The Propagation of Disturbances: In Dispersive Media (Classic Reprint) - Tapa blanda

Excerpt from The Propagation of Disturbances: In Dispersive Media

The equations (7) and (8) give for U precisely the same expression as in (3) accordingly the various points of view give consistent results.

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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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Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com

This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.