The paper presents analytical and numerical results of radiation phenomena at the far field and solution of the acoustic wave equation with boundary conditions imposed by the pipe wall. A semi-infinite pipe with partial lining and interior perforated screen is considered. The study is important because of its applications in noise reduction in exhausts of automobile engines, in modern aircraft jet and turbofan engines. This problem is described by a Wiener-Hopf equation and then solved numerically. The solution involves three infinite sets of coefficients satisfying three infinite systems of linear algebraic equations. Numerical solutions of these systems are obtained for various values of the parameters of the problem and their effects on the radiation phenomenon are shown graphically.