The acoustic waveforms produced by an unheated supersonic and shock free jet operating at a gas dynamic Mach number of 3 and an acoustic Mach number of 1.79 are examined over a large spatial domain in the (x,r)-plane. Under these operating conditions, acoustic waveforms within the Mach cone comprise sawtooth-like structures which cause a crackling sound to occur. The crackling structures produced by our laboratory-scale nozzle are studied in a range-restricted environment, and so, they are not the consequence of cumulative nonlinear waveform distortions, but are rather generated solely by local mechanisms in, or in close vicinity to, the jet plume. Our current work focuses on characterizing the temporal and spectral properties of these shock-structures. A detection algorithm is introduced which isolates the shock-structures in the temporal waveforms based on a pressure rise time and shock strength that satisfy user defined thresholds. The average shapes of the shock-structures are shown to vary along polar angles centered on the post-potential core region of the jet. Spectral characteristics of the crackling structures are then determined using conventional wavelet-based time–frequency analyses. Differences between the global wavelet spectrum and the local wavelet spectrum computed from instances when shocks are detected in the waveform show how shock-structures are more pronounced at shallow angles to the jet axis. The findings from this energy-based metric differ from those obtained using the skewness of the pressure and the pressure derivative.