3. The velocity of waves on a rope under a tension of 40 N is 10 m/s. If the tension is reduced to 10 N, what will be the new speed of

Question

3. The velocity of waves on a rope under a tension of 40 N is 10 m/s. If the tension is reduced
to 10 N, what will be the new speed of the wave?
HAI

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RuslanHeatt 3 years 2021-08-01T02:35:17+00:00 1 Answers 9 views 0

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  1. Verity
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    2021-08-01T02:36:21+00:00
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    Answer:

    5 m/s

    Explanation:

    The speed of a wave in a string is related to the tension in the string by the equation

    v=\sqrt{\frac{T}{\mu}}

    where

    v is the speed of the wave

    T is the tension in the string

    \mu is the linear density of the string

    We can rewrite the equation as

    \frac{\sqrt{T}}{v}=\sqrt{\mu}

    In this problem, the tension in the string is changed; however, its linear mass density remains constant. So we can write:

    \frac{\sqrt{T_1}}{v_1}=\frac{\sqrt{T_2}}{v_2}

    where:

    T1 = 40 N is the initial tension in the string

    v1 = 10 m/s is the initial speed of the wave

    T2 = 10 N is the final tension in the string

    Solving for v2, we find the final speed of the wave:

    v_2=v_1 \sqrt{\frac{T_2}{T_1}}=(10)\sqrt{\frac{10}{40}}=5 m/s

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