Two wires of radii `r` and `2 r` are welded together end to end . The combination is used as a sonometer wire and is kept under a tension `T`. The welded point lies midway between the bridges. The ratio of the number of loops formed in the wires , such that the joint is a node when the stationary waves are set up in the wire is

Options

A. `2:1`
B. `1:2`
C. `1:sqrt2`
D. `sqrt2:1`

Answer

B

Explanation

For stationary waves `n_1=n_2`
`(P_1)/(2L) sqrt(T/(m_1)= P/2sqrt(T/m_2) therefore (P_1)/(sqrt(m_1)) = (P_2)/(sqrt(m_2))`
`P_1/P_2 = sqrt(m_1/m_2) = sqrt((rhov_1)/(rhov_2)) = sqrt(r_1^2/r_2^2) = r_1/r_2 = ( r)/(2r) = 1/2`