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Standing Waves on a string & pipe

  1. Dec 18, 2012 #1
    1. The problem statement, all variables and given/known data

    A string 40.0cm long of mass 8.50g is fixed at both ends and is under a tension of 425N. When the string is vibrating in its third overtone, you observe that it causes a nearby pipe, open at both ends, to resonate in its third harmonic. The speed of sound is 344m/s. a) How long is the pipe? b) What is the fundamental frequency of the pipe?


    2. Relevant equations

    Fn=(nV)/(2L)
    λn=(2L)/n
    V=√(F/μ) where μ=m/L


    3. The attempt at a solution

    Really stuck on this one. I know I can find the velocity of the string with the given information but am not sure how I can relate the velocity of the string to the velocity of the pipe. Any suggestions would be much appreciated.

    m/L= 0.0085kg/0.400m = 0.0213kg/m
    Vstring=√(425N/0.0213kg/m) = 141.3m/s
     
  2. jcsd
  3. Dec 18, 2012 #2

    Doc Al

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    Staff: Mentor

    What's the frequency of the vibrating string?
     
  4. Dec 18, 2012 #3
    So the third overtone would mean n=4....

    so fn=(4*141.3m/s)/(2*0.400m) = 706.5Hz

    so the frequencies of the string and pipe must be related, I'm just not sure how.
     
  5. Dec 18, 2012 #4

    Doc Al

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    Staff: Mentor

    Good.
    They are the same! (They resonate.) So what's the fundamental frequency of the pipe?
     
  6. Dec 18, 2012 #5
    I think I get it :smile:

    fpipe = nV/2L
    706.5Hz = (3*344m/s)/(2L)
    L = 0.730m

    fo = v/2L
    fo = (344m/s)/(2*0.730m)
    fo = 236Hz

    thank you so much, really appreciate it :)
     
  7. Dec 18, 2012 #6

    Doc Al

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    Staff: Mentor

    Good! :approve:
     
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