A piano wire has a linear mass density of μ = 4.85 ✕ 10−3 kg/m. Under what tension (in N) must the string be kept to produce waves with a wa

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A piano wire has a linear mass density of μ = 4.85 ✕ 10−3 kg/m. Under what tension (in N) must the string be kept to produce waves with a wave speed of 595.00 m/s?

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Trúc Chi 5 years 2021-08-17T13:43:35+00:00 1 Answers 28 views 0

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  1. diemthu
    0
    2021-08-17T13:45:23+00:00
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    Answer:

    The string must have a tension of 1717.021 newtons to have a wave speed of 595 meters per second.

    Explanation:

    This is a case where transversal waves occur. The formula of speed for transversal waves is:

    v = \sqrt{\frac{T}{\mu} }

    Where:

    v – Speed of the transversal wave, measured in meters per second.

    \mu – Linear mass density, measured in kilograms per meter.

    T – Tension, measured in newtons.

    The tension is now cleared:

    T = v^{2}\cdot \mu

    If v = 595\,\frac{m}{s} and \mu = 4.85\times 10^{-3}\,\frac{kg}{m}, the tension needed is:

    T = \left(595\,\frac{m}{s} \right)^{2}\cdot \left(4.85\times 10^{-3}\,\frac{kg}{m} \right)

    T = 1717.021\,N

    The string must have a tension of 1717.021 newtons to have a wave speed of 595 meters per second.

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