Answer Happy

A pipe of length L that is closed at both ends is set to vibrate along its length so that its periodic acceleration sets up a standing wave in the air molecules inside it. The harmonics of such a wave are the same as those in a string of length L. A particular standing wave of this sort has 31 displacement nodes. If a length x were to be cut out and removed from the original pipe, the remainder would be a closed pipe (open at one end and closed at the other) in which a standing wave with 8 displacement nodes would have the same frequency as the standing wave in the original pipe. What is x in terms of L? a) L/2 b) L/4 c) 2L/3 d) 3L/4 e) 5L/6