Physics - Wave on String Question with Solution | TestHub

A sonometer wire is fixed at both ends.

In the fundamental mode, the wire vibrates in $1$ loop, forming $2$ nodes and $1$ antinode.

In general, for the $p$-th overtone, the wire vibrates in $p+1$ loops.

For the third overtone, $p=3$.

Number of loops $=3+1=4$.

Each loop corresponds to one antinode, so there are $4$ antinodes.

The number of nodes is always one more than the number of loops for a string fixed at both ends.

Number of nodes $=4+1=5$.

Thus, there are $5$ nodes and $4$ antinodes.

Answer: 5 nodes and 4 antinodes.