Hear a violin 3D-printed of polymer:
http://3dprintedinstruments.wikidot.com/printed-instrumentshosted at
https://youtu.be/XU3AZmf6O7Iit could have sounded worse. But it's very far from a decent violin.
Printing a violin or a woodwind's reed is the most difficult challenge and I don't imagine plastic to succeed in that task, especially if the shape is just copied from the wooden parts, which is meant for very different material properties.
But for instrument parts that don't essentially vibrate, like the body of a recorder or the mouthpiece of a woodwind, we're on the verge of home-printing them.
Which I feel ironic, because chip-making manufacturing processes are obviously cheaper than 3D printing for them. A woodwind mouthpiece is only a part of hard rubber, it has a simple shape except for the reed seat which is just copied automatically by the grinding machine from a pattern. So cheaper home printing results from the many profits in the sales chain.