Not my words...
Silencers work by suppressing the gases that leave a gun barrel when it is fired. Special ammunition used with silencers travels slower than the speed of sound, avoiding the sonic boom caused by ordinary bullets.
Silenced firearms are not entirely silent -- they do not muffle the mechanical sounds of a gun's moving parts -- but they do reduce the sound to a level that is not noticeable in a crowd or from far away. The silencer also hides the bright muzzle flash that usually appears when a gun is fired.
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Here is another explination.
It is amazing that gun silencers are able to silence guns, but they work on a very simple principle.
Imagine a balloon. If you pop a baloon with a pin, it will make a loud noise. But if you were to untie the end of the balloon and let the air out slowly, you could do it making very little noise. That is the basic idea behind a gun silencer.
To fire a bullet from a gun, gunpowder is ignited behind the bullet. The gunpowder creates a high-pressure pulse of hot gas. The pressure of the gas forces the bullet down the barrel of the gun. When the bullet exits the end of the barrel, it is like uncorking a bottle. The pressure behind the bullet is immense however - on the order of 3,000 PSI - so the POP that the gun makes as it is uncorked is extremely loud.
A silencer screws on to the end of the barrel and has a huge volume compared to the barrel (20 or 30 times greater). With the silencer in place, the pressurized gas behind the bullet has a big space to expand into. So the pressure of the hot gas falls significantly. When the bullet finally exits through the hole in the silencer, the pressure being uncorked is much, much lower - perhaps 60 PSI. Therefore the sound the gun makes is much lower.
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Btw, I'm going to be purchasing a few within the next few weeks. A 10/22 integrated silencer and probably something for my M16