On the ray equivalent of a group of modes

摘要: The raylike behavior of a cluster normal modes furnishes useful concept for determining the interference properties normal‐mode pressure field. In previous investigations, selected group has been heuristically smeared out into continuum, and it established that maximum lies along path traversed by ’’modal ray’’ central mode in group. This approximate analysis does not quantify corresponding amplitude cluster. A rigorous basis may be provided Poisson summation modes, which procedure incorporates systematically only transition to continuum but also effect truncation bundle. As result, shown completely equivalent, phase amplitude, ray field plus remainder. equivalence remains intact even convergence zones other regions where simple acoustics must corrected uniform asymptotic treatment. remainder can minimized an appropriate ’’optimum’’ choice number bundle, weighting first last included modes. Numerical calculations ducting environment are presented support these conclusions.