Sound scattering and transmission through a circular cylindrical aperture revisited using the radial polynomials

The problem of sound scattering and transmission through a circular cylindrical aperture in a flat thick rigid wall has been revisited rigorously using the radial polynomials. The acoustic power transmission and back scattering coefficients have been presented in the form of highly convergent hypergeometric series described earlier in the literature for vibrating circular pistons and plates based on the crucial property of the polynomials in terms of the Hankel transform. The problem is solved by using the continuity conditions at both aperture outlets. The complex integrals necessary to satisfy the continuity conditions are expressed as the exact formulas, which makes the final results for the acoustic power coefficients much more accurate than in the case of numerical integration. A significant improvement has also been reached in numerical efficiency. On average, the calculations are 500 times more efficient compared to numerical integration with no accuracy loss. Additionally, the acoustic pressure on the aperture outlets has been presented exactly in the form of a highly convergent hypergeometric series as well as using the modal impedance coefficients.