I ran over a big piece of concrete years ago, and bent the exhaust pipe. I had it fixed then, but heard noises every time I would drive over a small body of water. Now, I've started to hear a loud noise when I accelerate. I think that the spot where the exhaust was bent before must have rusted, and developed a hole that needs to be patched.
The scenario you described seems likely, however, the only way to know for sure would be to get your exhaust system checked. I recommend that you have a mechanic, such as one from YourMechanic, come to you and run a thorough diagnosis of the noise coming from your exhaust.
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