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) $\sqrt{\frac{m_1+m_2}{m_1}}$
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Answer:
Correct Answer: 43. (b)
Solution:
- (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, $\lambda \propto \sqrt{T}$
$\Rightarrow \frac{\lambda_1}{\lambda_2}=\frac{\sqrt{T_1}}{\sqrt{T_2}}$
$\Rightarrow \frac{\lambda_2}{\lambda_1}=\sqrt{\frac{m_1+m_2}{m_2}} \square m_2$
