I live in a 5 year old house. We are getting a random foghorn like noise in the house. It happens at random times. Middle of the day to middle of the night. No one is using water at the time of the noise. It is a single story house with copper water piping. I have searched the attic for the noise to no avail. It does not appear to be coming from either of the 2 water heaters or the heater/ac system. I have been up since 4am this morning looking for the problem... it is now 6am as I am typeing. What could it be?

Ahhhh! The dreaded potty monster, a fearful sound in the middle of the night. Terror in the toilet so to speak.
The problem is caused by the ballcock trying to fill while water is seeping out of the tank. The sound you hear is the washer vibrating against the seat of the ballcock. First check there linkage between the flapper and the flush lever. It should have 1/4" of play when your tank is filled. Next feel the flat side of your flapper. Does it have wavey edges? Do your hands come away black? Replace it if it does. And last check the seat itself. Any nicks or rough spots? If so click on back. There are replacement seats that glue right over the old one and are easy to replace. One of the above should take care of your howling. This happened in a new house some years ago. Only at night and in the early morning. They thought the house was haunted and were about to move out. I caught it in the powder room toilet. It would vibrate and the pipes in the wall would pick it up and carry it all over the house. Hope this helps, Tom