Physics of Wind Musical Instruments

Auburn University, Auburn AL

Investigators

Abstract

Sound generation in wind instruments such as the recorder, flute, and trumpet involves the motion of a compressible fluid (air). This motion can be extremely complicated, and can lead to vortex formation and other phenomena found in strongly driven fluids. Such complex fluid motion is generally found in the mouthpiece of a wind instrument or near constrictions such as toneholes, where experimental observations are most difficult. This project will use advanced computational methods to study the fluid dynamics of air inside and around several wind instruments. 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 a variety of wind instruments. The computational results will also be compared, where possible, with experimental results obtained with custom made instruments as part of this project or through the experimental work of other groups. The undergraduate and graduate students who will be involved in this project will engage in experimental work and will also work on the modeling. This modeling experience will prepare them for careers in advanced scientific computing, since the methods used to solve the Navier-Stokes for a musical instrument are applicable to many problems of technological interest. The physical laws that describe the fluid dynamics central to wind instruments are well known. These laws are expressed in the Navier-Stokes equations, a set of nonlinear partial differential equations which are applicable to many situation involving fluid flow . The complexity of the Navier-Stokes equations is such that their application to realistic musical instruments (and other complicated systems) demands a computational solution, which is now feasible with available high performance parallel computers. This project will use the approach known as "direct numerical simulation" to obtain solutions of the Navier-Stokes equations for a variety of wind instruments. This will be achieved 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 predictions of the modeling results, leading to new insights into these instruments. Several hypothetical new instrument geometries will also be studied, work that may identify new geometries that produce specific tonal properties not found in current instruments. The techniques that are developed in this project will be applicable in all wind instruments and will therefore be of broad interest to the field of musical acoustics and beyond.