Spectral energy balance in wind instruments

Abstract

The nonlinear flow control mechanism in cane- and lip-reed wind instruments is explored by comparing the pressure p across the reed and the volume flow u exciting the air column under playing conditions. The pressures pu upstream and pd downstream of the reed are measured over time and their waveforms are subtracted to obtain the pressure difference p. The input impedance Zd of the instrument mouthpiece downstream of the reed is also measured, and the flowu estimated as the ratio pd/Zd. In this case, u includes both the airflow through the reed aperture and the air displaced directly by motion of the reed. The relation of u as a function of p gives the flow control characteristics. At low playing levels, u(p) is nearly linear, but becomes progressively nonlinear at louder playing levels, as predicted. For each spectral component, the variation of u with p is then separated into a linear part, which can be considered to describe the linear feedback mechanism, and a nonlinear part that is ultimately responsible for spreading energy among different components. Viewed in this way, individual spectral components can be identified as net energy producers or consumers.