Two wires `W_(1) "and"W_(2)` have the same radius r and respective densities `p_(1) "and" p_(2)` such that `p_(2) = 4p_(1).` They are joined together at the point O, as shown in the figure. The combination is used as a sonometer wire and kept udner tension T. The point O is midway between the two bridges. When a stationary waves 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-

Options

A. `4 : 1`
B. `1 : 2`
C. `1 : 1`
D. `1 : 3`

Answer

B

Explanation

`f_(1) = f_(2)`
`f = (P)/(2l) sqrt((T)/(pi r^(2) rho))`
`f_(1) = f_(2)`
`(P_(1))/(sqrt(rho_(1))) = (P_(2))/(sqrt(rho_(2)))`
`(P_(1))/(P_(2)) = (1)/(2)`