Two string A and b of lengths, $L_a=80\;cm$ and $L_B=x\;cm$ respectively are used separately in a sonometer. The ratio of their densities $(d_A/d_B)$ is $0.81$ The diameter of B is one -half that of A. If the string have the same tension and fundamental frequency the value of x is :

Question

$$\begin {array} {1 1} (a)\;33 & \quad (b)\;102 \\ (c)\;144 & \quad (d)\;130 \end {array}$$