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Frequencies of the first three overtones in a string?

  1. Nov 24, 2015 #1
    1. The problem statement, all variables and given/known data

    A violin has an A string in tune at 440.0 Hz; as is the E string at 660.0 Hz. The tension force on each of the strings is 25.0 N. The linear density of the A string is 1.00 g/m. What are the frequency of the first three overtones for each string?

    2. Relevant equations
    f = v/ λ
    λ = 2L/n
    v = √(T/P)

    f = frequency
    λ = wavelength
    v = velocity of wave
    L = string length
    T = tension
    P = Linear Density in kg/m
    n = number of loops

    3. The attempt at a solution
    String A:

    f = (n√(T/P))/2L
    L = 0.17967748671

    f = (2√(T/P))/2L for the 1st overtone
    f = (3√(T/P))/2L for the 2nd overtone
    f = (4√(T/P))/2L for the 3rd overtone

    Is this path right?
     
  2. jcsd
  3. Nov 24, 2015 #2
    Do this without a calculator.
     
  4. Nov 24, 2015 #3
    Oh yeah, thanks!
     
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