Interested Bystander
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There was definitely a delay with the bat, but I don't think it showed the microphone in the distance recording the gun shooting. Did it?
Here is the link BUT, interestingly, on watching a second time there is also a slight delay with the sound from the gun but not nearly as much. However, this serves to tell me that my recollection can be called into doubt. I thought there was no delay from the gun. What I thought I saw and heard the first time, was not quite what I registered viewing the video second time around.
[video=youtube;9BMMeYM7jRo]http://www.youtube.com/watch?v=9BMMeYM7jRo[/video]
I should add here that I don't think this is a particularly good experiment from the OP scenario but I was interested in the sound waves because bullets in modern guns fire at supersonic speeds and the wave packet will travel much faster than ordinary accoustic sound to begin with but dissipates over distance and eventually travels at the same speed.