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A 2.49-m-long string, fixed at both ends, has a mass of 7.17 g. If you want to set up a standing wave in this string having a frequency of 455 Hz and 5 antinodes, what tension should you put the string under?

  • physics - ,

    String mass per unit length is
    w = 0.00717/2.49 = 2.88*10^-4 kg/m

    With five antinodes, the wavelength is
    L = 2/5 * 2.49 = 0.996 m

    The frequency is f = 455 Hz

    The wave speed is C = L*f = 453.2 m/s

    The tension T must provide that wave speed.

    sqrt(T/w) = 453.2 m/s

    Solve for T, in Newtons

    T = w*(453.2)^2 = 59.2 N

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