Examples Illustrating the Characteristics of Waveguide Propagation

摘要: As we have often pointed out, when considering the propagation of sound in a shallow water waveguide, it is primary importance to take into account interaction with bottom. The hardest quantity quantify this absorption bottom, which leads fall signal intensity distance. Formally, decay due complex eigenvalues Sturm–Liouville problem (3.7), or equivalently constants \( {\xi_l} \) having an imaginary part {\gamma_l} = 2{\rm Im} (i.e., attenuation coefficients normal modes). Despite fact that values are easily obtained numerically, though not experimentally, more detailed study their analytic behavior advisable, particularly as function parameters problem. We should first look at mode number l \), since dependence crucial explain structure field formed large distance from source, including its modal composition and total intensity. Moreover, performing approximate calculations averaged intensity, simplified formulae for required. These can be interpreted framework ray (or WKB) theory.