Impedance of the unbaffled cylindrical pipe outlet for the plane wave incident at the outlet - SANOWSKA, Anna (Archives of Acoustics, 1978)
The paper presents formulae for the impedance of the outlet of semi-infinite cylindrical wave-guide derived by considering the propagation of a plane wave and accounting for the generation of higher Bessel modes due to the diffraction at the opened end of the wave-guide. For this purpose expressions for the refraction and transformation coefficients of the basic mode were derived by solving exactly the wave equations with suitable boundary conditions using Wiener-Hopf factorization.