The requirements for carry-on musical instruments is here. Scroll down to near the bottom for the section on musical instruments.

According to that, you get a normal carry-on plus a musical instrument no bigger than specified (a violin should meet that) plus a personal item. If you have a hard-side case you shouldn't have any problem, but I'm guessing you wouldn't want to put it under the seat in front of you if you have a soft-side case.

Jim