What happen to the frequency of transverse vibration of a stretched string if its tension is halved and the area of cross section of the str

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What happen to the frequency of transverse vibration of a stretched string if its tension is halved and the area of cross section of the string is doubled?

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Hải Đăng 5 years 2021-07-14T23:38:45+00:00 1 Answers 160 views 1

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  1. diemkieu
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    2021-07-14T23:39:48+00:00
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    Answer:

    The fundamental frequency of the stretched string is:

    f= \frac{1}{2} \sqrt{\frac{T}{L} } [ T = Tension and μ = mass per unit length]

    Here,

     μ = \frac{m}{L} = \frac{Vp}{L} = Ap

    f= \frac{1}{2} \sqrt{\frac{T}{Ap} }

    If T is halved and A is doubled,

    f= \frac{1}{2} \sqrt{\frac{T'}{A'p} } = \sqrt{\frac{1}{2* 2* A* p} } = \frac{1}{2} (\frac{1}{2} \sqrt{\frac{T}{Ap} } = \frac{1}{2} f

    Thus, the frequency is reduced to half if its tension is halved and the area of cross-section of the string is doubled.

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