What would make the outlets with a GFI have a buzzing noise?

Some GFIs have an audible alarm and buzz when they trip.

Answer

I have found that a GFI that has been painted over or corroded stuck will cause a buzz when it is overloaded and trying to trip. The problem is when it is painted over and seized open it cannot trip and causes a buzz.

I would first start by having the GFI that is closest to the problem switch replaced then check the switch again.

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