Sound radiation into uniformly flowing fluid by compact surface vibration

Abstract

This paper describes a model problem where compact surface vibration radiates sound into a subsonically flowing fluid. There are two distinct acoustic effects. First, the radiation is increased by flow by an amount proportional to 5M2 and that increase is shown by a general argument to arise from an enhanced surface damping and work done by the flow to overcome drag in the ratio 2:1. Second, the acoustic source strength is affected and resonance frequencies are significantly modified by flow. The main effect is that flow induces on the surface a force proportional to the displacement which opposes the action of natural surface elasticity. A critical velocity exists beyond which the surface is unstable; the stability limit is determined. The surface motion might be regarded as an acoustic monopole, but since aerodynamic fields are determined by the rate of change of the rate of mass outflow, the frequency dependence is more that of a quadrupole. Convective amplification of the sound is also shown to be that characteristic of quadrupole sources. This result indicates that real simple fields may be more sensitive to convection than might be expected from past studies of simple inhomogeneities satisfying a convected wave equation.