On the Edgetone

Abstract

The feedback mechanism of classical low-speed edgetones in which the action at the edge is interpreted as an acoustical source is developed in detail. A theoretical development indicating that the acoustic field is primarily due to the dipole associated with the fluctuating fluid force on the edge has been verified. It is the hydrodynamic field of the dipole which disturbs the jet, whose instability characteristics are shown to depend acutely on the Reynolds and Strouhal numbers, and the orifice-edge distance. The gain criterion is developed in detail, it being shown how the eigenfrequencies (which can form no algebraic sequence) arise; the lower limit to the orifice-edge distance is discussed, yielding an estimate of the “linear” instability of the stream. The amplitude of the established edgetone depends on the nonlinear behavior of large-amplitude stream disturbances and the corresponding upper limit to the edge force proves to be in satisfactory agreement with measurements, thus yielding acceptable expressions for the sound pressure. Multiple tones and the circumstances of the hysteretic frequency jumps are discussed. The basic action depends only on Reynolds number for geometrically similar systems, while the sound power depends on the cube of the Mach number also.