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 \(λ_1\) is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is \(λ_2\).The ratio \(\displaystyle \frac{λ_1}{λ_2}\) is