Question

Two wires are kept tight between the same pair of supports. The tensions in the wires are in the ratio $2:1$. The radii are in the ratio $3:1$ and the densities are in the ratio $1:2$. The ratio of their fundamental frequencies are

• A. $1:2$
• B. $2:3$
• C. $3:4$
• D. $4:9$

Answer 1

Answer: (B)

$2:3$

$\frac{f_1}{f_2}=\frac{\frac{1}{2l}\sqrt{\frac{T_1}{{\mu }_1}}}{\frac{1}{2l}\sqrt{\frac{T_2}{{\mu }_2}}}=\sqrt{\frac{T_1{\rho }_2{A}_2}{T_2{\rho }_1{A}_1}}=\sqrt{\frac{T_1{\rho }_2\pi r_2^2}{T_2{\rho }_1\pi r_1^2}}=\frac{2}{3}$