Question 60 of 142

Two wires ${W}_{1}$ and ${W}_{2}$ have the same radius $r$and respective, densities ${\rho }_{1}$ and ${\rho }_{2}$, such that ${\rho }_{2}=4{\rho }_{1}$ . 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 ${W}_{1}$ to ${W}_{2}$ is