Travelling wave

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Question

A speed of transverse wave on a straight wire (mass 6.0 g, length 60 cm) and area of cross-section of wire $1.0 m m^{2}$ is $90 m / \sec$ . If the young’s modulus of wire is $16 \times 10^{11} N / m^{2}$ . The extension of wire over a natural length is ______mm

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Solution

Speed of sound in string
$V = \sqrt{\frac{T}{μ}} \Rightarrow 90 = \sqrt{\frac{\frac{Y A Δ l}{l}}{\frac{m}{l}}} = \sqrt{\frac{16 \times 10^{11} \times 10^{- 6} \times Δ l}{6 \times 10^{- 3}}} \Rightarrow Δ l = 0.03 m m .$

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