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Wave Propagation in Strings with Continuous and Concentrated Loads

Published online by Cambridge University Press:  24 October 2008

Harold Jeffreys
Affiliation:
St John's College

Abstract

The motion of a light string loaded with equal masses at regular intervals has been discussed by operational methods. It is found that the system, though possessing only a. finite number of degrees of freedom, shows most of the characteristic features of dispersion. The operator e−σx/c that occurs in the discussion of uniform continuous strings is found to arise as the limit of an operator defined wholly in terms of definite integration, and its interpretation involves a theorem analogous to Taylor's theorem, but apparently more general. There is no phenomenon analogous to the conduction of heat. Any irregularity in the distribution of mass, however, produces strong internal reflexion of the shortest waves, and may provide a mechanism for conduction.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1927

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References

* Cambridge Math. Tracts (in the press).Google Scholar

* Ann. d. Phys. 44, 1914, 916934.Google Scholar

* A general discussion of the related problem of thermal conduction in solids, with references, is given by Born, M., Atomtheorie des festen Zustandes, 1923, 708.Google Scholar