The Propagation of Disturbances : In Dispersive Media (Classic Reprint).cT H Havelock
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Author: T H Havelock
Page Count: 104 pages
Published Date: 27 Sep 2015
Publisher: Forgotten Books
Publication Country: United States
Language: English
Type: PDF
ISBN: 9781331928928
File Name: The.Propagation.of.Disturbances.In.Dispersive.Media.(Classic.Reprint).pdf
Download Link: The Propagation of Disturbances In Dispersive Media (Classic Reprint)
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Excerpt from The Propagation of Disturbances: In Dispersive Media
It appears however that as early as 1839 Hamilton had made investigations into the rate of advance of a finite train of waves in a dispersive medium; unfortunately his researches were only published in short abstracts and have been entirely overlooked until recently. Later extensions have originated in the group method of approximation due to Lord Kelvin. These methods, and their applications, occupy the first five chapters of this Tract, including a short discussion of the action of a prism. The sixth chapter is devoted to the important dynamical significance of group velocity in connection with the rate of transmission of energy. In the last chapter we deal with more general methods of treating the Fourier integral which represents the disturbance, more especially in cases where it represents a discontinuous function, that is where the medium is such that there may be a definite wave-front travelling with finite velocity.
2. Definitions of Simple Group. If one observes a finite train of waves advancing over the surface of still water, it will be seen that the individual waves move more quickly than the group as a whole; as the group advances new waves arise at the rear, move through the group, and disappear at the front. For an explanation of this phenomenon, which seems to have been recorded first by Scott Russell, we must analyse the group into component simple harmonic waves of various wave-lengths, each component moving with the phase-velocity appropriate to its wave-length. Leaving the particular problem for more detailed study later, we begin with an ideally simple case.
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