In a pipe organ, air is forced to flow through hollow pipes with precisely determined lengths. One end of the pipe is always open, to allow air into the pipe. The other end may be opened or closed. (a) If a pipe is to generate a note with a frequency of 256 Hz (middle C) when closed at one end, how long should the pipe be? (b) What are the frequencies of the next two harmonics produced by this pipe? (These are the pitches of the next two standing waves that the pipe will admit.) (c) What fundamental frequency will the pipe produce if both ends are open? (d) What are the frequencies of the next two harmonics when both ends are open? (These are the pitches of the next two standing waves that the pipe will admit.)

In a pipe organ, air is forced to flow through hollow pipes with precisely determined lengths. One end of the pipe is always open, to allow air into the pipe. The other end may be opened or closed. (a) If a pipe is to generate a note with a frequency of 256 Hz (middle C) when closed at one end, how long should the pipe be? (b) What are the frequencies of the next two harmonics produced by this pipe? (These are the pitches of the next two standing waves that the pipe will admit.) (c) What fundamental frequency will the pipe produce if both ends are open? (d) What are the frequencies of the next two harmonics when both ends are open? (These are the pitches of the next two standing waves that the pipe will admit.)