A platinum wire that is 1.20 m long has a radius of 0.500 mm and is fixed at ends. In its third harmonic it vibrates at 512 Hz. The density

Question

A platinum wire that is 1.20 m long has a radius of 0.500 mm and is fixed at ends. In its third harmonic it vibrates at 512 Hz. The density of platinum is 21.4 × 103 kg/m3. What is the tension in the wire?

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Diễm Thu 3 years 2021-09-05T12:47:17+00:00 1 Answers 1 views 0

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  1. Nem
    0
    2021-09-05T12:49:16+00:00
    Reply

    Answer:

    2820 N

    Explanation:

    Let assume that

    Ft = µ(2fL)^2

    tension = µ(2*frequency*length)²  

    wavelength = 2*length

    In general, for a wire fixed at both ends,

    λ_n = 2L/n

    n is the harmonic number

    v = f_n * λ_n = f_n * 2*L/n

    = √(T/µ)

    = √(T/(ρA))

    so  

    T = (f_n * 2 * L / n)² * ρA

    Given that,

    f_3 = 512 Hz,

    L = 1.2 m,

    n = 3,

    ρ = 21.4 × 10⁻³ kg/m³,

    and with the radius can easily find the area A

    A = πr²

      = π(0.005)²

      = 7.85 ×10⁻⁵

    When I plug these values in, I get tension T = 2820 N.

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