Question

Both the strings, shown in figure, are made of same material and have same cross-section. The pulleys are light. The wave speed of a transverse wave in the string AB is $V_1$ and in CD it is $V_2$. Then $\frac{V_1}{V_2}$ is

• A. 1
• B. 2
• C. $\sqrt{2}$
• D. $\frac{1}{\sqrt{2}}$

Answer 1

The correct option is D

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

Applying Newton's laws of motion,
Tension in string AB = T

Tension in string CD = 2T

speed of transverse wave on string, $v\propto \sqrt{T}$

V $\propto$ $\sqrt{T}\Rightarrow \frac{v_1}{v_2}$ = $\sqrt{\frac{T}{2T}}$ = $\frac{1}{\sqrt{2}}$