Large-eddy simulation is combined with the Ffowcs Williams–Hawkings equation to investigate the noise generation by a 10-bladed rotor ingesting the turbulent wake of a circular cylinder in a low-Mach-number flow. Two rotor advance ratios corresponding to zero thrust and a thrusting condition are considered. The computed sound pressure levels agree well with the experimental measurements at Virginia Tech over a wide range of frequencies. The broadband acoustic spectra exhibit a strong tonal peak at the cylinder vortex-shedding frequency, a second peak at the rotor blade passing frequency, and a minor peak at the trailing-edge vortex-shedding frequency. Consistent with experimental results, the rotor at the thrusting advance ratio produces stronger sound than that at zero thrust. The blade acoustic dipole strength increases with the radial distance to the hub until near the blade tip. Fluctuating velocities in the wake are responsible for virtually all the rotor acoustic response except at the blade-passing frequency, where the mean wake velocity defect also makes a strong contribution. Blade-to-blade correlations and coherence of dipole sources are relatively weak. The classical Sears theory is shown to provide a reasonable prediction of the rotor turbulence-ingestion noise at the important mid-frequencies, based on which the appropriate Mach number scaling for the ingestion noise is identified. Distortions of wake turbulence by the rotor are found to be relatively small, and including their effect on the upwash velocity only slightly improves the Sears theory prediction.