In this post among others, I’ve been attempting amateur forensic analysis on gunshots at Trump at the Butler Rally. But the best answers will come from the experts in the field, so I looked them up and found great explanation of how audio can be used to determine distance:
In this example from Maher and Shaw (cited below), the microphone was placed downrange by 91 meters (~300 feet) at 5 meters off to the side of the path of a .308 Winchester bullet. While the bullet shock wave (the bullet snap or crack) got picked up by the microphone at 25 milliseconds (0.025 seconds), the blast was heard at 175 ms.
NOTE: Being off the bullet path by 5 meters in the above, the microphone would be approximately 16 feet away from where the bullet passed by. At the Trump rally, microphones might have been double that distance from the podium (32 feet from the podium), or even farther.
As I suspected, precise estimation involves more math than I’ve been doing up to this point:
In this fine explanation, the muzzle blast follows path B straight to the microphone situated at 8 meters off of the bullet path. The only thing governing the time to get there is the speed of sound (Mach 1). But bullet shock waves propagate outward at an angle pre-determined by bullet speed. The one above follows path C.
This means that, even though I had purported to have ruled out a shooter on top of the water tower, I would have to go back and rework the calculations in order to verify that that is the case. Ideally, a hearing or a trial with an expert witness able to prove presence/absence of shooters at various locations would help us reveal what happened.
Reference
DECIPHERING GUNSHOT RECORDINGS. ROBERT C. MAHER AND STEVEN R. SHAW. https://wetlands.msuextension.org/rmaher/publications/maher_aesconf_0608_1-8.pdf