# Modelling the Sound of a Gun's Smokeless Powder Explosion

I am seeking to synthesize the sound of a gunshot.

I am aware the firing of a gun is made up of many parts, but I would like to handle the explosion of smokeless powder in the bore first.

Here's what I've learned so far in my own research on the topic (or at least, what I think I know):

• Smokeless powder deflagrates, rather than detonates. This means it does not create supersonic pressure waves.
• The "meat" of an explosion can be thought of as a wave of gases expanding outward extremely rapidly. You can see this in Schlieren images of gunshots, even.
• Explosions are very "noisy" by nature - that is, their frequency content is pseudorandom and chaotic. Like wind or white/pink/etc. noise, while unlike, say, a musical instrument playing, with pure tones induced by resonance.

I am using a self-written program to do this synthesis, and if I may digress slightly, I can randomly generate noise and control its frequency falloff dynamically. So this should be a piece of cake if I can set the right parameters up.

Beyond this, though, I am sadly stumped. I cannot find any literature on how the sound of a deflagrating explosion manifests itself and propagates. Here are some points of curiosity:

• Explosions have a very clear falloff from low to high frequencies. How does this result from rapidly expanding gas? Can it be modelled/predicted?
• How much resistance does this gas encounter from the air? How fast should it dissipate, and in what way should the explosion's sound power decay?

• I intend to simulate the sound the gun's shooter would hear. So this will be reasonably close by to the metaphorical "speaker".
• The 3D environment will have only an idealized flat ground for the sound to possibly reflect off of.
• This will assume a 62 grain smokeless powder charge and a 5.7mm-diameter gun barrel, 14.5 inches long.
• Atmospheric conditions will be 60% humidity, average atmospheric pressure, and 20° Celsius temperature.
• I am not an expert in the field but I believe that what you are trying to do is rather complex. I am not sure whether you should look into non-linear acoustics or not (I can't really understand how you may end up without a shockwave from an explosion). My B.Eng. dissertation project was on (small scale) plasma shockwaves in air and after some rather short distances the wave degenerated to spherical waves and then (approximation of a) plane wave (as is known by the treatment of linear acoustics). Regarding your system though, I believe you should resort to some numerical (cont.) Commented Mar 23, 2023 at 21:45
• (conted.) methods such as Finite or Boundary Element method. Irrespectively of the chosen method though I believe your task should be broken into various parts. First you should model the deflagration (not familiar with the term) and the "generation" of the source and then treat the acoustical part of your system which could possibly comprise of a point source in a pipe with specific boundary conditions (at least as a first level approximation). Commented Mar 23, 2023 at 21:47
• When the bullet exits the barrel, it's like uncorking a bottle gas that's under enormous pressure. In the absence of a Hugh Jass suppressor, the sound of the sudden expansion of that gas is going to completely overwhelm any other sound that any other part of the process makes. The way it's going to sound to a human ear will be pretty much the same no matter how the gas became pressurized.* Commented Mar 23, 2023 at 22:59
• * One exception. If you are standing far enough down range, and a high-velocity rifle bullet passes over your head, you may hear the supersonic "crack" of the bullet before you hear the blast from the muzzle of the rifle. Commented Mar 23, 2023 at 23:01