Recording A - the Maths

The delay times were measured using a Soundscape DAW (digital audio workstation).
Soundscape uses a timecode format of hours, minutes, seconds, frames and samples - so the measured delays must first be converted to seconds.
All of the recordings are made and edited in 16 bit stereo, with a sample rate of 44.1 kHz and at 25 frames per second.
With these settings, there are 1764 samples in each frame of 1/25th second.

Here are the delay times as measured for the 5 positions in the SW quadrant:-

Position 1 - 10 frames, 1048 samples = 10.59 frames = 0.423 secs
Position 2 - 8 frames, 1504 samples = 8.852 frames = 0.354 secs
Position 3 - 8 frames, 1120 samples = 8.634 frames = 0.345 secs
Position 4 - 7 frames, 68 samples = 7.039 frames = 0.281 secs
Position 5 - 5 frames, 248 samples = 5.140 frames = 0.206 secs
This delay was used to calculate the speed of sound for the first five positions. Distance from the recording position to the reflecting stone was measured with an odometer as being 35.6 m. Sound travelled from the recording position to the stone, then back again, so distance (x) = 35.6 x 2 = 71.2 m
4/1/08 - this calculated SOS disregarded.

So, to confirm where the echoes originated, the delay times of positions 1 - 5 were converted to distance, using the formula: x= ct

Position 1 - delay of 0.423 s. To find distance: x = ct = 346 x 0.423 = 146.36 m. But this distance is from the sound source to reflector and back again.
So, distance from recording position to reflector (one way only) = 146.36/2 = 73.18 m - Now 69.8 m
Position 2 - delay of 0.354 s - distance = 346 x 0.354 = 122.5/2 = 61.25 m - Now 58.4 m
Position 3 - delay of 0.345 s - distance = 346 x 0.345 = 119.37/2 = 59.69 m - Now 57 m
Position 4 -delay of 0.281 s - distance = 346 x 0.281 = 97.42/2 = 48.71 m - Now 46.3 m
Position 5 - delay of 0.206 s - distance = 346 x 0.206 = 71.28/2 = 35.6 m - Now 34 m

Recording position 6 was by the Obelisk, in the SW quadrant. As seen, the large number of stones in this area produced a more complex pattern of echoes.
Here are the delay times:-

Position 6 (1) - 2 frames, 504 samples = 2.286 frames = 0.0914 secs
Position 6 (2) - 2 frames, 696 samples = 2.394 frames = 0.096 secs
Position 6 (3) - 2 frames, 1320 samples = 2.748 frames = 0.1099 secs
Position 6 (4) - 3 frames, 1284 samples = 3.728 frames = 0.149 secs
Position 6 (5) - 4 frames, 1728 samples = 4.980 frames = 0.1992 secs
Position 6 (6) - 7 frames, 708 samples = 7.401 frames = 0.296 secs

The last of the six echoes - 0.296 secs - was assumed to be a reflection from one of the large stones of the Southern Circle.
Here, a discrepancy became apparent: if speed of sound c = 346 m/s then using the formula x = ct indicates that it is 0.296 x 346 = 102.4/2 = 51.2 m away;
yet the stone was measured with the odometer as being exactly 50m away. This indicates that the speed of sound had changed, so it was re-calculated.

If speed of sound c = x/t then c = 100/0.296 = 337.84 m/s - slower than in the SW quadrant.

The distances to the six reflective surfaces can now be calculated with the re-calculated speed of sound - rounded to 338 m/s
4/1/08 - this calculated SOS disregarded - now 330 m/s

If x = ct then:

Position 6 (1) - delay of 0.0914 s - distance = 338 x 0.0914 = 30.89/2 = 15.44 m - now 15 m
Position 6 (2) - delay of 0.096 s - distance = 338 x 0.096 = 32.45/2 = 16.22 m - now 15.8 m
Position 6 (3) - delay of 0.1099 s - distance = 338 x 0.1099 = 37.15/2 = 18.57 m - now 18.1 m
Position 6 (4) - delay of 0.149 s - distance = 338 x 0.149 = 50.36/2 = 25.18 m - now 24.6 m
Position 6 (5) - delay of 0.1992 s - distance = 338 x 0.1992 = 67.33/2 = 33.66 m - now 32.9 m
Position 6 (6) - delay of 0.296 s - distance = 338 x 0.296 = 100.05/2 = 50 m - now 48.8 m