"Street Musician: 'What is the difference between a flutist and a flautist?' Famous Musician: 'I don't know.' Street Musician: '50 dolars a week, man.'" --unnamed writer, in New York Stories (paraphrased)
This flute signifies Hamlet's reference in the quote "...do you think I am easier to be played on than a pipe? Call me what instrument you will..you cannot play upon me." This refers to Hamlet's recollection of Rozencrantz and Guildenstern and their lies. He knows what they are doing and says that they can not fool him and play him so easy, just like a flute.