Impedance at Mouth of Organ Pipe

Abstract

Using velocity and pressure probes, the complex impedances at the mouths of closed and open organ pipes have been measured just inside the mouth and just outside, on either side of the jet. Outside the pressure leads the velocity by roughly 90° at each harmonic frequency and impedance magnitude increases approximately proportional to frequency as expected from linear end correction theory. Inside, the fundamental component of pressure is only a few degrees ahead of velocity in phase, while the higher harmonic components have a somewhat larger phase difference. This is in qualitative agreement with results of Ingard for nonlinear orifice impedance made for similar range of parameters. Fourier analysis of jet driving-pulse phase indicates that discontinuous overblow of closed pipe as contrasted with relatively smooth overblow of open pipe is due to sudden increase in “active” impedance of the jet associated with critical amplitude of third harmonic at which jet begins to enter pipe twice in a cycle. [Work supported by ONR.]