AWCAWD

Judging from the tone of the sound it is rather the heat shield attached to the undercarriage than the one on the exhaust pipe. If you are lucky it might have only hit by a stone and bent it. The most likely scenario is that the steel screw that holds the aluminum heat shield corroded so much that it no longer holds it in place (something similar as shown in the attached image).
BTW. This sound is clearly coming form underneath and not from the "engine area".
Good luck fixing it. You will have to go innovative as the "thread" on the screw (these are special, they are not pitched) is most likely gone.