• # question_answer A uniform rope of length L and mass m1 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 : A)  $\sqrt{\frac{{{m}_{1}}}{{{m}_{2}}}}$                    B)  $\sqrt{\frac{{{m}_{1}}+{{m}_{2}}}{{{m}_{2}}}}$ C)   $\sqrt{\frac{{{m}_{2}}}{{{m}_{1}}}}$                   D)   $\sqrt{\frac{{{m}_{1}}+{{m}_{2}}}{{{m}_{1}}}}$

${{T}_{1}}={{m}_{2}}g$                 ${{T}_{2}}=({{m}_{1}}+{{m}_{2}})g$                 $Velocity\propto \sqrt{T}$                 $\lambda \propto \sqrt{T}$                 $\frac{{{\lambda }_{1}}}{{{\lambda }_{2}}}=\frac{\sqrt{{{T}_{1}}}}{\sqrt{{{T}_{2}}}}$                 $\Rightarrow$ $\frac{{{\lambda }_{2}}}{{{\lambda }_{1}}}=\sqrt{\frac{{{m}_{1}}+{{m}_{2}}}{{{m}_{2}}}}$