Hi Elfin, welcome
My suggestion would be simply to check, clean and reseat: battery terminals, fuses & grounds. I'd also ask how the battery is going as if its on its way out can cause all sorts of electrical gremlins.
Can't see how that would cause your noise though.. Its not the catalytic converter stuffed up is it? I'd suggest getting an exhaust shop to take a look see perhaps and verify all good & no broken mounts etc.
Plenty of knowledgeable folk on here that will help you get to the bottom of it in sure.
Cheers.