Physics - Wave on String Question with Solution | TestHub

In a sonometer experiment, the string is fixed at both ends.

For the second overtone, the string vibrates in the third harmonic, which means it forms $3$ loops.

The length of each loop is $\frac{L}{3}$.

Nodes are formed at the ends of each loop, i.e., at $x=0,\frac{L}{3},\frac{2L}{3},L$.

The amplitude of vibration is maximum at the antinodes, which are located exactly midway between the consecutive nodes.

The positions of the antinodes are:
$x_1=\frac{0+\frac{L}{3}}{2}=\frac{L}{6}$

$x_2=\frac{\frac{L}{3}+\frac{2L}{3}}{2}=\frac{L}{2}$

$x_3=\frac{\frac{2L}{3}+L}{2}=\frac{5L}{6}$

Thus, the amplitude is maximum at lengths $\frac{L}{6},\frac{L}{2},\frac{5L}{6}$.

Answer: $\frac{L}{6},\frac{L}{2},\frac{5L}{6}$