The Physics of Wind Instruments

Abstract

Musical instruments have been studied by physicists for centuries due to their complex mechanisms and the presence of many pieces of fundamental physics within. This dis- sertation aims its focus on wind instruments which are particularly difficult to model because the equations that govern air flow are nonlinear. The last couple of decades have seen the rise of fast and cheap computing power which make it possible for re- searchers to use first principles approaches employing the Naiver-Stokes equations. The goals of this project were to improve the design of the recorder using simulations that are based on first principles physics, to understand the effect of a musician’s blowing profile on the tone of the recorder, and to present and discuss a model for a clarinet reed that will be part of fully distributed model of the clarinet. This thesis explores how simulations based on the Navier-Stokes equations can be used to get new insights into wind instruments. Specifically, these simulations which are all based on the Navier- Stokes equations are used to (1) understand how small alterations to the geometry of the recorder will affect the dynamical playing range for fundamental modes of a recorder. The new design was identified using simulation results then validated via experiments on 3D printed recorders. (2) A full sized soprano recorder that mimics the geometry of the Yamaha YRS-23 was used to study the effect of blowing profile on the tone of the instrument. The presence of inharmonic frequencies in the attack transient of the tone were detected which affect the tone color of the instrument. (3) A model of the reed of the clarinet is presented; this particular model of the reed allows more efficient computa- tions in Navier-Stokes simulations of the clarinet. Instrument makers typically improve instrument design by using guided intuition. The work in this dissertation provides in- sights on how wind instrument design can be improved by using a more quantitative, scientific, and collaborative approach between instrument makers and scientists.