Some airlines do not specifically mention musical instruments. Carry a copy of the Transportation Security Administration’s guidelines. Violins usually are no problem. Banjos and guitars sometimes can be carried on. Usually the airlines are pretty good about it. If there is a problem ask politely to see a supervisor or the captain. Being polite will go a long way towards being allowed to carry on your instrument and making it possible for others to do so, too.
Following are some sites on musical instruments as carry on baggage. If you have another airlines link that it not listed here email me and I will post it.
Also, included here is a copy of a letter from the TSA to the president of the American Federation of Musicians.