Linear-response reflection coefficient of the recorder air-jet amplifier

TL;DR

This paper measures the linear response of a recorder's air-jet amplifier using a waveguide reflectometer, enabling analysis of its stability and reflection coefficient without gain saturation effects.

Contribution

It introduces a method to measure the reflection coefficient of the air-jet amplifier independently of gain saturation by using an open-loop setup with a waveguide reflectometer.

Findings

Reflection coefficient varies with blowing pressure and frequency.

The system's stability depends on whether the feedback loop is closed or open.

Results test and evaluate flute drive models under simplified conditions.

Abstract

In a duct-flute such as the recorder, steady-state oscillations are controlled by two parameters, the blowing pressure and the frequency of the acoustic resonator. As in most feedback oscillators, the oscillation amplitude is determined by gain-saturation of the amplifier, and thus it cannot be controlled independently of blowing pressure and frequency unless the feedback loop is opened. In this work, the loop is opened by replacing the recorder body with a waveguide reflectometer: a section of transmission line with microphones, a signal source, and an absorbing termination. When the mean flow from the air-jet into the transmission line is not blocked, the air-jet amplifier is unstable to edge-tone oscillations through a feedback path that does not involve the acoustic resonator. When it is blocked, the air-jet is deflected somewhat outward and the system becomes stable. It is then possible to measure the reflection coefficient of the air-jet amplifier versus blowing pressure and acoustic frequency under linear response conditions, avoiding the complication of gain-saturation. The results provide a revealing test of flute drive models under the simplest conditions and with few unknown parameters. The strengths and weaknesses of flute drive models are discussed.