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

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.