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  • A wire of density <img alt="12 \times 10^{-3} \mathrm{~kg} \mathrm{~cm}^{-3}" src="https://entrancecorner.oncodecogs.com/gif.latex?12%20%5Ctimes%2010%5E%7B-3%7D%20%5Cmathrm%7B%7Ekg%7D%20%5Cmathrm%7

A wire of density 12 \times 10^{-3} \mathrm{~kg} \mathrm{~cm}^{-3} is stretched between two clamp 4 \mathrm{~m} apart. The resulting strain in the wire is 6.4 \times 10^{-4} The lowest frequency of the transverse vibrations in the wire is (Young's modulus of wire y=9 \times 10^{10} \mathrm{~N} / \mathrm{mL} ) (to the nearest integer) 

Option: 1

500 Hz


Option: 2

600 Hz


Option: 3

650 Hz


Option: 4

550 Hz


Answers (1)

$$ \begin{aligned} & P=\frac{12 \times 10^{-3} \mathrm{~kg}}{10^{-6 \mathrm{~m}^{3}}}=12 \times 10^{3} \mathrm{~kg} / \mathrm{m} \\ & \frac{T}{A}=T E \\ & T=Y A E \\ & \text { a) } t=4 \mathrm{~m} E \\ & E=6.4 \times 10^{-4} \\ & f=\frac{V}{2 l}=\frac{1}{2 l} \sqrt{\frac{T}{M}} \\ & =\frac{1}{2 l} \sqrt{\frac{Y E A l}{m}} \\ & =\frac{1}{2 l} \sqrt{\frac{H E}{P}} \\ & =\frac{1}{2 \times 4} \sqrt{\frac{9 \times 10^{0} \times 6.4 \times 10^{-4}}{12 \times 10^{3}}} \\ & \frac{6}{8} \times 48 \times 10^{2} \\ & \text { = 600 Hz } \end{aligned}

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Kshitij

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