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15 October, 07:33

A steel cable has a cross-sectional area 4.49 * 10^-3 m^2 and is kept under a tension of 2.96 * 10^4 N. The density of steel is 7860 kg/m^3. Note that this value is not the linear density of the cable. At what speed does a transverse wave move along the cable?

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  1. 15 October, 07:59
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    The transverse wave will travel with a speed of 25.5 m/s along the cable.

    Explanation:

    let T = 2.96*10^4 N be the tension in in the steel cable, ρ = 7860 kg/m^3 is the density of the steel and A = 4.49*10^-3 m^2 be the cross-sectional area of the cable.

    then, if V is the volume of the cable:

    ρ = m/V

    m = ρ*V

    but V = A*L, where L is the length of the cable.

    m = ρ * (A*L)

    m/L = ρ*A

    then the speed of the wave in the cable is given by:

    v = √ (T*L/m)

    = √ (T/A*ρ)

    = √[2.96*10^4 / (4.49*10^-3*7860) ]

    = 25.5 m/s

    Therefore, the transverse wave will travel with a speed of 25.5 m/s along the cable.
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