In the diagram shown below, both the strings $A B$ and $C D$ are made of same material and have same cross-section. The pulleys are light and fictionless. If the speed of wave in string $A B$ is $v_1$ and in $C D$ is $v_2$, then $\frac{v_1}{v_2}$ is

• A

  1
• B

  $\sqrt{2}$
• C

  2
• Correct answer
  D

  $1 / \sqrt{2}$

Solution

Let the speed of wave in string be $v$ and tension in string be $T$. $$ \begin{gathered} v \propto \sqrt{T} \\ \frac{v_{A B}}{v_{C D}}=\sqrt{\frac{T}{2 T}}=\frac{1}{\sqrt{2}} \end{gathered} $$

Hence, the correct answer is option: 'D'.