The Low Frequency Approximation of the Sound Radiation Power of Two Vibrating Circular Pistons Embedded in Two Different Rigid Planes of a Three-wall Corner

W.P. Rdzanek, W.J. Rdzanek and K. Szemela Department of Mechatronics and Control Science, Faculty of Mathematics and Natural Sciences, University of Rzeszów, Prof. St. Pigonia 1, 35-310 Rzeszów, Poland

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The problem of sound radiation by a system consisting of two vibrating circular pistons embedded in two of three different planes perpendicular to one another forming a three-wall corner is considered. The earlier published results dealing with the sound radiation by sources vibrating in a three-wall corner are the basis of analysis. According to the earlier studies, the exact formulae for acoustic power of radiation of two circular pistons are used. The formulae are expressed as double Fourier integrals. The active and reactive, self and mutual, components are separated from them as well as the corresponding expressions of the acoustic power of mirror images of the piston sources. The acoustic power of the two sources are expressed in the form: of the Rayleigh formulae whereas, in the case of the mirror images, it is expressed in the form of the single series expansion containing spherical Bessel and Neumann functions. In the case of the mutual acoustic power of the sources, approximate formulae are presented for low frequencies. On the basis of the results obtained, the corresponding formulae valid for a two-wall corner are presented as the limiting transitions. All the results presented can be useful, e.g. in designing the room acoustics and outdoor system everywhere the free field conditions are disturbed by the acoustic waves reflected at rigid vertical walls for the wavelengths being considerably shorter than the geometric sizes of the walls.

DOI: 10.12693/APhysPolA.125.A-135 PACS numbers: 43.20.Bi, 43.20.El, 43.20.Fn, 43.20.Rz