Formation of an Acoustic Field in a Waveguide by a Spherical Sound Source

Abstract

This paper presents the initial output and calculated ratios for a full acoustic pressure field in a waveguide with soft boundaries. In addition, the paper describes the basic steps for obtaining the data of the initial and calculated ratios, as well as approaches and methods for analyzing the field in the waveguide for the case where the sound source is not point, but spherical. Based on the obtained relationships, a computer model was developed and analyzed and further studies were developed.This work contains the formulation and partial solution of the problem of forming a complete acoustic field in a waveguide with soft boundaries. Estimates were given to approximate the direct field in a certain approximation. The calculated ratios for the approximation of the reflected field along the OZ direction are also given. The above relations can be used in further studies, in particular to extend the reflection field calculations to the entire first quadrant, since the problem is symmetric. This can be done using the so-called imaginary source method.To analyze the reflected field, a direct spherical field was represented by a set of plane normal waves. Since only normal waves are used for approximation, the approximated field describes a spherical one with a certain approximation. The expression to describe the reflected field was obtained from the classical expression for the approximation of a spherical wave by a set of planes. A reflection coefficient was found to describe the approximated reflected field. It can be considered a design in this case. It is useful for describing the reflected field along the OZ axis. The obtained coefficient can be used in further studies, in particular, to extend the reflection field calculations to the entire first quadrant, since the problem is symmetric. This can be done using the so-called imaginary source method.A mathematical computer model was developed in MATLAB to analyze the results. The calculations were performed for different waveguide depths and operating frequencies. In the model, the waveguide fills the water and the air serves as the boundary, so the boundaries of the waveguide are acoustically soft.The paper deals with a flat problem within the first quadrant.In general, this paper presents the formulation and solution of the problem of forming acoustically soft surfaces. In this case, the calculated ratios for the approximation of the direct field in a given approximation (taking into account only homogeneous waves) are given. And also the calculated ratios for the approximation of the reflected field along the OZ direction.The results are basic and can be applied to formulate and solve the problems of sounding shallow seas in the framework of elastic and hydroelectric productions.The paper also provides general expressions for the search of a reflected field based on Fresnel zones.