It would seem that the OP has two .wav files recorded in a system like this:

We have two identical audio sources triggered at the same time. Audio source 1 is a negligible distance from the recording mic. Audio source 2 is a distance x from the recording mic. We activate them both and record a .wav file.

The OP notes that the more distant audio file has a different pitch, probably due to higher frequencies dropping off more quickly than lower ones over a distance.

We really need to calculate the distance x then we can solve for the time using the speed of sound. If you know (or can figure out) the rate of frequency attenuation through your medium, that would work. I suspect there would be some amplitude attenuation that you could use as well which is a more common calculation for this problem.