Q. In brass, the velocity of longitudinal wave is 100 times the velocity of the transverse wave. If $Y = 1 \times 10^{11}\ NM^{- 2}$, then stress in the wire is
A) $1 \times 10^{13}\ Nm^{- 2}$
B) $1 \times 10^{9}\ Nm^{- 2}$
C) $1 \times 10^{11}\ Nm^{- 2}$
D) $1 \times 10^{7}\ Nm^{- 2}$
Explanation
(d) $v_{L} = \sqrt{\frac{Y}{\rho}},\ v_{T} = \sqrt{\frac{T}{m}} = \sqrt{\frac{T}{\pi r^{2}\rho}}$
$\frac{v_{L}}{V_{T}} = \sqrt{\frac{Y}{\rho} \times \frac{\pi r^{2}\rho}{T}} = \sqrt{\frac{Y}{T/\pi r^{2}}} = \sqrt{\frac{Y}{stress}}$
$\therefore stress = \frac{Y}{\left( v_{L}/v_{r} \right)^{2}} = \frac{1 \times 10^{11}}{(100)^{2}} = 10^{7}Nm^{- 2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.