A sinusoidal wave of angular frequency 1,203 rad/s and amplitude 3.1 mm is sent along a cord with linear density 3.9 g/m and tension 1,871 N

Question

A sinusoidal wave of angular frequency 1,203 rad/s and amplitude 3.1 mm is sent along a cord with linear density 3.9 g/m and tension 1,871 N. What is the average rate at which energy is transported by the wave to the opposite end of the cord? Give SI unit.

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Verity 4 years 2021-07-28T21:25:08+00:00 1 Answers 12 views 0

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  1. Neala
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    2021-07-28T21:27:06+00:00
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    Answer:

    18.7842493212 W

    Explanation:

    T = Tension = 1871 N

    \mu = Linear density = 3.9 g/m

    y = Amplitude = 3.1 mm

    \omega = Angular frequency = 1203 rad/s

    Average rate of energy transfer is given by

    P=\dfrac{1}{2}\sqrt{T\mu}\omega^2y^2\\\Rightarrow P=\dfrac{1}{2}\sqrt{1871\times 3.9\times 10^{-3}}\times 1203^2\times (3.1\times 10^{-3})^2\\\Rightarrow P=18.7842493212\ W

    The average rate at which energy is transported by the wave to the opposite end of the cord is 18.7842493212 W

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