Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



An unperiodic concentrated sonic pulse

Author: J. L. Synge
Journal: Quart. Appl. Math. 46 (1988), 65-75
MSC: Primary 83A05; Secondary 35Q20, 76Q05
DOI: https://doi.org/10.1090/qam/934682
MathSciNet review: 934682
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Abstract: The purpose of this note is to define an unperiodic source which gives a highly concentrated pulse of scalar radiation. The source involves four constants, and concentration is obtained by giving small values to dimensionless combinations of those constants. The field is axially symmetric, and there is a focal point which travels along the $ x$-axis with the speed of propagation; the focal field remains constant for some time, decaying after that. The method is that of the retarded potential, but presented in terms of equivalent Minkowskian geometry of space-time, the speed of propagation playing the part of the speed of light in relativity. The obvious application is to sonic communication in water, but no attempt is made to interpret the source in physical terms.

References [Enhancements On Off] (What's this?)

  • [1] R. Courant and D. Hilbert, Methods of mathematical physics, II, p. 204, Interscience, New York, 1962
  • [2] J. L. Synge, Relativity: The special theory, p. 429, North-Holland, Amsterdam, 1965
  • [3] J. L. Synge, op. cit., p. 431

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DOI: https://doi.org/10.1090/qam/934682
Article copyright: © Copyright 1988 American Mathematical Society

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