The Fundamental frequency of an open organ pipe

  1. 1. The problem statement, all variables and given/known data

    The fundamental frequency of an open organ pipe corresponds to the note middle C (f = 261.6 Hz on the chromatic musical scale). The third harmonic (f3) of another organ pipe that is closed at one end has the same frequency. Compare the lengths of these two pipes.


    2. Relevant equations

    frequency = harmonic number x (speed of sound in the pipe)/(2)(length of the vibrating air column)
    frequency = harmonic number x (speed of sound in the pipe)/(4)(length of the vibrating air column)


    3. The attempt at a solution

    I'm not sure where to go from here
     
  2. jcsd
  3. rl.bhat

    rl.bhat 4,435
    Homework Helper

    Chegg
    Hi jen0519, welcome to PF.
    Your relevant equation for open pipe is correct. But for closed pipe it is wrong.
    It should be
    Frequency = (2n + 1)(Speed of the sound)/4(length of the vibrating air column.)
     
  4. It's normal to express this as
    For the open pipe
    Frequency= n(v/2L) where n=1,2,3,etc
    For the closed pipe
    Frequency=n(v/4L) where n=1,3,5, etc
    or
    Frequency=(2n-1) (v/4L) where n=1,2,3, etc
    L is length of the pipe, v is speed of sound in the pipe
     
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