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Change guitar string tension

  1. Jun 13, 2016 #1
    1. The problem statement, all variables and given/known data
    You have a ukulele and you change the strings tension so that it becomes tighter. First the frequency was 431 Hz and after we tightened the string the frequency. how much bigger does the force have t be to get that frequency?

    2. Relevant equations

    PA*V^2 = F (P = density, A = area)
    V=f*lambda

    3. The attempt at a solution
    F2 = PA V2=PAf22 * lambda2
    F1 = PA V2=PAf12 * lambda2
    Then i divided F2 by F1 and I got:
    f22/f12
    which equals to 1,06. My answer is 6 precent bigger.

    So my questions are: can I assume that lambda is going to remain the same? Is my solution correct?
     
  2. jcsd
  3. Jun 13, 2016 #2

    haruspex

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    If lambda here represents the wavelength of the wave in the string, yes you can assume it remains the same. The string length did not change, and we are only interested in the fundamental.
    You seem to have omitted the new frequency from the problem statement.
     
  4. Jun 14, 2016 #3
    Sorry, the new frequency is 444Hz. Why can we assume that? That was my initial thought but then I thought wouldn't the wavelength differ if the string is tighter?
     
  5. Jun 14, 2016 #4

    haruspex

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    What is the equation relating the wavelength of the nth harmonic to the length of the string?
     
  6. Jun 14, 2016 #5
    it is l=n*lambda/2
     
  7. Jun 14, 2016 #6

    haruspex

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    Right. So if we are only interested in the fundamental, that fixes n as 1. And the length l of the string does not change. So what does that tell you about lambda?
     
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