Q102 / 160 · JIPMER 2010 · Physics
Two vibrating strings of the same material but lengths $L$ and $2 L$ have radii $2 r$ 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 $v_1$ and the other with frequency $v_2$. The ratio $v_1 / v_2$ is
- A2
- B4
- C8
- Correct answerD1
Solution
Fundamental frequency,
$\begin{array}{ll}
& v=\frac{1}{2 l} \sqrt{\frac{T}{m}}=\frac{1}{2 l} \sqrt{\frac{T}{\pi r^2 \rho}} \\
\text { or } & v \propto \frac{1}{l r} \\
\therefore & \frac{v_1}{v_2}=\frac{l_2 r_2}{l_1 r_1}=\frac{2 L \times r}{L \times 2 r}=1
\end{array}$
Hence, the correct answer is option: 'D'.