Sound Sources in Aerodynamics-Fact and Fiction

Abstract

Introduction N is distinguished from sound only in that it is an unwanted irritant. There is no measure of signal continuity or harmony that can classify a sound as noise. Its noisiness depends on the sensitivity of a listener and that sensitivity can vary with circumstances and time. The control of noise calls for definite measures and standards and those standards must reflect the magnitude of the noise nuisance. Since that is a subjective matter, it follows that the units of noise measurements are inevitably influenced by psychological issues. Because of this noise control is not as rational a subject as others in mechanics. But the basic phenomenon of sound is entirely rational. Sound is a vibration of the air. It travels; an underwater pistol shot can be heard around the world and China's offshore islands hear clearly the news and comments shouted at them through powerful loudspeakers some 30 km away. Those sound waves carry tens of kilowatts of acoustical power, the equivalent of the world's noisiest aircraft, and when one recalls that the ear is accustomed to monitoring the human whisper, an acoustic power level of only 10 ~ W, one can marvel at the amplitude range over which the sound is essentially linear. The ear detects pressure variations as small as 10 atm and can be damaged if subjected to variations in excess of 10 ~ atm. Pressure fluctuations adjacent to the loudest jet aircraft reach a tenth of an atmosphere. Generally, therefore, sound pressure variations are weak, as are their associated aerial motions, and the mechanics of sound can be understood within the context of linear theory. In linear theory, waves add without distortion; multiple conversations at a cocktail party do not interfere. Though linear sound is such a definite phenomenon, conforming precisely with the rational laws of mechanics, the source of that sound is not. That is an issue not dissimilar to the distinction between noise and sound; it is largely a point of view and subject to rational analysis only when some axiomatic position is taken. A source must first be defined. This point is true of all linear waves, be they optical, mechanical, or electrical, the issue being illustrated by considering the difficulty that an observer of a perfectly reconstructed holographic image would have in determining the source of the light field; and this example illustrates also that wave fields, identical in extensive regions of space, can have completely different sources. It is not possible to determine from a wave field what its source must have been. Of course, in linear fields one can make a good guess, holographic reconstructions are not very common. We rarely make mistakes in giving the most obvious interpretation to visual images. Blind bats are effective hunters of prey they track by interpreting, the origin of scattered sound waves. The essential ambiguity in that interpretation bothers them not at all; but it becomes important once nonlinearities are admitted. Sources of sound in aerodynamics are frequently nonlinear and we shall see that determining whether certain features are, or are not, sources of sound, is sometimes influenced greatly by matters of formal definition. There is no doubt that if a flow is known precisely then its distant wave field is also known, but aerodynamicists are led to conjecture what aspects of a flow cause the noise field observed at a distance without a detailed knowledge of the flow; there is no unambiguous procedure by which that can be done. Confidence in their conjectures must be established slowly by testing source location schemes in situations where the flow is understood and by examining details of sound production in simple flows that are known exactly. Unfortunately, not very many unsteady compressible flows are known exactly and much of recent progress in aerodynamic noise has concerned the development of asymptotic solutions to definite model problems; it is those solutions that give confidence in the source identifications made by formal but rather arbitrary prescriptions. Not all that is heard is sound. The air stream about the unprotected ears of a motor cyclist can be painfully noisy even though a negligible part of the pressure variations within the turbulent eddies that bother him so much propagate away as sound. They can be made to propagate by the action, for example, of a resonator, and that is the principle of the wind instruments. Resonators and the way sound propagates from them have been understood as long as acoustics has been a science, but the mechanics of their excitation, i.e., the basic source process, is much more difficult to grasp. Some of that difficulty is caused by the pseudosound in which unsteady pressures are nonlinearly related to fluid motion and which are not organized like proper sound into propagating waves.