A uniform rope of length L and mass mi 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. \[\sqrt{\frac{{{m}_{1}}+{{m}_{2}}}{{{m}_{1}}}}\]