Measuring Amplitude of sound wave FFT
These are interesting results.  Your comment "The X axis represents the distance travelled in metres (from 3.5m away to 0.5m away from the sound source). " seems to contradict "With this explanation, '0' represents 0.5m from sound source, while '3.0' represents 3.5m from sound source."  The latter seems to be the one that fits your data better.

What is more pronounced is the fluctuations you are getting.  Taking the speed of sound at 343 meters per second:

$$ \frac{343~\text{meters}/\text{second}}{500~\text{cycles}/\text{second}} = 0.686~\text{meters/cycle} $$

With standing waves, the nodes are at half the wavelength, which corresponds closely to the size of your fluctuations in the graph.  So as your robot is moving through the room, it looks like you are measuring the standing wave nodes.