Two wires W_1 and W_2 have the same radius r and respective densities ρ_1 and ρ_2 such that ρ_2=4 ρ_1. They are joined together at the point O, as…

Two wires $\displaystyle \mathrm{W}_1$ and $\displaystyle \mathrm{W}_2$ have the same radius r and respective densities $\displaystyle \rho_1$ and $\displaystyle \rho_2$ such that $\displaystyle \rho_2=4 \rho_1$. They are joined together at the point O, as shown in the figure. The combination is used as a sonometer wire and kept under tension T. The point O is midway between the two bridges. When a stationary wave is set up in the composite wire, the joint is found to be a node. The ratio of the number of antinodes formed in $\displaystyle \mathrm{W}_1$ to $\displaystyle \mathrm{W}_2$ is :