I have the constant sound in my bathroom as if water is running somewhere. The sound is loudest under one of the sinks. I checked the water meter outside, but the dial is not turning so it's not water. This is a single family home, so the sound is not coming from any other place. What could cause this and could it be a real problem?

Does your meter have a very small triangular poniter in the center of the dial, if the pointer turns water is moving.

Does your meter have a very small triangular poniter in the center of the dial, if the pointer turns water is moving.
It does have that type of pointer... I had someone flush the toilet while I was looking at the meter just to make sure that it was working correctly... afterward there was no movement on the meter

Then your sound is not water. Could be a furnace fan, a/c condenser, etc... but notwater