediately above shows the importance of blowing pres- sure and lip force(s) for reed players. Complicating life for players is that control parameters often affect several output properties. For example, blowing pressure and lip force both affect each of loudness, pitch, and spectrum.
Another aspect of control involves the player’s vocal tract. A vibrating reed produces acoustic waves in both directions, and the acoustic force acting on the reed is approximately proportional to the series combination of the impedances of the bore and vocal tract. Especially at high frequencies, where the impedance peaks of the bore are weaker (Figure 6), resonances in the tract can affect pitch and timbre or con- trol multiphonics. Tuning the tract resonances is necessary for playing the high range of the saxophone and for the fa- mous clarinet portamento that begins Gershwin’s Rhapsody in Blue (Chen et al., 2008, 2009).
The diversity and complexity of woodwinds and the range of interesting physical effects involved continue to engage the attention of researchers. Excellent technical treatments of woodwind acoustics are given by Nederveen (1998), Fletch- er and Rossing (1998), and Chaigne and Kergomard (2016). My lab concentrates on the musician-instrument interaction (reviewed by Wolfe et al., 2015) and provides introductions with sound files and video (Music Acoustics, 1997).
Acknowledgments
I thank my colleagues, students, and the Australian Research Council for their support and Yamaha for instruments.
56 | Acoustics Today | Spring 2018
References
Almeida, A., Verguez, C., and Caussé, R. (2007). Quasistatic nonlinear char- acteristics of double-reed instruments. The Journal of the Acoustical Society of America 121, 536-546.
Angster, J., Rucz, P., and Miklós, A. (2017). Acoustics of organ pipes and future trends in the research. Acoustics Today 13(1), 10-18
Atema, J. (2014). Musical origins and the stone age evolution of flutes. Acoustics Today 10(3), 25-34.
Auvray, R., Ernoult, A., and Fabre, B. (2014). Time-domain simulation of flute- like instruments: Comparison of jet-drive and discrete-vortex models. The Journal of the Acoustical Society of America 136, 389-400.
Chen, J. M., Smith, J., and Wolfe, J. (2008). Experienced saxophonists learn to tune their vocal tracts. Science 319, 776.
Chen, J. M., Smith J., and Wolfe, J. (2009). Pitch bending and glissandi on the clarinet: Roles of the vocal tract and partial tone hole closure. The Journal of the Acoustical Society of America 126, 1511-1520.
Chaigne, A., and Kergomard, J. (2016). Acoustics of Musical Instruments. Springer-Verlag, New York.
Dalmont, J.-P., and Frappé, C. (2007). Oscillation and extinction thresholds of the clarinet: Comparison of analytical results and experiments. The Journal of the Acoustical Society of America 122, 1173-1179.
Fletcher, N. H., and Rossing, T. D. (1998). The Physics of Musical Instruments, 2nd ed. Springer-Verlag, New York.
Li, W., Almeida, A., Smith J., and Wolfe, J. (2016). The effect of blowing pres- sure, lip force and tonguing on transients: A study using a clarinet-playing machine. The Journal of the Acoustical Society of America 140, 1089-1100.
Moore, T. (2016). Acoustics of brass musical instruments. Acoustics Today 12(4), 30-37.
Music Acoustics (1997). From UNSW Sydney newt.phys.unsw.edu.au/music. Accessed September 27, 2017.
Nederveen, C. J. (1998). Acoustical Aspects of Wind Instruments. Northern Il- linois University, DeKalb, IL.
Wolfe, J., Chen, J. M., and Smith, J. (2010). The acoustics of wind instruments – and of the musicians who play them. Proceedings of the 20th International Congress on Acoustics, ICA-2010, Sydney, Australia, August 23-27, 2010, pp. 4061-4070.
Wolfe, J., Fletcher, N. H., and Smith, J. (2015). Interactions between wind instru- ments and their players. Acta Acustica united with Acustica 101, 211-223.
Biosketch
Joe Wolfe is a professor of phys- ics at the University of New South Wales (UNSW) Sydney, where he leads a lab researching the acous- tics of the voice and musical instru- ments, especially woodwinds, brass, and didgeridoo. In the past, he has
worked at Cornell University, Ithaca, NY, at CSIRO (Austra- lia’s national research organization), and the École Normale Supérieure, Paris. He has received national and internation- al awards for research and teaching. Outside of physics, he plays double reeds and the saxophone. His trumpet concerto has been performed several times, and his quartet has had concert performances on all continents except Antarctica.