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