2005 hyundai accent. rattling/vibrating noise

I have a 2005 hyundai accent, 62000 miles. When I accelerate there is a vibrating/rattling noise that sounds like it’s in the back left side. It only happens sometimes. It happens when i accelerate slowly or up a hill, and if i press on the gas it stops. I thought it was the muffler, but I got the car inspected in May and it was fine. It’s been doing it since before then. My dad said it might be a loose heat shield vibrating. It seems to be getting more frequent with humid weather. Should I be worried?

sorry back right side

earthquake.

Sorry, had to say that in light of recent news. ( my daughter is in Woodbridge VA 20 miles from epicenter. )

Is it a metalic sound or plastic ?
But I still think you’re on the right track looking at exhaust parts.
Noises like that are hard to find in the shop. Look all the way through, even the tail pipe mounting.
Look also at fender liners, splash shields and the like, test wiggling each to see if it sounds the same.