Wave Propagation on an Acoustically Perturbed Jet

Abstract

Theories of the initiation and propagation of transverse sinuous disturbances on an air jet emerging from a flue slit into a transverse acoustic velocity field are reviewed and brought into a form suitable for comparison with experiment. Available experimental data is then reviewed and is found to be only moderately well accounted for by the existing theory. A new series of experimental determinations of wave velocity on a jet .under conditions relevant to sound generation in musical instruments is then described, these measurements extending over a larger range of frequencies and blowing pressures than earlier measurements. For jets with Reynolds number below about 1000 the wave velocity is found to be constant along the length of the jet and to depend not upon the jet velocity V but rather upon the integral J of v2 across the width of the jet. At low frequencies, w, the wave velocity is approximately 0.7 (J w)l/3, in agreement with existing theory, but at higher frequencies it becomes independent of co and approximately given by 50 J (where S.I. units are implied). Wave amplification along the jet is also· studied and the wave amplitude found to increase like exp (μx) where μ is positive only below a cPitical frequency w*, dependent on the jet parameters. For the jets studied, μis of order 1x103 m-1 below w*. A simple theory based on dimensional analysis is proposed to describe these experimental results.