Two uniform stretched string A and B, made of steel , are vibrating 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 :

Question

$$\begin {array} {1 1} (a)\;2:3 & \quad (b)\;1:2 \\ (c)\;1:3 & \quad (d)\;1:4 \end {array}$$