Question

A uniform thin rope of length $12\text{m}$ and mass $6\text{kg}$ hangs vertically from a rigid support and a block of mass $2\text{kg}$ is attached to its free end. A transverse short wave-train of wavelength $6\text{cm}$ is produced at the lower end of the rope. What is the wavelength of the wave train (in$\text{cm}$) when it reaches the top of the rope?

• A. $3$
• B. $6$
• C. $12$
• D. $9$

Answer 1

The correct option is C $12$



As we know, $v=f\lambda$ and $v=\sqrt{\frac{T}{\mu }}$

$\Rightarrow v\propto \lambda \propto \sqrt{T}$

$\Rightarrow \frac{{\lambda }_1}{{\lambda }_2}=\frac{\sqrt{T_1}}{\sqrt{T_2}}$

Here, $T_1=2g;T_2=8g$

$\Rightarrow {\lambda }_2={\lambda }_1\frac{\sqrt{T_2}}{\sqrt{T_1}}=6\times \frac{\sqrt{8g}}{\sqrt{2g}}=12\text{cm}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(C\right)$ is the correct answer.