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Fundamental frequency and tension

  1. Feb 27, 2010 #1
    1. The problem statement, all variables and given/known data

    A guitar string has a fundamental frequency of 429 Hz when its tension is 259 N.
    The string is being tuned to a fundamental frequency of 388 Hz. What is the required tension?

    2. Relevant equations

    v = sqrt(T/u): where v is the speed, T is the tension and u is the linear mass density
    f1 = v/2L: where f1 is the fundamental frequency, v is the speed again and L the length of the string

    3. The attempt at a solution

    sqrt(T/u) = f1(2L)
    sqrt(259/u) = 858L

    I tried to use the speed equations to find u or L, which would allow me to calculate the v after and then get the frequency, but I'm still left with 2 unknowns. Am I using the wrong equations to solve this?
     
  2. jcsd
  3. Feb 27, 2010 #2
    You have two equations, one for f1=429Hz and one for f2=259Hz
    Write each one as f=v/2L and substitute for v in terms of T and u
    Then do f2/f1=
     
  4. Feb 27, 2010 #3
    Oh I get it now. It should have been obvious but I was just having trouble with cancelling out the unknown terms. Thanks I managed to get the answer.
     
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