I am conducting an experiment in physics where i move a styrofoam sheet away from a source of sound. The sound emitted is a 440hz acoustic frequency continuous. Has anyone observed any relationship between the distance of the source and the amount of sound absorbed by a barrier before?
There are two factors that might muddy your results.
First, sound is absorbed by the air, so however you are measuring the sound level after it has hit the barrier, you won't know how much of the measured absorption was due to the air or the barrier, unless you measure twice - once right in front and once behind.
Second, the intensity of a continuous sound drops by about 6 dB for every doubling of distance, so once again, you'll have to measure both in front of the barrier and behind in order to isolate just the effects of the barrier.
You should also do this experiment outside in an open field so you know there aren't reflections from walls or ceiling, and I think you can safely discount reflections from grassy soil at 440 Hz.
Instead of measuring in front and behind the barrier, it might be easier to measure the intensity at the distance in question without the barrier, then introduce the barrier and record the drop in intensity.
Regarding your actual question, you should expect to find that the amount absorbed by the material is a fixed property of the material for a given frequency, and it won't change in a significant way no matter how far away the material is.
If you want to make your experiment and results more interesting, you could try measuring absorption at different frequencies and/or stacking multiple identical panels together and measuring whether two panels absorbs twice as much as one, whether three panels absorbs three times as much, etc.