Question

Two wires of the same material and having the same radius have their fundamental frequencies in the ratio 1:2 and under tension in the ratio 1:8, Compare ratio of their lengths.

Answer 1

$\frac{n_1}{n_2}=\frac{1}{2}$ $\frac{T_1}{T_2}=\frac{1}{8}$

$n=\frac{1}{2l}\sqrt{\frac{T}{2\mu }}$

$\frac{l_1}{l_2}=\frac{\sqrt{T_1}}{n_1}\times \frac{n_2}{\sqrt{T_2}}=\sqrt{\frac{1}{8}}\times 2$

$\frac{l_1}{l_2}=0.707:1$