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Physics need help

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A guitar string is struck and found have a frequency of 2048Hz. If both tension and length are doubled, what is the new frequency of the string?

  • Physics need help - ,

    The fundamental frequency (first harmonic) of a plucked string is given by
    f=(1/2L)√(T/ρ)
    where L=length, T= tension and ρ=mass/unit length

    So we see that the frequency is inversely proportional to the length, and proportion to the square-root of the tension.
    If both of them are doubled, then new frequency, f1 is can be obtained by :
    f1=f*(1/2)*&radic(2)
    =f/&radic(2)
    =2048/1.414213562
    =1448 Hz approximately

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