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Calculating the speed of sound in air

  1. Jun 10, 2009 #1
    1. The problem statement, all variables and given/known data
    In a resonance tube, using a tuning fork of frequency 325 Hz,the first two resonance lengths are observed at 25.4cm and 77.4cm.The speed of sound in air is
    1. 318m/s 2. 338m/s 3.358m/s 4.378m/s 5. 368m/s


    2. Relevant equations

    v=f*lambda

    3. The attempt at a solution
    Since the question states 25.4cm and 77.4cm as the 1st two resonance lengths,25.4cm has to be the length of the tube at the fundamental frequency and 77.4cm at the 1st overtone.
    And since 77.4cm is approximately 3 times the fundamental length of 25.4cm,I'm assuming it's a closed pipe.

    Therefore, lambda/4 = 0.254m
    lambda=1.016m
    Then using v=f * lambda
    =325*1.016
    I get v =330.2m/s which is not among the choices given, so I'm really hoping someone could help me out here.
    Thanks
     
    Last edited: Jun 10, 2009
  2. jcsd
  3. Jun 10, 2009 #2
    Think about the question again;

    "the first two resonance lengths are observed at 25.4cm & 77.4cm" means the distance between the first two anti-nodes = 52cm, so effectively the "length" in the equation is 52

    frequency = [tex]\frac{Speed}{2 * Length}[/tex]
    325 = [tex]\frac{Speed}{2 * 0.52}[/tex]
     
  4. Jun 11, 2009 #3
    Thanks. I get it now. I get a velocity of 338m/s
     
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