On my 1995 Toyota Corolla there was a persistent buzzing noise coming from, what I had thought to be, under the hood. It turned out to be coming from the front bumper cover because it had separated from the material underneath it as it aged. As a result the bumper cover was vibrating when the engine was idling giving the impression that the noise was coming from the engine itself. The noise doesn't show up all of the time, it seems to be worse in cold weather when the plastic is less flexible.
To help reduce the vibrating I stuffed some landscaping material that is used to prevent weed growth under the openings around the underside of the bumper. The reason I used landscaping cloth is because it was the best choice that I could think of that could take the weather and it doesn't hold water so there wouldn't be a sopping wet cloth or something under the bumper possibly setting up to cause more problems.
So if you have a noise coming from under your hood and you just can't put your finger on the source, check your bumper. Just lift up on it some and see if the noise goes away.
