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 wave length of the pulse when it reaches the top of the rope is $\lambda _2$. The ratio $\lambda _2\,/\,\lambda _1$ is
NEET 2016, Medium
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Wavelength of pulse at the lower end,
$\lambda_{1} \propto$ velocity $\left(v_{1}\right)=\sqrt{\frac{T_{1}}{\mu}}$
Similarly, $\lambda_{2} \propto v_{2}=\sqrt{\frac{T_{2}}{\mu}}$
$\therefore \quad \frac{\lambda_{2}}{\lambda_{1}}=\sqrt{\frac{T_{2}}{T_{1}}}=\sqrt{\frac{\left(m_{1}+m_{2}\right) g}{m_{2} g}}$
$=\sqrt{\frac{m_{1}+m_{2}}{m_{2}}}$
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