Two uniform strings A and B made of steel are made to vibrate under the same tension. If the first overtone of A is equal to the second overtone of B and if the radius of A is twice that of B, the ratio of the lengths of the strings is :-

Options

A. `1:2`
B. `1:3`
C. `1:4`
D. `1:6`

Answer

B

Explanation

Given `n_(2)=n_(3)`
`implies (2)/(2l_(A))sqrt((T)/(pir_(A)^(2)rho))=(3)/(2l_(B))sqrt((T)/(pir_(B)^(2)rho))`
`implies (l_(A))/(l_(B))=(2r_(B))/(3r_(A))implies (l_(A))/(l_(B))=(2)/(3)xx(r_(B))/(2r_(B))=(1)/(3)`.