## 5pMU11. Spectral energy balance in wind instruments.

### Session: Friday Afternoon, December 6

### Time: 4:45

**Author: P. L. Hoekje**

**Location: Dept. of Phys., Univ. of N. Iowa, Cedar Falls, IA 50614-0150**

**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.

ASA 132nd meeting - Hawaii, December 1996