Two strings (A, B) having linear densities μ_A=2 × 10^-4 kg / m and, μ_B=4 × 10^-4 kg / m and lengths L_A=2.5 m and L_B=1.5 m respectively are…

Two strings $\displaystyle (A, B)$ having linear densities $\displaystyle \mu_A=2 \times 10^{-4} \mathrm{~kg} / \mathrm{m}$ and, $\displaystyle \mu_B=4 \times 10^{-4} \mathrm{~kg} / \mathrm{m}$ and lengths $\displaystyle L_A=2.5 \mathrm{~m}$ and $\displaystyle L_B=1.5 \mathrm{~m}$ respectively are joined. Free ends of $\displaystyle A$ and $\displaystyle B$ are tied to two rigid supports $\displaystyle C$ and $\displaystyle D$, respectively creating a tension of $\displaystyle 500$ N in the wire. Two identical pulses, sent from $\displaystyle C$ and $\displaystyle D$ ends, take time $\displaystyle t_1$ and $\displaystyle t_2$, respectively, to reach the joint. The ratio $\displaystyle t_1 / t_2$ is :