Q. Transverse waves of same frequency are generated in two steel wires $A$ and $B.$ The diameter of $A$ is twice of $B$ and the tension in $A$ is half that in $B.$ The ratio of velocities of wave in $A$ and $B$ is
A) $1\ :3\sqrt{2}$
B) $1\ :2\sqrt{2}$
C) $1\ :2$
D) $\sqrt{2}\ :1$
Explanation
(b) $v = \sqrt{\frac{T}{m}} = \sqrt{\frac{T}{\pi r^{2}\rho}}$
$v \propto \frac{\sqrt{T}}{r} \Rightarrow \frac{v_{A}}{v_{B}} = \sqrt{\frac{T_{A}}{T_{B}}}.\frac{r_{B}}{r_{A}} = \sqrt{\frac{1}{2}.}\frac{1}{2} = \frac{1}{2\sqrt{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.