Abstract
Work is devoted to the analysis of errors meeting in literature in treatment of a spatial part of a phase of running sound waves. In some cases, it is not taken into consideration that this part of a phase is formed by scalar product of vectors which does not depend on a choice of system of co-ordinates. Taking into account the necessary corrections in record of a phase of plane waves, it is shown that the decision of the homogeneous wave equation in the form of “belated” potentials is simultaneously and the decision of the equations of movement of a liquid, and “outstripped” potentials does not satisfy them. The analysis of coefficients of reflection and passage of running waves in non-uniform space is carried out. It is shown that on boundary of spaces with different sound speeds, a turning point of a sound wave is the point of full internal reflection. The way of calculation of coefficients of reflection and passage is offered by consideration of all three waves on boundary of spaces as vectors with the set directions and amplitude of a falling wave. Calculation of coefficients of reflection and passage of a sound wave in a wave-guide of canonical type along the chosen trajectory by two methods—under traditional formulas and a vector method is carried out. Results of calculation practically coincide.
Highlights
The most widespread acoustics of ocean is representation of a sound wave in the form of a running wave along a trajectory
The purpose of the given work consists of the following: explanation of the reasons of a wrong writing of a spatial part of a phase of a running wave, elimination of mathematical errors in its records and change of physical treatments of separate well-known results. It concerns the use of the wave equation at research of propagation of sound waves in liquids, a way of reception of coefficients of reflection (CR) and passage (CP) sound waves in works [4,5,6,7], and their dependence on an angle of departure of sound wave’s trajectories from a source
Calculation of coefficients of reflection and passage is based on representation of a sound wave in the liquid space in the form of a running wave along a trajectory
Summary
The most widespread acoustics of ocean is representation of a sound wave in the form of a running wave along a trajectory (ray). The purpose of the given work consists of the following: explanation of the reasons of a wrong writing of a spatial part of a phase of a running wave, elimination of mathematical errors in its records and change of physical treatments of separate well-known results. It concerns the use of the wave equation at research of propagation of sound waves in liquids, a way of reception of coefficients of reflection (CR) and passage (CP) sound waves in works [4,5,6,7], and their dependence on an angle of departure of sound wave’s trajectories from a source. Calculation of CR and CP, received by two methods, along a trajectory of a sound wave in a wave-guide of canonical type is carried out
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