The screeching of peeling tape is a familiar albeit annoying sound. However, despite decades of study, its source has remained elusive. Herein we demonstrate that this sound is produced by a discrete train of weak shocks emanating from the fine fractures which travel supersonically with respect to the surrounding air, in the transverse direction within the detaching adhesive. Each sound pulse is generated when a fracture tip reaches the edge of the tape. We verify this using two microphones synchronized with clips from two simultaneous high-speed video cameras, one observing the fracture motions in the adhesive through the transparent substrate, while the other captures schlieren imaging of the shock fronts in the air.