This aeroacoustics research focuses on sound-field generated by a supersonic Mach 3 jet. The work is based on a high-speed dataset detected by Charles E. Tinney and John Valdez in the facilities of the University of Texas at Austin through schlieren imaging technique which is focused on the hydrodynamics field and acoustic near-field. During the treatment, we will use Data-Driven Modal Analysis, a powerful mathematical tool, which can separate the most important components of the sound-field: results of Proper Orthogonal Decomposition and multi-scale Proper Orthogonal Decomposition will be deeply analyzed to recognize known patterns. The so obtained modes show wavy patterns, and the study of the main wave features like propagation path, and traveling speed allows us to identify them as Mach waves: they occur when turbulent structures inside the inner layer of the jet travel with a supersonic convective speed, and travel along a 45° inclined propagation path at speed of sound.