The AMA doesn't have noise regulations.

They do have some suggestions posted, however.

Some forms of competition have very specific nose rules.

It's not uncommon for people to mistake either the AMA recommendations or a particular competition class noise rules for general AMA rules.

As Crashem noted, individual fields may have their own noise regulations.

My home field has no noise regulations because no one lives very close to us. I even fun an old OS .61FS (four stroke, pre-surpass line) open stack, no muffler at all. It doesn't sound loud because it's low frequency noise, but it's actually pretty noisy on the ground.

If you want to reduce noise on your plane, there are lots of things you can do, different mufflers, prop brands and sizes, airframe vibration noise, and more.