Question

A copper wire is held at the two ends by rigid support. At ${30}^{\circ }C$ the wire is just taut with negligible tension. The speed of transverse waves in this wire at ${10}^{\circ }C$ is
($\alpha =1.7\times {10}^{-5}{/}^{\circ }C,Y=1.3\times {10}^{11}N/m^2,d=9\times {10}^{3}kg/m^3$)

• A. $80m/\sec$
• B. $90m/\sec$
• C. $100m/\sec$
• D. $70m/\sec$

Answer 1

The correct option is D $70m/\sec$

Using the formula of the coefficient of linear expansion of wire,

$\Delta l=l\alpha \Delta \theta \rho =9\times {10}^{3}kg/m^{3}F=YA\alpha \Delta \theta$

Speed of transverse wave is given by

$V=\sqrt{\frac{f}{\mu }}(\mu =\frac{\rho V}{l}=\frac{Al\rho }{l}=A\rho )V=\sqrt{\frac{YA\alpha \Delta \theta }{A\rho }}V=\sqrt{\frac{1.3\times {10}^{11}\times 1.7\times {10}^{-5}\times ({30}^o-{10}^o)}{9\times {10}^3}}V=\sqrt{\frac{44.2\times {10}^6}{9\times {10}^3}}V=\sqrt{4.9\times {10}^3}V=\sqrt{49\times {10}^2}[V=70m/sec]$

Hence option (D) is correct