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 b...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.展开更多
This paper is proposed to consider the propagation of sound waves in the liquid as a result of special deformation of the medium. Mechanical vibrations of the membrane, (diaphragm) creating a sound wave, transfer from...This paper is proposed to consider the propagation of sound waves in the liquid as a result of special deformation of the medium. Mechanical vibrations of the membrane, (diaphragm) creating a sound wave, transfer from layer to layer in medium without causing synchronous oscillations of the fluid particles. It can be assumed that the deformation of the liquid is similar to the driving force (pressure) in the direction perpendicular to the plane of the vibrating membrane. Usually, the running wave functions are used to describe the sound waves, but they do not contain the direction of propagation. It is proposed to consider that the amplitude of the wave is a vector coinciding with the vector tangent to the path of the wave. This would allow for a change of direction of propagation without changing its phase, in which the direction of wave is not present. It proposed a method of calculating a vector of amplitudes of the reflected and transmitted sound waves based on the laws of conservation of impulse and energy of the waves and the boundary conditions defined by Snell’s law. It is shown that one of the two solutions of the wave equation does not apply to real physical process of sound wave’s propagation in the liquid.展开更多
There is a new method of calculating the trajectory of sound waves (rays) in layered stratified speed of sound in ocean without dispersion. A sound wave in the fluid is considered as a vector. The amplitudes occurring...There is a new method of calculating the trajectory of sound waves (rays) in layered stratified speed of sound in ocean without dispersion. A sound wave in the fluid is considered as a vector. The amplitudes occurring at the boundary layers of the reflected and refracted waves are calculated according to the law of addition of vectors and using the law of conservation of energy, as well as the laws that determine the angles of reflection and refraction. It is shown that in calculating the trajectories, the reflected wave must be taken into account. The reflecting wave’s value may be about 1 at certain angles of the initial wave output from the sours. Reflecting wave forms the so-called water rays, which do not touch the bottom and the surface of the ocean. The conditions of occurrence of the water rays are following. The sum of the angles of the incident and refracted waves (rays) should be a right angle, and the tangent of the angle of inclination of the incident wave is equal to the refractive index. Under these conditions, the refracted wave amplitude vanishes. All sound energy is converted into the reflected beam, and total internal reflection occurs. In this paper, the calculation of the amplitudes and beam trajectories is conducted for the canonical type of waveguide, in which the speed of sound is asymmetric parabola. The sound source is placed at the depth of the center of the parabola. Total internal reflection occurs in a narrow range of angles of exit beams from the source 43° - 45°. Within this range of angles, the water rays form and not touch the bottom and surface of ocean. Outside this range, the bulk of the beam spreads, touching the bottom and the surface of the ocean. When exit corners, equal and greater than 77°, at some distance the beam becomes horizontal and extends along the layer, without leaving it. Calculation of the wave amplitudes excludes absorption factor. Note that the formula for amplitudes of the sound waves applies to light waves.展开更多
In this paper, one of analogies available in the literature between movement of a material particle and ray propagation of a sound in liquid is used. By means of the equations of Hamilton describing movement of a mate...In this paper, one of analogies available in the literature between movement of a material particle and ray propagation of a sound in liquid is used. By means of the equations of Hamilton describing movement of a material particle, analytical expression of a tangent to a trajectory of a sound ray at non-uniform ocean on depth is received. The received expression for a tangent differs from traditional one, defined under law Snelius. Calculation of trajectories, and also other characteristics of a sound field is carried out by two methods: first—traditional, under law Snelius, and second—by the analogy to mechanics method. Calculations are made for canonical type of the sound channel. In the region near to horizontal rays, both methods yield close results, and in the region of steep slope, the small distinction is observed.展开更多
文摘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.
文摘This paper is proposed to consider the propagation of sound waves in the liquid as a result of special deformation of the medium. Mechanical vibrations of the membrane, (diaphragm) creating a sound wave, transfer from layer to layer in medium without causing synchronous oscillations of the fluid particles. It can be assumed that the deformation of the liquid is similar to the driving force (pressure) in the direction perpendicular to the plane of the vibrating membrane. Usually, the running wave functions are used to describe the sound waves, but they do not contain the direction of propagation. It is proposed to consider that the amplitude of the wave is a vector coinciding with the vector tangent to the path of the wave. This would allow for a change of direction of propagation without changing its phase, in which the direction of wave is not present. It proposed a method of calculating a vector of amplitudes of the reflected and transmitted sound waves based on the laws of conservation of impulse and energy of the waves and the boundary conditions defined by Snell’s law. It is shown that one of the two solutions of the wave equation does not apply to real physical process of sound wave’s propagation in the liquid.
文摘There is a new method of calculating the trajectory of sound waves (rays) in layered stratified speed of sound in ocean without dispersion. A sound wave in the fluid is considered as a vector. The amplitudes occurring at the boundary layers of the reflected and refracted waves are calculated according to the law of addition of vectors and using the law of conservation of energy, as well as the laws that determine the angles of reflection and refraction. It is shown that in calculating the trajectories, the reflected wave must be taken into account. The reflecting wave’s value may be about 1 at certain angles of the initial wave output from the sours. Reflecting wave forms the so-called water rays, which do not touch the bottom and the surface of the ocean. The conditions of occurrence of the water rays are following. The sum of the angles of the incident and refracted waves (rays) should be a right angle, and the tangent of the angle of inclination of the incident wave is equal to the refractive index. Under these conditions, the refracted wave amplitude vanishes. All sound energy is converted into the reflected beam, and total internal reflection occurs. In this paper, the calculation of the amplitudes and beam trajectories is conducted for the canonical type of waveguide, in which the speed of sound is asymmetric parabola. The sound source is placed at the depth of the center of the parabola. Total internal reflection occurs in a narrow range of angles of exit beams from the source 43° - 45°. Within this range of angles, the water rays form and not touch the bottom and surface of ocean. Outside this range, the bulk of the beam spreads, touching the bottom and the surface of the ocean. When exit corners, equal and greater than 77°, at some distance the beam becomes horizontal and extends along the layer, without leaving it. Calculation of the wave amplitudes excludes absorption factor. Note that the formula for amplitudes of the sound waves applies to light waves.
文摘In this paper, one of analogies available in the literature between movement of a material particle and ray propagation of a sound in liquid is used. By means of the equations of Hamilton describing movement of a material particle, analytical expression of a tangent to a trajectory of a sound ray at non-uniform ocean on depth is received. The received expression for a tangent differs from traditional one, defined under law Snelius. Calculation of trajectories, and also other characteristics of a sound field is carried out by two methods: first—traditional, under law Snelius, and second—by the analogy to mechanics method. Calculations are made for canonical type of the sound channel. In the region near to horizontal rays, both methods yield close results, and in the region of steep slope, the small distinction is observed.
