Montana State University Proprietary 1
Summary of Gun Shot Acoustics
Robert C. Maher, Montana State University 4 April 2006
Audio recordings of gun shots can provide information about the gun location with respect to the
microphone(s) and the speed and trajectory of the projectile. The principal difficulty when
interpreting such recordings arises from reverberation (overlapping acoustic signal reflections)
due to the gun shot sound reflecting off and diffracting around nearby surfaces.
Muzzle Blast
A conventional firearm uses a confined explosive charge to propel the bullet out of the gun
barrel. The hot, rapidly expanding gases cause an acoustic blast to emerge from the barrel. The
acoustic disturbance lasts 3-5 milliseconds and propagates through the air at the speed of sound
(c). The sound level of the muzzle blast is strongest in the direction the barrel is pointing, and
decreases as the off-axis angle increases.
A microphone located in the vicinity of the gun shot will detect the muzzle blast signal once the
sound propagation travels at the speed of sound from the gun to the microphone position.
However, the muzzle blast signal will also reflect off the ground and off other nearby surfaces,
resulting in a complicated received signal consisting of multiple overlapping reflections.
Supersonic Projectiles: Shock Wave Considerations
Depending on the size of the charge, the mass of the bullet, and other factors, the bullet may be
traveling at supersonic speed. A supersonic bullet causes a characteristic shock wave pattern as it
moves through the air. The shock wave expands as a cone behind the bullet, with the wave front
propagating outward at the speed of sound. The shock wave cone has an inner angle,
θ
M =
arcsin(1/M), where M = V/c is the Mach Number. The geometry is shown in Figure 1.
With a very fast bullet, M is large and
θ
M becomes small, causing the shock wave to propagate
nearly perpendicularly to the bullet's trajectory. For example, a bullet traveling at 3000 feet per
second at room temperature has M=2.67, giving
θ
M = ~22°. On the other hand, if the bullet is
only slightly faster than the speed of sound, M is approximately unity,
θ
M is nearly 90°, and the
shock wave propagates nearly parallel to the bullet's path.
If two or more microphones are located at known locations within the path of the shock wave,
the time of arrival difference(s) can be used to estimate the shock's propagation direction. Note,
however, that determining the bullet's trajectory from the shock propagation vector requires
knowledge of the bullet velocity, V. If V is not known, then M and
θ
M are also not known, and
the bullet's trajectory cannot be determined exactly without additional spatial information.
