a
Wavelength of pulse at the lower end,

\(\lambda_{1} \propto\) velocity \(\left(v_{1}\right)=\sqrt{\frac{T_{1}}{\mu}}\)

Similarly, \(\lambda_{2} \propto v_{2}=\sqrt{\frac{T_{2}}{\mu}}\)

\(\therefore \quad \frac{\lambda_{2}}{\lambda_{1}}=\sqrt{\frac{T_{2}}{T_{1}}}=\sqrt{\frac{\left(m_{1}+m_{2}\right) g}{m_{2} g}}\)

\(=\sqrt{\frac{m_{1}+m_{2}}{m_{2}}}\)