Bmx asked in Science & MathematicsPhysics · 2 months ago

A cord carries a wave of average power 20 mW and period 40 ms. ?

A cord carries a wave of average power 20 mW and period 40 ms. The cord has mass density

3 g/m and is tensioned to 15 N. What is the amplitude of the wave?

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  • NCS
    Lv 7
    2 months ago
    Favourite answer

    P = ½µω²A²v

    P = 20E-3 W

    µ = 3E-3 kg/m

    ω = 2π / period = 2π / 4E-2s = 157 rad/s

    v = √(T/ρ) = √(15N / 0.003kg/m) = 70.7 m/s

    Dropping units for ease (A is in meters)

    20E-3 = ½ * 0.003 * 157² * A² * 70.7

    A² = 7.6e-6 m²

    A = 0.0027 m = 2.7 mm

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  • 2 months ago

    BY v = √[T/µ]

    =>v = √[15/(3 x 10^-3)]

    =>v = √[5 x 10^-3]

    =>v = 7.07 x 10^-2 m/s

    As ω = 2π/T = (2 x 3.14)/(40 x 10^-3)

    =>ω = 157 rad/sec

    Now BY E = 1/2µω^2 A^2v

    =>20 x 10^-3 = 1/2 x 3 x 10^-3 x (157)^2 x A^2 x 7.07 x 10^-2

    =>A = √[7.65 x 10^-3]

    =>A = 8.75 x 10^-2 m OR 8.75 cm

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