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  • A wire of length  having tension <img alt="\mathrm{T}" src="https://entrancecorner.oncodecog

A wire of length \mathrm{l} having tension \mathrm{T} and radius \mathrm{r} vibrates with natural frequency \mathrm{f}. Another wire of same metal with length 21 having tension \mathrm{2T} and radius \mathrm{2r} will vibrate with natural frequency -
 

Option: 1

\mathrm{f}
 


Option: 2

\mathrm{2 f}
 


Option: 3

\mathrm{2 \sqrt{2} f}
 


Option: 4

\mathrm{\frac{f}{2 \sqrt{2}}}


Answers (1)

best_answer

\mathrm{ f=\frac{v}{2 l}=\frac{\sqrt{T / v}}{2 l}=\frac{\sqrt{T / \rho S}}{2 l} }

\mathrm{ f=\frac{\sqrt{T / \pi r^2 \rho}}{2 l} }

\mathrm{ f \propto \frac{\sqrt{T}}{r l}}

Now, tension, length and radius all are doubled, Hence \mathrm{ f^{\prime}=\frac{f}{2 \sqrt{2}}}

Hence option 4 is correct.

Posted by

Ritika Jonwal

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