You could try poking around with a small diameter rod. I would probably suggest calling a local university's geology department and ask about what is likely in your area.
A point to consider: if it is really a sink hole and not just compacting soil, you may just be seeing the remaining covering over the top of the real hole. That hole can be very deep. Dangerously so.
This will be the extra credit information. There is a process called dome formation that can occur in limestone (or anything that can be dissolved by water I suppose). A dome forms in the rock and then "climes" up to the surface leaving a circular shaft. One I saw in Pennsylvania was in a farmers field. PA has lots of limestone and caves. He would throw fill in from time to time. Finally it ate his tractor. Not all the way just a wheel. Turned out he had broken through the center of a dome pit. He was hanging over a hole that went straight down, as I recollect, 275' and about 30' in diameter. As a side note: it was the most extensive cave system ever found in PA at the time (may still be). The entrance to the system was only about 50' from the bottom of the dome pit so anyone entering had to go up and down a free hanging rope or ladder for the entire distance. A major benefit of this is it kept tourists and boy scouts with string from messing up the cave.
This sort of thing can happen in other materials when the water table drops by a large amount. If the bed rock you are sitting on is limestone, there could be real caves down there. It seems to me that Georgia probably has something else in general but I don't really know.
Anyway, be careful.