[Waves] Standing waves problem (possibly )

  1. 1. The problem statement, all variables and given/known data
    The A-string (440Hz) on a piano is 38.9cm long and is clamped tightly at both ends. If the string is under 667-N tension, what is its mass?


    2. Relevant equations
    [tex]\lambda[/tex] = vT
    [tex]\mu[/tex] = mass/length
    v = [tex]\sqrt{F/\mu}[/tex]


    3. The attempt at a solution
    I don't really know which equations to use


    I don't know if it's right
    For fundamental harmonics, L = [tex]\lambda[/tex]/2
    so 0.389m = [tex]\lambda[/tex]/2
    [tex]\lambda[/tex] = 0.778m
    [tex]\lambda[/tex] = vT
    0.778 = [tex]\sqrt{F/\mu}[/tex] (1/440Hz)
    0.778 = [tex]\sqrt{667/\mu}[/tex] (1/440Hz)
    [tex]\mu[/tex] = 0.00569 = mass / 0.389m
    mass = 0.0022kg
     
    Last edited: Sep 16, 2010
  2. jcsd
  3. kuruman

    kuruman 3,448
    Homework Helper
    Gold Member

    Your third equation is incorrect. The square root of F/μ is the speed of propagation v, not the wavelength.
     
  4. oh right. correction!
     
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