97 Cobra making a loud humming on Accel

It sounds like a possibility of the rear end needing some work. They'll make a humming/howling noise under load. I'd start with checking the oil level in the differential case, see if it smells burnt or is dirty. Sometimes changing it can help. Make sure to use the Motorcraft friction modifier if you decide to change the rear end oil!

Just throwing this out there, but do you know if it has a short-throw shifter? An aftermarket shifter like a Steeda removes all of the rubber spacers for a better feel when shifting. It also allows some whinning from the transmission because it vibrates throught the metal and makes a humming or whinning noise inside the cabin. I have a Tri-ax and my car whines so much it sounds supercharged, especially in 3rd gear. Just an idea. If the lubricant levels look good and it drives good this might be the cause. Did it do this since you bought it?