The sources of sound during the interactions of two identical two-dimensional inviscid vortex pairs are investigated numerically by using the vortex sound theory and the method of contour dynamics. The sound sources are identified and then separated into two independent components, which represent the contributions from the vortex centroid dynamics and the microscopic vortex core dynamics. Results show that the sound generation mechanism of the latter is independent of the type of vortex pair interaction, while that of the former depends on the jerks, accelerations and vortex forces on the vortex pairs. The power developed by the vortex forces is found to be important in the generation of sound when the vortex cores are severely deformed and their centroids are close to each other. The isolated source terms also explain the appearance of wavy oscillations on the time variations of the sound source strengths in the vortex ring and the two-dimensional vortex interaction systems.