A uniform rope of length L and mass m₁ hangs vertically from a rigid support.  A block of mass m₂ is attached to the free end of the rope.  A transverse pulse of wavelength ${\mathrm{\lambda }}_1$ is produced at the lower end of the rope.  The wavelength of the pulses when it reaches the top of the rope is ${\mathrm{\lambda }}_2$.  The ratio ${\mathrm{\lambda }}_2/{\mathrm{\lambda }}_1$ is ;