Question

A uniform rope of length $L$ and mass $m_1$ hangs vertically from a rigid support. A block of mass $m_2$ is attached to the free end of the rope. $A$ transverse pulse of wavelength ${\lambda }_1$ is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is ${\lambda }_2.$
The ratio $\frac{{\lambda }_2}{{\lambda }_1}$ is:-

• A. $\sqrt{\frac{m_1}{m_2}}$
• B. $\sqrt{\frac{m_1+m_2}{m_2}}$
• C. $\sqrt{\frac{\overline{m_2}}{m_1}}$
• D. $\sqrt{\frac{m_1+m_2}{m_1}}$

Answer 1

Answer: (B)

$V=\sqrt{\frac{T}{\mu }}\Rightarrow V_1=\sqrt{\frac{m_{2}g}{\mu }}$
$\Rightarrow V_2=\sqrt{\frac{\left(m_1+m_2\right)g}{\mu }}$
$V=f\lambda$
$\lambda \propto V$
$\frac{{\lambda }_1}{{\lambda }_2}=\frac{V_1}{V_2}$
$\frac{{\lambda }_2}{{\lambda }_1}=\sqrt{\frac{m_1+m_2}{m_2}}$