Karasoy, TanerYagimli, Mustafa2024-06-132024-06-1320241300-18841304-491510.17341/gazimmfd.11714522-s2.0-85179760337https://doi.org/10.17341/gazimmfd.1171452https://hdl.handle.net/11501/1367Purpose: In this study, it is aimed to bring an unusual mathematical perspective by using semi-analytical mathematical solution methods, unlike the sound intensity determination formulas available in acoustics, and this scientific approach is supported by numerical data. Theory and Methods: Galerkin Weighted Residues Method (WRM) and Spherical Harmonic Functions, which have been used frequently in sound problems in recent years, are used for the solution of sound wave equations in spherical coordinates, which have not been observed in the literature before, in determining the periodic pressure values of sound.Results: Based on the directivity coefficient and spherical harmonic functions in detecting sound pressure levels in the near field, The Critical Distance Threshold, ??????ini, was defined and combined with data from WRM. It has been observed that the Critical Distance threshold value provides very sensitive results in near field distance calculations. The importance of the number of weight functions of WRM in long distance calculations has especially emerged.Conclusion: The critical distance threshold value has an important place in all mathematical analyzes. In the determination of this value, the effect of spherical harmonic functions and the multiplicity of weight functions are clearly seen.eninfo:eu-repo/semantics/openAccessSpherical Sound Wave EquationsGalerkin Weighted Residual MethodsSpherical Harmonic FunctionsSound Pressure LevelFieldDecompositionTransmissionDuctsArticle9422Q293339WOS:001147255200008N/A