The Ann Arbor city noise ordinance is part of the city code. You can find the Ann Arbor city code online (you'd be looking for chapter 119, NOISE CONTROL), or you can find the relevant parts of the city noise ordinance directly on the city web site. Complaints can go to the Ann Arbor Police Department's non-emergency phone number at 734-994-2911; before you call the law to break things up, talk to your neighbors.
In Ypsilanti, this form to file a noise complaint can be delivered to the Ypsilanti Police Department.
If you need a noise permit in Ann Arbor, fill out this form (pdf) and return it to the City Clerk. It will need to be approved by the Ann Arbor Police Department and by the City Clerk's office. You need 5 days notice and an $8.00 permit fee.
There's a 2007 post on Ron Suarez's blog noting loopholes in the city noise ordinance regarding commerical lawn care services.
The loophole concerns an exception to the Ordinance allowing lawn services to operate in residential neighborhoods at a very loud noise level (up to 90 decibels). The specific section in the Ordinance is Chap. 119, Sec. 9:364-365. This allowable noise level is louder than the noise from the average factory (75 decibels) and nearly as loud as that in the front row seats of a rock concert (110 decibels).
A comment notes that noise is measured on a logarithmic scale, so 90db is much less loud than 110db. Still, it's pretty loud.
City Council regularly hears requests to change or modify the noise ordinance. The marching band was the target of a 2003 complaint:
After several years of waking to the music, Van't Hul requested Tuesday that the Ann Arbor City Council change the city's noise ordinance law so that loud public music can only be played after 9 a.m, extending the current law by two hours. This would force the marching band to change its practice schedule.
"Nothing the University has done is illegal," said Van't Hul. But he added that the noise is a problem that could be changed quickly. "All it is, is just postponing (the marching band's) drums for a few hours. That's all. There's a lot of working people in Ann Arbor who need to get some sleep."
Enforcement of the noise ordinance is done by the city police. Here's a 2006 fall party season account of enforcement (Michigan Daily)
Police may issue noise violations after 11 p.m. if any noise can be heard beyond the property line.
Dresleski said officers rarely show up at house parties unless the department receives a neighbor's noise complaint.
"We don't care if you party all night unless it interferes with others' rights to peace and quiet," said Dresleski.
The Ann Arbor police now chart noise violations by address - instead of by person receiving the violation - and the price of the ticket goes up with each offense.
(inspired by a query that came to my blog; my neighbors are for the most part quiet enough, and if there's any loud noises at 11pm from my house it's from my two year old crying)