It has been suggested that the frequency spectrum of an acoustic emission burst may be a partial ’’signature,’’ identifying the source. To explore this possibility we have studied in some detail, theoretically and experimentally, two qualitatively different simulated acoustic emissions. The first is the fracture of small (20–40 μm) silicon carbide grains on a steel slab. The second is the impact of a small elastic sphere of various materials on the same slab. Our primary objective has been to test our understanding of the medium response, and, consequently, the extent to which we can determine the source spectrum from the observed spectrum.