Question

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. $1\mspace{6mu}:\mspace{6mu} 3\sqrt{2}$
• B. $1\mspace{6mu}:\mspace{6mu} 2\sqrt{2}$
• C. $1\mspace{6mu}:\mspace{6mu} 2$
• D. $\sqrt{2}\mspace{6mu}:\mspace{6mu} 1$

Answer 1

Answer: (B)

$1\mspace{6mu}:\mspace{6mu} 2\sqrt{2}$

Answer 2

$v = \sqrt{\frac{T}{m}} = \sqrt{\frac{T}{\pi r^{2}\rho}}$

$v \propto \frac{\sqrt{T}}{r} \Rightarrow \frac{v_{A}}{v_{B}} = \sqrt{\frac{T_{A}}{T_{B}}}.\frac{r_{B}}{r_{A}} = \sqrt{\frac{1}{2}}.\frac{1}{2} = \frac{1}{2\sqrt{2}}$