Question

When the string of a sonometer of length $L$ between the bridges vibrates in the second overtone, the amplitude of vibration is maximum at

• A. $\left(\frac{L}{2}\right)$
• B. $\left(\frac{L}{4}\right)$ and $\left(\frac{3L}{4}\right)$
• C. $\frac{L}{6},\frac{L}{2}$ and $\frac{5L}{6}$
• D. $\frac{L}{8},\frac{3L}{8},\frac{5L}{8}$

Answer 1

The correct option is C $\frac{L}{6},\frac{L}{2}$ and $\frac{5L}{6}$

When string is vibrating in second overtone, there are 3 loops formed as shown.

Let length of string $=L$, there are total of 3 antinodes
$\Rightarrow \frac{3\lambda }{2}=L$
$\Rightarrow \lambda =\frac{2L}{3}$
Antinodes will be formed at,
$\frac{\lambda }{4},\frac{3\lambda }{4},\frac{5\lambda }{4}$
Position of antinodes in terms of string length are $\frac{L}{6},\frac{3L}{6}$ and $\frac{5L}{6}$