Abstract
Using the ray method, an investigation has been carried out on the structure of caustics in the wa- veguide assuming the canonical distribution of the sound velocity with depth. Monochromatic point source of sound was on the axis of the waveguide. There is considered water rays only. It is shown that the spatial part of the phase of a running sound wave does not contain the wave propagation direction and is always a positive quantity. When the trajectories are calculated, it is assumed that inversion of rays occurs at an angle of total internal reflection where the reflection coefficient is equal to unity. This eliminates the horizontal part of the trajectories. At other points, the reflection coefficient is assumed to be zero, and the passing coefficient is equal to unity. With this change in the calculation of ray’s trajectories, the basic structure of the caustics remained the same. It is shown that the boundary line of the caustic is a number of foci in which rays intersect with similar angles out of the source and have neighbour times of propagation. Structure of the sound field along the boundary line of the caustic is periodic. Its period coincides with the wavelength of the field radiated by the source.
Highlights
We assume that the area of the caustic is that part of the waveguide’s space, in which through each point passes two or more rays leaving the source at different but close angles and their phases in the spatial or temporal representation are close or coincide
The aim of this work is to: 1) additional analysis mentioned in [9]-[12] mistakes in writing the spatial phase of the sound wave and the influence of these errors on the calculation of the sound field in liquid media, and 2) calculation of caustics at the same distances from the source as in [8], but taking into account the reflection coefficient, considering that it is equal to unity at an angle of full internal reflection, and zero at all other angles along the path, and 3) comparison new calculating with those in [8]
As well as fluctuations in pressure and particle velocity of the liquid caused by the sound source, usually described by a running wave, that satisfy the equations of fluid motion, [13]: p ( x, z,t ) = Acosψ,ψ = ψ r −ψ t =
Summary
We assume that the area of the caustic is that part of the waveguide’s space, in which through each point passes (intersect) two or more rays leaving the source at different but close angles and their phases in the spatial or temporal representation are close or coincide. Caustics arise at various distances from the source, above and below the axis of the waveguide It is calculated the spatial structure of the sound field in the area of caustics as a two-dimensional function of the coordinates: the distance from the source and depth of caustic. The aim of this work is to: 1) additional analysis mentioned in [9]-[12] mistakes in writing the spatial phase of the sound wave and the influence of these errors on the calculation of the sound field in liquid media, and 2) calculation of caustics at the same distances from the source as in [8], but taking into account the reflection coefficient, considering that it is equal to unity at an angle of full internal reflection, and zero at all other angles along the path, and 3) comparison new calculating with those in [8]
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