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22 April, 03:24

The linear density of a string is 1.9 * 10-4 kg/m. A transverse wave on the string is described by the equation y = (0.034 m) sin[ (2.8 m-1) x + (38 s-1) t] What are (a) the wave speed and (b) the tension in the string?

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  1. 22 April, 05:12
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    a. v = 13.572 m / s

    b. T = 2.578 x 10 ⁻³ N

    Explanation:

    μ = 1.9 x 10 ⁻⁴ kg / m

    y = y ₙ * sin (kx + wt)

    a.

    y = 0.034 m * sin (2.8 m⁻¹) x + (38 s⁻¹) t

    R = 2.8 m⁻¹

    W = 38 s⁻¹

    To determine speed of the string

    v = W / R = 38 / 2.8

    v = 13.572 m / s

    b.

    v = √ T / μ

    v ² = T / μ

    To determine the tension on the string

    T = v ² * μ

    T = 13.572 m/s * 1.9 x 10 ⁻⁴ kg / m

    T = 2.578 x 10 ⁻³ N
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