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. `1//4`
B. `1//3`
C. `1//2`
D. `2//3`

Answer

C

Explanation

`n_(1)=(p)/(2L)sqrt((T)/(rhopir^(2)))`, `n_(2)=(q)/(2L)sqrt((T)/(rhopi(2r)^(2)))`
`n_(1)=n_(2)implies(p)/(q)=(1)/(2)`