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

Answer 1

Answer: (B)

$1:2\sqrt{2}$

The velocity of the wave in a string is given as:

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

$v\propto \frac{\sqrt{T}}{r}$

$\Rightarrow \frac{v_A}{v_B}=\sqrt{\frac{T_A}{T_B}}\cdot \frac{r_B}{r_A}$

$=\sqrt{\frac{1}{2}}\cdot \frac{1}{2}=\frac{1}{2\sqrt{2}}$