Hostname: page-component-848d4c4894-mwx4w Total loading time: 0 Render date: 2024-06-21T04:33:49.437Z Has data issue: false hasContentIssue false
  • English
  • Français

On the scattering of evanescent waves into sound

Published online by Cambridge University Press:  21 April 2006

J. E. Ffowcs Williams  and
D. C. Hill
J. E. Ffowcs Williams
Affiliation:
Cambridge University Engineering Department, Trumpington Street, Cambridge CB2 1PZ, UK
D. C. Hill
Affiliation:
Cambridge University Engineering Department, Trumpington Street, Cambridge CB2 1PZ, UK
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper concerns the conversion of momentum and energy from evanescent surface waves into sound. Exact results are obtained from surface waves of specified form on a confined region of an otherwise rigid plane surface. The model chosen is simple enough for exact analysis while approximating some of what we believe to be significant aspects of sound generation by vibrating surface panels.

We find that the evanescent wave approaching an edge gives up all of its energy into sound, a sound which is beamed mainly parallel to the direction of the surface-wave phase velocity. The surface remains energetically inactive, but exerts a force on the fluid in the opposite direction to the incoming wave. This force is balanced by a nonlinear mean pressure gradient in the field of the evanescent wave, and by momentum in the sound field.

Sound is also produced when a similar evanescent wave emerges from an edge. The surface has then to provide the necessary energy for both waves. These waves induce a mean axial force at the boundary which forces the fluid in the direction of the receding evanescent wave.

A similar wave travelling across a finite panel in the otherwise rigid plane surface is observed to have some characteristics of the previous two cases, but there is no axial force arising from the mean pressure gradient.

These results are applied to the problem of a semi-infinite tensioned membrane, and the energy radiation under light fluid loading is determined for the case of high and low free membrane wave speeds.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 184 , November 1987 , pp. 101 - 121
Copyright
© 1987 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Davies, H. G. 1974 Natural motion of a fluid-loaded semi-infinite membrane. J. Acoust. Soc. Am. 55, 213–219.Google Scholar
Gradshteyn, I. S. & Ryzhik, I. M. 1980 Table of Integrals, Series, and Products. (Corrected and enlarged edition.) Academic.
Hill, D. C. 1986 Starting mechanics of an evanescent wave field. J. Fluid Mech. 165, 319–333.Google Scholar
King, L. V. 1934 On the acoustic radiation pressure on spheres. Proc. R. Soc. Lond. A 147, 212.Google Scholar
Levine, H. 1980 A note on sound radiation into a uniformly flowing medium. J. Sound Vib. 71, 1–8.Google Scholar
Möhring, W. 1982 Wave energy, wave momentum, and propagation of sound in flows. Fortschritte der Akustik, FASE/DAGA '82.
Taylor, G. I. 1942 The motion of a body in water when subjected to a sudden impulse. Scientific Papers of G. I. Taylor, Vol. 3. Aerodynamics and the Mechanics of Projectiles and Explosives (ed. G. K. Batchelor), pp. 306–308. Cambridge University Press.