Question

In brass, the velocity of longitudinal wave is 100 times the velocity of the transverse wave. If $Y=1 \times 10^{11}\, N / m ^{2}$, then stress in the wire is

• A. $1 \times 10^{13} \,N / m ^{2}$
• B. $1 \times 10^{9}\, N / m ^{2}$
• C. $1 \times 10^{11} \,N / m ^{2}$
• D. $1 \times 10^{7} \,N / m ^{2}$

Answer 1

Answer: (D)

As $v_{L}=\sqrt{\frac{Y}{\rho}}$ and $v_{T}=\sqrt{\frac{T}{\mu}}=\sqrt{\frac{T}{\pi r^{2} \rho}}$
$\therefore \,\,\,\frac{v_{L}}{v_{T}}=\sqrt{\frac{Y}{\rho} \times \frac{\pi r^{2} \rho}{T}}=\sqrt{\frac{Y}{T / \pi r^{2}}}=\sqrt{\frac{Y}{\text { stress }}}$
$\therefore \,\,\,$ Stress $=\frac{Y}{\left(v_{L} / v_{T}\right)^{2}}=\frac{1 \times 10^{11}}{(100)^{2}}=1 \times 10^{7} \,N / m ^{2}$