A small town has decided to forego the use of electrical power and send energy through town via mechanical waves on ropes. They use rope wit

Question

A small town has decided to forego the use of electrical power and send energy through town via mechanical waves on ropes. They use rope with a mass per length of 1.50 kg/m under 6000 N tension. If they are limited to a wave amplitude of 0.500 m, what must be the frequency of waves necessary to transmit power at the average rate of 2.00 kW

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Orla Orla 2 weeks 2021-09-05T08:41:29+00:00 1 Answers 0 views 0

Answers ( )

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    2021-09-05T08:43:11+00:00

    Answer:

    the required frequency of waves is 2.066 Hz

    Explanation:

    Given the data in the question;

    μ = 1.50 kg/m

    T = 6000 N

    Amplitude A = 0.500 m

    P = 2.00 kW = 2000 W

    we know that, the average power transmit through the rope can be expressed as;

    p = \frac{1}{2}vμω²A²

    p = \frac{1}{2}√(T/μ)μω²A²

    so we solve for ω

    ω² = 2P / √(T/μ)μA²

    we substitute

    ω² = 2(2000) / √(6000/1.5)(1.5)(0.500)²

    ω² = 4000 / 23.71708

    ω² = 168.65

    (2πf)² = ω²

    so

    (2πf)² = 168.65

    4π²f² = 168.65

    f² = 168.65 / 4π²

    f² = 4.27195

    f = √4.27195

    f = 2.066 Hz

    Therefore, the required frequency of waves is 2.066 Hz

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