Aim of the paper is to gain a physical understanding of the main noise generating mechanisms related to vorticity and turbulence downstream the disk of a marine propeller in open water. Through the application of the Ffowcs Williams and Hawkings acoustic analogy (FWH) for permeable surfaces, the analysis of the noise field generated by the INSEAN E779A propeller model at different advancing ratios allows to detect correlations between acoustic signatures in the near/mid field and wake evolution. Turbulence noise-induced effects are captured by combining the FWH formulation with a Detached Eddy Simulation (DES) of the flow past the propeller. Besides, a phase-locked post-processing of the unsteady DES data on the acoustic surface is used to yield FWH signatures governed by vorticity effects, which are then compared with the pressure fluctuations predicted by the Bernoulli equation, within a potential hydrodynamics platform solved by a Boundary Integral Element Method (BIEM). It is found that turbulence is the most annoying source of propeller noise, whereas vorticity-driven phenomena are important only in a narrow region surrounding the propeller. Moreover, numerical results highlight that acoustic pressures are correlated to the vortex pairing hydrodynamic phenomenon associated to a blade-to-shaft harmonic energy transfer, detected in literature by time-resolved visualizations and velocimetry measurements.