New Method in Calculating the Trajectory of Sound Waves at Stratified Ocean

Abstract

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.