Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-26T01:10:00.791Z Has data issue: false hasContentIssue false
  • English
  • Français

Generation of an acoustic pulse by a baffled circular piston

Published online by Cambridge University Press:  20 January 2009

P. Chadwick  and
G. E. Tupholme
P. Chadwick
Affiliation:
School of Mathematics and Physics, University of East Anglia, Norwich
G. E. Tupholme
Affiliation:
School of Mathematics and Physics, University of East Anglia, Norwich
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The generation of acoustic disturbances in a fluid of semi-infinite extent by the motion of a circular piston surrounded by a plane rigid baffle has been studied quite extensively (see (1), (2), (3), (4) and further references given in these papers). Attention has been devoted mainly to the case in which the piston executes a harmonic oscillation of small amplitude, and only comparatively recently has Oberhettinger (2) demonstrated how the time-harmonic solution can be used to solve the more general problem in which the normal velocity of the piston is an arbitrary function of time. The purpose of the present paper is two-fold. Firstly, we point out that for arbitrary normal motion of the piston the " baffled piston problem " can be solved directly, and in a particularly simple manner, by means of a technique involving integral transforms which has been applied by Mitra (5) and Eason (6) to the study of shear wave propagation in an elastic half-space. Secondly, we give a more detailed account than appears to be available in the literature of the structure of the sound pulse generated by the arbitrary normal motion of a baffled piston.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 15 , Issue 4 , December 1967 , pp. 263 - 277
Copyright
Copyright © Edinburgh Mathematical Society 1967

References

REFERENCES

(1) Wells, C. P. and Leitner, A., Quart. Appl. Math. 15 (1957), 430–434.CrossRefGoogle Scholar
(2) Oberhettinger, F., J. Res. Nat. Bur. Standards, 65B (1961), 1–6.CrossRefGoogle Scholar
(3) Oberhettinger, F., J. Res. Nat. Bur. Standards, 65B (1961), 203–204.CrossRefGoogle Scholar
(4) Williams, A. O. Jr., J. Acoust. Soc. Amer. 36 (1964), 2408–2410.CrossRefGoogle Scholar
(5) Mitra, A. K., Proc. Nat. Inst. Sci. India, 27A (1961), 470–475.Google Scholar
(6) Eason, G., Quart. J. Mech. Appl. Math. 17 (1964), 279–292.CrossRefGoogle Scholar
(7) Tupholme, G. E., Proc. Cambridge Philos. Soc., to be published.Google Scholar
(8) Sneddon, I. N., Fourier Transforms (McGraw-Hill, 1951).Google Scholar
(9) ErdÉlyi, A. et al. (editors), Tables of Integral Transforms, Vol. 1 (McGraw-Hill, 1954).Google Scholar
(10) Watson, G. N., A Treatise on the Theory of Bessel Functions, 2nd edn.Cambridge University Press, 1944).Google Scholar
(11) Keller, J. B., Proc. 8th Symp. Appl. Math. Amer. Math. Soc. (McGraw-Hill, 1958), pp. 27–52.Google Scholar
(12) Jones, D. S., Philos. Trans. Roy. Soc. London Ser. A. 247 (1955), 499–528.Google Scholar