Waves - Result Question 41

43. 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 $\lambda_2 / \lambda_1$ is

[2016]

(a) $\sqrt{\frac{m_1}{m_2}}$

(b) $\sqrt{\frac{m_1+m_2}{m_2}}$

(c) $\sqrt{\frac{m_2}{m_1}}$

(d) $\sqrt{\frac{m_1+m_2}{m_1}}$

Show Answer

Answer:

Correct Answer: 43. (b)

Solution:

  1. (b) From figure, tension $T_1=m_2 g$

$T_2=(m_1+m_2) g$

As we know

Rigid support

Velocity $\propto \sqrt{T}$

So, $\lambda \propto \sqrt{T}$

$\Rightarrow \frac{\lambda_1}{\lambda_2}=\frac{\sqrt{T_1}}{\sqrt{T_2}}$

$\Rightarrow \frac{\lambda_2}{\lambda_1}=\sqrt{\frac{m_1+m_2}{m_2}} \square m_2$