Some Simple Formulae for Normal Mode Wave Numbers, Cutoff Frequencies, and the Number of Modes Trapped by a Sound Channel

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 calculation is desired, the computation time can be reduced considerably if the mode wavenumbers can be estimated in advance. In such a case, the WKB method can be used to obtain formulate which, although they are approximate, are given in closed form. In this paper 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.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1982
Accession Number
ADA124948

Entities

People

  • Dale D. Ellis

Organizations

  • Defence Research and Development Canada

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Abstracts
  • Acoustic Phenomena
  • Acoustic Propagation
  • Acoustics
  • Boundaries
  • Classification
  • Computations
  • Eigenvalues
  • Equations
  • Frequency
  • Integrals
  • Mathematical Analysis
  • National Security
  • Ocean Environments
  • Phase Velocity
  • Underwater Acoustics
  • Underwater Sound

Fields of Study

  • Physics

Readers

  • Atmospheric Science / Meteorology, specifically Wind Wave Turbulence.
  • Calculus or Mathematical Analysis
  • Wave Propagation and Nonlinear Chaotic Dynamics.