In the present work, the radiation of sound waves from a coaxial duct is considered. This coaxial duct has an inner wall which is infinite and has piecewise acoustically absorbent material, while the outer wall is semi-infinite and rigid. The analytical solution of the problem is found by means of the Wiener-Hopf technique. Applying the Fourier transformation to the boundary value problem, the explicit expression for the scattered field is obtained. In the end, some numerical results are displayed for different parameters and compared to rigid case.