A numerical approach for the calculation of an acoustic held is applied to the case of a spinning vortex pair to investigate the sound generation by quadrupole sources in unsteady vortical flows. Based on the unsteady hydrodynamic information from the known incompressible flowfield, the perturbed compressible acoustic terms derived from the Euler equations are calculated. Nonreflecting boundary conditions are developed to obtain highly stable solutions. Calculated results are compared with analytical solutions obtained by the method of matched asymptotic expansions. The possibility of predicting the effect of convective mean flow is also tested. It is concluded that the sound generated by the quadrupole sources of unsteady vortical flows without a sound-generating body or surface can be calculated by using the source terms of hydrodynamic now fluctuations.