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A wire of linear density is 8×10^_3 kg/m and length 2m is stretched by a weight of 20kg the fundamental frequency of vibration of the wire is wire is answe​

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Answered by nirman95
22

Given:

A wire of linear density is 8×10^_3 kg/m and length 2m is stretched by a weight of 20kg.

To find:

Value of fundamental frequency?

Calculation:

  • First see the diagram !

 \sf \dfrac{ \lambda}{2}  = l

 \sf  \implies\lambda  = 2l

Now, fundamental frequency is :

 \sf \: f =  \dfrac{v}{ \lambda}

 \sf  \implies\: f =  \dfrac{ \sqrt{ \dfrac{T}{ \mu} } }{ \lambda}

  • 'T' is tension and '\mu' is linear mass density.

 \sf  \implies\: f =  \dfrac{ \sqrt{ \dfrac{mg}{ \mu} } }{ \lambda}

 \sf  \implies\: f =  \dfrac{ \sqrt{ \dfrac{20 \times 10}{8 \times  {10}^{ - 3} } } }{2l}

 \sf  \implies\: f =  \dfrac{ \sqrt{ \dfrac{20 \times 10}{8 \times  {10}^{ - 3} } } }{2 \times 2}

 \sf  \implies\: f =  \dfrac{1.58 \times  {10}^{2}  }{2 \times 2}

 \sf  \implies\: f =  39.5 \: hz

So, fundamental frequency is 39.5 Hz

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