According to the TSA (Transportation Security Administration) website, you may take your instrument on board a plane as long as it is in a case and fits within TSA size requirements. Many (most) TSA personnel are not aware of this policy. You should print out the policy and have it with you to help train the TSA personnel as you go.
It is still a very good idea to contact your airline in advance and work out the details before you travel.
The following is a link to the TSA website policy:
The TSA is responsible for security access to airline gates. They are a government agency and they are not connected to any airline.
The TSA policy is to allow you to carry on an instrument, but the particular airline may have another policy. Call your airline and work out the details before you go to the airport.
“My TSA” is an app for iPhones and iPads for real-time travel information on airport staus and information of what can be carried to the gates and on-board aircraft. It is a free download from the Apple App Store.