Might be the infamous "tuning fork" exhaust hanger. It's a metal exhaust hanger that bolts onto the back of your engine and bolts to the downpipe/cat depending on which car you have. They're on all civics. It could have broken loose or could be touching something.

That exhaust hanger is really a POS and usually responsible for all kinds of messed up exhaust sounds. They do frequently rust out and break just like the Honda/Acura's exhaust B-pipes do every 3-5 years. Joe's right. It's probably rusted out by now.