Under the speed of sound, but they all differ a bit and they are calculated in fps (feet per second) For example a bullet that travels about 1000fps might equal about 680 mph.
Our airbags in our cars are set off by gun powder. Air bags deploy at 200mph. (and wow, you can really get an injury from that, my friend was belted in, and her air bag caused her to have multiple ribs smashed, punctured lung) ouch. However, had she not been belted and no airbag.. who knows.
I tend to agree the sound is so hard to explain, and loud, its almost simultaneous, but some gun shots are not really felt right away (shot gun yes, your head basically explodes and there is nothing for an M.E. to even look at)
smaller caliber gun such as a 25. Its a little pretty clean looking hole, and I venture to guess you are stunned at first, that delay when you are stunned into silence, or might put your hand to your head, you feel pressure first, then a burn. Often times since your nerves are all damaged at the wound side and below, its just dead nerves, 100% numb. The pain will start once the surrounding tissue and nerves start to light up like they are on fire. (the gun powder example) one of the biggest memories of the typical gun shot victim is ears ringing because it was loud, they are disoriented at first, especially shot to the head (anything in and about the base of skull, back of head, mid brain to brain stem i am not certain they would remember much? Usually they are out and down pretty instantly) The temple area, especially if it exits forward, at some angle exiting the face, just anything excellent straight into the brain, you are screaming after a few seconds or just dazed and holding your head tight. One is often left with rupture ear drums (although if shot in the head that's the least of your problems)
so it burns! and you just hold it tight and pray it was the front of your head/forehead/face, so you might survive it and make a near full recovery. There is a kind of cancer tumor that grows on the front lobe area.. commonly removed is nearly the whole front lobe and you heal and you go about your business.. (back of the brain, not so much...)