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Homework Help: Standing waves and tension

  1. Apr 21, 2010 #1
    upload.jpg



    1. The problem statement, all variables and given/known data
    see question 2a, b

    2. Relevant equations
    a) v=f(wavelength)
    b) v= sqrt(F/(m/L))

    3. The attempt at a solution
    a) f=2.5 Hz, t=1.0 s and one wavelength on the graph is I guess 0.4 m?
    v=2.5(.4)=1 m/s
    b) f=5.0 Hz, tension same
    v= sqrt(F/(m/L)) means that a change in frequency will not change the velocity?
    1=5(wavelength)
    wavelength= 0.2 m?


    1. The problem statement, all variables and given/known data
    see question 3a, b

    2. Relevant equations
    fn=(n/2L)(sqrt(F/(m/L))

    3. The attempt at a solution
    a)since this is a second harmonic, f2 = 2(2/L)(sqrt(F/(m/L)) = (1/L)(sqrt(F/(m/L))... wavelength = L

    quadrupling F would mean that f=(1/L)(sqrt(4F/(m/L)) = (2/L)(sqrt(F/(m/L))
    since f does not change, only way that these two will be equal is if the above is divided by 2
    (2/2L)(sqrt(F/(m/L)) = (1/L)(sqrt(F/(m/L))
    thus wavelength = 2L, so the new picture should just contain half of the wave?

    b)tripling tension would mean that wavelength = sqrt(3)L... this shouldn't be possible right? since a standing wave needs to be connected at both ends (nodes) and having a wavelength of 1.7L would not connect on one end...


    please help! thanks
     
    Last edited: Apr 21, 2010
  2. jcsd
  3. Apr 21, 2010 #2
    I think you should start off by looking at the first calculation. You've picked up an extra factor of 10 somewhere.
     
  4. Apr 21, 2010 #3
    edited, but do things seem right or are they wrong 2b and 3a, b are the ones im not sure on
     
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