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 p[inf u] upstream and p[inf d] downstream of the reed are measured over time and their waveforms are subtracted to obtain the pressure difference p. The input impedance Z[inf d] of the instrument mouthpiece downstream of the reed is also measured, and the flow u estimated as the ratio p[inf d]/Z[inf d]. 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.