First off, you say dug, but I would think it was drilled. Also, at 700 feet, I assume it goes into bedrock. There are a few explanations I can think of. One is that several veins were drilled through and water is trickling from an upper vein. Another is that the seal between the casing and bore is leaking.
I would assume there is a report on file for the well. A downhole camera would reveal the source of the sound.