I'm not sure if it's a wireless doorbell or not. We can't hear the doorbell upstairs unless this contraption is plugged in to the socket. Then when the doorbell rings, it plays, "America the Beautiful".
I unplugged it after the second time and slept happily.
Husband went outside after the second time and found where he could see some tracks in the dewy grass leading up to the house, and then running away from the house.
So, there is an actual culprit.
But, thanks for the tip...if there had been no tracks in the grass, we would have been realy confused!