United · Violin

Maybe

Cabin, if space

Protected by the federal rule as long as there is bin space when you board, so board as early as you can. United asks for a hard case.

You can buy it a seat on this airline.

United rules

A violin, guitar or other small instrument may be carried on in a hard case. In the bin it counts as your carry-on bag; under the seat, as your personal item.
US federal rule: the airline must accept it if it can be stowed and there is space when you board. There is no priority over other bags.
A seat can be bought for an instrument under 165 lb (75 kg). Call 1-800-864-8331; an agent must approve the item.
The instrument seat must be next to yours and the item stays belted in for the whole flight.
United Express flights use smaller aircraft with smaller bins.

Before you leave for the airport

Measure the case and weigh it packed. Staff measure the case, never the instrument.
Check the fare. The cheapest fares often include only an under-seat bag.
Check who operates each leg. The operating airline's rule applies.
A seat for the instrument is booked by phone, often 48 hours or more ahead.
Photograph the instrument and case before you leave home.
Board as early as you can.