How well do lumped-element models describe acoustic amplification in the recorder? Free

Nearly 50 years have passed since Cremer and Ising [Acustica 19, 142-153 (1967)] established lumped-element feedback models as the dominate paradigm for understanding flute-family musical instruments. Modern versions of these models include one feedback path through the resonant acoustic flow in the pipe, and a second path that accounts for edge-tone phenomena. They also incorporate results of later experimental and theoretical work on jet formation, jet deflection, and growth of instabilities along the jet. In this work, we test a lumped model of the recorder air-jet amplifier by replacing the recorder body with a waveguide reflectometer. When the mean flow from the air-jet into the waveguide is not blocked, the air-jet amplifier is unstable to edge-tone oscillations. When it is blocked, the air-jet is deflected somewhat outward, gain is reduced, 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 lumped flute drive models under simple conditions and with few unknown parameters. The strengths and weaknesses of modern flute drive models are discussed.