A weird sound from Xmas tree lights

I put up my Christmas tree yesterday, with two strings of lights, each string plugged into a separate socket on the same receptacle. About three hours after turning the lights on, I noticed a low humming sound coming from the room. When I unplugged one string of lights, nothing happened. When I unplugged the other string, the humming stopped. Plug it back in, the humming starts again.
Now here's the weird part (at least to me): the humming is not actually emanating from the lights, the cord, the receptacle or anything else on that entire side of the room. The hum (which is quite noticeable) seems to come from near the ceiling 3/4 of the way across this 17-foot-long room. The hum is present whether the regular light fixtures are on or off, and there's nothing else electrical in the room.
The hum is just loud enough to cause me some concern -- not from the noise (which is not unpleasant) but from its volume, which is enough to suggest that something conceivably might not be safe. But I'm completely stymied by the fact that the Christmas tree seems to be a ventriloquist, throwing the noise some ten feet away. (Literally, I can stand "between" the tree and the hum.)
Any ideas?
Jim Beaver

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