Question

A copper wire is held at the two ends between two rigid supports. At ${30}^{o}C$, the wire is just taut,with negligible tension. If $Y=13\times {10}^{11}N{m}^{-2},\alpha =1.7\times {10}^{-5}{(}^{\circ }C{)}^{-1}$ and density $\rho =9\times {10}^{3}kg{m}^{-3}$, then the speed of transverse wave in this wire at ${10}^o$C is:

• A. $90m{s}^{-1}$
• B. $70m{s}^{-1}$
• C. $60m{s}^{-1}$
• D. $100m{s}^{-1}$

Answer 1

The correct option is B $70m{s}^{-1}$

$V=\sqrt{\frac{T}{m}}=\sqrt{\frac{Y\alpha \Delta t}{\rho }}$

where Thermal force $=$ Tension in wire $=T=YA\alpha \Delta t$

and linear density $=m=A\rho$

So, now putting in the derived expression,

$V=\sqrt{\frac{13\times {10}^{11}\times 1.7\times {10}^{-5}\times 10}{9\times {10}^3}}=70m/s$