Question

Two vibrating strings of the same material but lengths L and 2L have radii 2r and r respectively. They are stretched under the same tension. Both the strings vibrate in their fundamental modes, the one of length L with frequency $n_1$and the other with frequency $n_2$. The ratio $\frac{n_1}{n_2}$ is given by

• A. 2
• B. 4
• C. 8
• D. 1

Answer 1

The correct option is D 1

Fundamental frequency $n=\frac{1}{2l}\sqrt{\frac{T}{\pi r^2\rho }}$

where m = Mass per unit length of wire

$\Rightarrow n\propto =\frac{1}{lr}\Rightarrow \frac{n_1}{n_2}=\frac{r_2}{r_1}\times \frac{l_2}{l_1}=\frac{r}{2r}\times \frac{2L}{L}=\frac{1}{1}$