Question

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 $v_2$. Find $\frac{v_1}{v_2}$.

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

Answer 1

The correct option is A $\frac{1}{2}$

$T_{AB}=T_{TC}$

$T_{CD}=2T$

$T_{AB}$ is tension in the string AB

$T_{CD}$ is the tension in the string CD

$\Rightarrow$ The acceleration between tension and the wave speed is given by

$V=T_{u}V\alpha T$ where

V is the wave speed of the transverse wave u is the mass per unit length of the string.

$\frac{V_1}{V_2}=\frac{T}{2T}=\frac{1}{2}$

$\frac{V_1}{V_2}=\frac{1}{2}$