The turbulent mixing noise radiated by a Mach 0.9 jet is investigated. The focus is put on the proper calculation of acoustic propagation effects by means of adjoint Green’s function that are tailored to the jet mean flow. Tam and Auriault’s statistical mixing noise model is recast for Pierce’s wave equation that is energy preserving. An unconditionally stable formulation to compute propagation effects is thus obtained. Adjoint fields are computed from the direct problem with help of the flow reversal theorem. A finite element solver is used to solve tailored adjoint Green’s functions, and corresponding adjoint fields are displayed. Acoustic predictions are carried out for a wide range of polar angles, and compared to measurements. A particular attention is given to predictions achieved at upstream observer angles. At these angles, the present model describes the physics of upstream travelling guided jet waves. The adjoint method provides a suitable framework to split the generation of sound from its propagation. It is illustrated how tailored adjoint Green’s functions filter the radiating part of Tam and Auriault’s sound source model, by weighting with propagation effects