Physics of Wind Musical Instruments

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High performance computers are now powerful enough to enable accurate computational studies of wind musical instruments based on the fundamental equations of fluid dynamics. The results of this project will pave the way to fundamental modeling studies of virtually all wind instruments. The students who engage in this work will acquire computational skills that can be applied to a variety of other problems in science and engineering. Indeed, modeling the sound produced by a wind instrument involves the same equations and the same computational issues that are encountered in studies of the sound produced by a jet turbine, the motion of a flapping wing, human phonation, and other important aerodynamics problems, so students involved in this project will be well versed in the advanced computational modeling methods needed to tackle a wide range of problems in science and engineering. Students will also learn about general experimental skills that can be used to make the musical instruments modeled in this project, as well as techniques for data acquisition and spectral analysis required in the study of these new instruments. In addition, the PI will develop instructional modules on acoustics and musical instruments for K-12 teachers and students who participate in outreach programs at Auburn University. Sound generation in wind instruments such as the recorder, flute, trumpet, and clarinet involves the motion of a compressible fluid (air). This motion can be extremely complicated, and can lead to vortex formation and various nonlinear phenomena found in strongly driven fluids. The project described in this proposal will use advanced computational methods to study the fluid dynamics of air inside and around a variety of wind instruments, including recorders, flutes, trumpets, and clarinets. This fluid motion is directly responsible for sound generation, so the results of this study will lead to a better understanding of the musical tones produced by wind instruments. The computational results will also be compared with experiments performed with custom made instruments, so as to test and validate the computational findings. A first principles description of the fluid dynamics of a wind instrument requires the solution of the Navier-Stokes equations, a set of nonlinear partial differential equations. This project will obtain solutions of the Navier-Stokes equations for a variety of wind instruments using state-of-the-art computational resources and custom designed algorithms for multicore computer architectures. These computational studies will be complemented with experimental measurements designed to test specific qualitative and quantitative predictions of the modeling results, leading to new insights into these instruments. Several hypothetical new instrument geometries will be studied, work that may identify new designs that produce specific tonal properties not found in current instruments. This project will also explore how to model key aspects of the player, such as the motion of the player’s lips and air flow through the player’s mouth. The techniques that are developed in this project will be applicable to all wind instruments and will therefore be of broad interest in the field of musical acoustics.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.