Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-26T07:41:41.331Z Has data issue: false hasContentIssue false
  • English
  • Français

On the propagation of disturbances from moving sources

Published online by Cambridge University Press:  24 October 2008

A. G. Walters
A. G. Walters
Affiliation:
Armament Research EstablishmentFort HalsteadSevenoaksKent
Get access Rights & Permissions [Opens in a new window]

Abstract

The concept of the Green's vibrational function given in an earlier paper by the author is used to obtain a general expression for the disturbance from a point source. The potential due to transient sources of sound moving with subsonic and supersonic velocities is derived from this. It is found that the Doppler effect for a supersonic source differs from that for a subsonic source. In the former case it is found that two frequencies are heard simultaneously from a source emitting a note of one frequency.

The theory is applied to determine some solutions of the two dimensional equation of supersonic, irrotational compressible flow, corresponding to the flow around an aerofoil taking into consideration the entropy changes at the shock wave.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 47 , Issue 1 , January 1951 , pp. 109 - 126
Copyright
Copyright © Cambridge Philosophical Society 1951

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

REFERENCES

(1)Walters, A. G.The solution of some transient differential equations by means of Green's functions. Proc. Cambridge Phil. Soc. 45 (1949), 69–80.CrossRefGoogle Scholar
(2)Watson, G. N.Theory of Bessel functions, 2nd ed. (Cambridge, 1944).Google Scholar
(3)Carslaw, H. S. and Jaeger, J. C.Operational methods in applied mathematics (Oxford, 1941), p. 228.Google Scholar
(4)Ward, G. N.Quart. J. Mech. Appl. Math. 2 (1949), 136.CrossRefGoogle Scholar
(5)Kármán, Th. von.Supersonic aerodynamics. J. Aero. Sci. 14 (1947), 373–400.Google Scholar
(6)Ackeret, J.Handbuch der Physik, 7 (Berlin, 1927), chap. 5 (Gasdynamik).Google Scholar
(7)Whittaker, E. T. and Watson, G. N.A course of modern analysis, 4th ed. (Cambridge, 1927), p. 501.Google Scholar
(8)Liepmann, H. W. and Puckett, A. E.Introduction to aerodynamics of a compressible fluid (New York, 1947).Google Scholar