This paper is concerned with the mathematical modelling of sound radiation from a semi-infinite unflanged annular duct due to a monopole acoustically-compact source located inside the duct. The acoustic field inside the duct is modelled using an appropriate Green's function solution and the noise propagation from the duct-exit through the shear layer to farfield is dealt with using a standard Wiener-Hopf solution. Results are presented for far-field noise and modal contribution for observers positioned at different polar angles. The effect of source radial and axial position and its frequency is thoroughly investigated. The effects of jet speed on the appearance of cone of silence and jet blockage at different frequencies are also studies. It is shown that the source position plays an important role on duct modes excitation and therefore far-field noise directivity.