The intnesity of Aeolian tones

Abstract

The generation of Aeolian tones is interpreted in terms of the theroy of aerodynamic sound. To do this, the intensity of the radiated sound is expressed in terms of the fluctuations in force upon a moving rigid body using the approximation that, at low mach numbers, these forces can be calculated assuming incompressibility of the flow. The fluctuations in lift and drag upon a circular cylinder at Reynolds numbers between 40 and 160 are calculated by integrating the fluctuations in momentum in the eddying wake, using the experimental data of Kovasznay (1949). It is found that the fluctuating lift per unit length is approximately where ρ is the density of the fluid and t the time, and that the magnitude of the fluctuations in drag is about 10% of this.The axial length scale of these force fluctuations was found by an auxiliary experiment to be very large for Reynolds numbers below 100. When 100 < R < 160, the lenth scale is approximately 17d, the transition apparently occurring as a result of the instability to three-dimensional disturbances of the laminar eddying wake. Using this datum, the mean square acoustic pressure generated by the motion about the cylinder at these Reynolds numbers is found to be where θ is the angle between the direction of observation and the incident stream, l the length of the cylinder and a the velocity of sound in the medium. Experiments undertaken to test this result directly, using sound intensity measurements from a whirling arm apparatus in an accoustically quiet room, gave very good agreement.At higher Reynolds numbers, when the cylindg wake is turbulent, the theory leads to a, similar expression for but with a smaller numerical factor. Analysis of previous experimental data on this basis gives good agreement, with a value of about 0·037 for the numerical constant. In view of this, it is likely that some of the earlier data which had appeared to give a Mach number dependence of M4, not M6, have been misinterpreted. Finally, mention is made of the conditions when the frequency of vortex generation is the same as the natural frequency of the wire, and the greatly increased intensity of the sound is seen to be the result of the greatly increased axial length scale of the force fluctuations.The relative simplicity of this phenomenon makes possible perhaps the least ambiguous confirmation yet found of some of the essential ideas in the theory of aerodynamic sound.