What would happen if I exceeded mach 1 over a regulated area? What would happen if I exceeded mach 1 over a regulated area? Are there any penalties in place for this violation?  

Would ATC actually know I’m flying supersonic or would they have to go out of their way to check my groundspeed and work out my approximate air speed?
It would be a violation of 14 CFR 91.817


  § 91.817 Civil aircraft sonic boom. (a) No person may operate a civil
  aircraft in the United States at a true flight Mach number greater
  than 1 except in compliance with conditions and limitations in an
  authorization to exceed Mach 1 issued to the operator under appendix B
  of this part.


It would be extremely easy to track such an aircraft, and the pilot would be dealt with upon landing.