A 13 kg hanging sculpture is suspended by a 95-cm-long, 5.0 g steel wire. When the wind blows hard, the wire hums at its fundamental frequen

Question

A 13 kg hanging sculpture is suspended by a 95-cm-long, 5.0 g steel wire. When the wind blows hard, the wire hums at its fundamental frequency. What is the frequency of the hum

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Ladonna 4 years 2021-09-02T03:22:25+00:00 2 Answers 12 views 0

Answers ( )

  1. haidang
    0
    2021-09-02T03:23:45+00:00
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    Explanation:

    Below is an attachment containing the solution.

  2. Sigrid
    0
    2021-09-02T03:23:45+00:00
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    Answer:

    f=81.96 \ Hz

    Explanation:

    Givens

    L=95cm

    m_{sculpture} =13kg

    m_{wire}=5g

    The frequency is defined by

    f=\frac{v}{\lambda}

    Where v is the speed of the wave in the string and \lambda is its wave length.

    The wave length is defined as \lambda = 2L = 2(0.95m)=1.9m

    Now, to find the speed, we need the tension of the wire and its linear mass density

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

    Where \mu=\frac{0.005kg}{0.95m}= 5.26 \times 10^{-3} and the tension is defined as T=m_{sculpture} g=13kg(9.81 m/s^{2} )=127.53N

    Replacing this value, the speed is

    v=\sqrt{\frac{127.53N}{5.26 \times 10^{-3} } }=155.71 m/s

    Then, we replace the speed and the wave length in the first equation

    f=\frac{v}{\lambda}\\f=\frac{155.71 m/s}{1.9m}\\ f=81.96Hz

    Therefore, the frequency is f=81.96 \ Hz

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