Some Aspects of Ray Representation Running Sound Waves in Liquid Spaces

• 作者: G. K. Ivanova V. P. Ivanov
• 来源期刊: 声学期刊(英文)
• 学科: 数学
• 关键词: Sound Running Waves Wave Equation Reflection PASSAGE LIQUID Space WAVE-GUIDE RAYS
• 年，卷（期）: 2013,（1）
• 页码范围: 7-13
• 页数: 7页
• 分类号: O1

摘要

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.