Aeroacoustic sound generation due to self-sustained oscillations by a series of compact axisymmetric cavities exposed to a grazing flow is studied both experimentally and numerically. The driving feedback is produced by the velocity fluctuations resulting from a coupling of vortex sheddings at the upstream cavity edges with acoustic standing waves in the coaxial pipe. When the cavities are separated sufficiently from each other, the whistling behavior of the complete system can be determined from the individual contribution of each cavity. When the cavities are placed close to each other there is a strong hydrodynamic interference between the cavities which affects both the peak amplitude attained during whistling and the corresponding Strouhal number. This hydrodynamic interference is captured successfully by the proposed numerical method.