Some simple formulae for normal mode wave numbers, cutoff frequencies, and the number of modes trapped by a sound channel

Authors

  • D.D. Ellis Defence Res. Estab. Atlantic, Dartmouth, NS, Canada

Keywords:

acoustic wave propagation, numerical methods, underwater sound, WKB calculations, normal mode wave numbers, cutoff frequencies, acoustic propagation, underwater sound channel, trapped modes, WKB method, gross features, sound speed profile shape

Abstract

To a good first approximation, acoustic propagation in an underwater sound channel is dominated by a finite number of trapped modes. However, exact solutions are known for only a few special cases, making it necessary in general to use numerical methods to solve the normal mode equation. But often one is interested only in the gross features, such as the number of modes or cutoff frequencies, and one does not need the detail provided by a complete normal mode calculation. Even if a normal mode wavenumbers can be estimated in advance. In such a case, the WKB method can be used to obtain formulae which, although they are approximate, are given in closed form. Formulae based on exact and WKB solutions are presented for the number of modes trapped in some simple sound channels and for the wave numbers and cutoff frequencies associated with these modes. The number of trapped modes is shown to depend on the gross features of the sound channel, while the distribution of modal wave numbers depends to a greater degree on the details of the sound speed profile shape

Downloads

Published

1982-10-01

How to Cite

1.
Ellis D. Some simple formulae for normal mode wave numbers, cutoff frequencies, and the number of modes trapped by a sound channel. Canadian Acoustics [Internet]. 1982 Oct. 1 [cited 2023 Dec. 3];10(4):7-15. Available from: https://jcaa.caa-aca.ca/index.php/jcaa/article/view/491

Issue

Vol. 10 No. 4 (1982)

Section

Technical Articles

License

Copyright on articles is held by the author(s). The corresponding author has the right to grant on behalf of all authors and does grant on behalf of all authors, a worldwide exclusive licence (or non-exclusive license for government employees) to the Publishers and its licensees in perpetuity, in all forms, formats and media (whether known now or created in the future)
i)    to publish, reproduce, distribute, display and store the Contribution;
ii)    to translate the Contribution into other languages, create adaptations, reprints, include within collections and create summaries, extracts and/or, abstracts of the Contribution;
iii)    to exploit all subsidiary rights in the Contribution,
iv)    to provide the inclusion of electronic links from the Contribution to third party material where-ever it may be located;
v)    to licence any third party to do any or all of the above.