Question

The speed of a transverse wave passing through a string of length $50\, cm$ and mass $10 \,g$ is $60\, ms ^{-1}$. The area of cross-section of the wire is $2.0 \,mm ^2$ and its Young's modulus is $1.2 \times 10^{11} \,Nm ^{-2}$. The extension of the wire over its natural length due to its tension will be $x \times 10^{-5} \,m$. The value of $x$ is

Answer 1

$ V _{ w }=\sqrt{\frac{ T }{\mu}} $
$ 60=\sqrt{\frac{ T }{10 \times 10^{-3}} \times 0.5} $
$T =\frac{(60)^2 \times 10^{-2}}{0.5}=72 N $
$ \Delta \ell=\frac{ F \ell}{ AY }=\frac{72 \times 0.5}{2 \times 10^{-6} \times 1.2 \times 10^{11}} $
$ =\frac{72 \times 5}{24} \times 10^{-5}=15 \times 10^{-5}$