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XI.—On Waves in a Dispersive Medium resulting from a Limited Initial Disturbance

Published online by Cambridge University Press:  15 September 2014

George Green
George Green
Affiliation:
University of Glasgow
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Extract

§ 1. In a former paper “On Group-Velocity and on the Propagation of Waves in a Dispersive Medium” (Proc. R.S.E., xxix. pp. 445–470, 1909), it was shown that group-velocity, or the principle of “stationary phase,” provides us with a satisfactory explanation of the modus operandi of dispersion; and the principle was applied to obtain an expression for the effect of a single impulse confined to the neighbourhood of a point of the medium. The present paper is intended to fulfil a promise given in § 29 of that paper, to show that by means of this principle we can arrive at the general features of the wave-system in a dispersive medium resulting from any limited initial disturbance.

Type
Proceedings
Information
Proceedings of the Royal Society of Edinburgh , Volume 30 , 1910 , pp. 242 - 253
Copyright
Copyright © Royal Society of Edinburgh 1910

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References

page 242 note * Boltzmann, Festschrift, 1904.

page 243 note * Proc. Lon. Math. Soc., t. xx., 1888.

page 244 note * See Lord Rayleigh, Phil. Mag., July 1909.

page 245 note * Phil. Mag., vol. xxiii., March 1887.

page 248 note * After this paper had been completed I found this result given in a very comprehensive paper by DrHavelock, T. H., “The Propagation of Groups of Waves in Dispersive Media,” in Proc. Roy. Soc., lxxxi., 1908 Google Scholar, obtained by a similar application of Lord Kelvin's 1887 result to that given in §§ 6, 7 above. The view of group-velocity given in my paper, Proc. R.S.E., 1909, is there fully discussed and illustrated.