The acoustic signature of a firearm is a critical area of study in forensic science and military application. The discharge of a firearm generates an acoustic signature caused by the rapid ignition of explosive materials, propelling the bullet forward. This initial sound, referred to as the muzzle blast, propagates spherically from the firearm. A supersonic bullet exiting the barrel also produces a conical shock wave, which travels outward and follows the trajectory of the projectile. The acoustic characteristics of this shock wave, as recorded by sensors, depend on parameters such as the bullet's velocity, dimensions, and the spatial separation between the bullet's path and the sensors. This chapter presents a study that utilizes tonal and temporal analysis to examine the acoustic characteristics and time-dependent behavior of shock waves detected by an acoustic sensor array. Significant parameters like spectral density, peak amplitude, rise time etc. are the main focus of this approach. Tonal analysis identifies spectral components specific to each caliber or weapon by applying fast Fourier transform (FFT) technique. Temporal analysis focuses on the time-domain features such as peak time, peak amplitude, rise time, decay time, and total duration of shock wave. By utilizing these techniques, the study enhances the understanding of shock wave behavior across various calibers of firearms.