I've wanted to make vegetable instruments for some time. I found a couple of links to a carrot flute and a carrot kazoo, but they did not have pictures. So I tried a few different techniques. Here's my recipe for Carrot Flute. I'm providing this in multiple forms. Instructable with pictures, short form instruction video, and long form experiences.
I recommend viewing the short form video, printing the instructable for your work time, then viewing the long form video (so that you can see what I did).
Short form video.