Application of partial areas method in the problem of sound radiation by a sphere in a waveguide with soft acoustically boundaries

Abstract

The paper considers the features of the formation of an acoustic field by a spherical source with complicated properties in a regular plane-parallel waveguide, which is of practical importance in marine instrumentation and oceanographic research. The calculation algorithm is based on the use of the Helmholtz equation and the Fourier method for each partial region and the conjugation conditions on their boundaries. The presented calculation allows one to get rid of the idealized boundary conditions on the source surface, with the subsequent determination of the excitation coefficients of the waveguide modes within the framework of the Sturm-Liouville problem. In this case, the attraction of the boundary conditions on the surface and the bottom of the sea, as well as the Sommerfeld conditions, makes it possible to obtain the real distribution of the field in the vertical sections of the waveguide. The obtained frequency dependences of the pressure and vibrational velocity components show their amplitude-phase differences, which reach 90 degrees, which partially explains the appearance of singular points in the intensity field in a regular waveguide. It has been determined that multiple reflections of sound waves from the boundaries of the working space and the space of the waveguide cause oscillations of the pressure components with a change in the amplitude level up to 6 dB. It was found that with an increase in the size of the source, a kind of resonance is formed in the working space, the frequency of which depends on the depth of the sea and corresponds to the region kr=x=5.8. It was found that when the acoustic field is formed in the working space, the frequency response of the impedance components is represented as a multiresonant dependence formed on the basis of the frequency characteristics of the lower modes and their combinations. Experimental studies have shown that the results of calculations of the mode composition of the acoustic field of the emitter, obtained in the conditions of the pool, correspond to the spatial characteristics of the mode components of the acoustic field with an error of up to 3 dB

Mode-Matching Method Applied to the Sound Reception Problem Using Helmholtz Resonator

“…The solutions to the problem in areas I and II must correspond to the known [7,8] solutions of the Helmholtz equations in rectangular coordinates obtained for regular waveguides and mode-matching components. Regarding area III, we note that when the environment bypasses the surfaces areas that include angular points, the oscillation velocity field is characterized by the presence of local features i.e., the effect of increasing to infinity of the oscillating velocity values when approaching the vertex.…”

“…The method was researched and implemented in acoustic practice by sci-entific schools of the Institute of Hydromechanics of the National Academy of Sciences of Ukraine and the Department of Acoustic and Multimedia Electronic Systems of the National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute". The main provisions for its application are introduced in [4][5][6][7].…”