A string is vibrating in its fifth overtone between two rigid supports \(2.4 \mathrm{~m}\) apart. The distance between successive node and antinode is

The correct option is (B).
If the string is clamped between two supports separated by L.
For the fundamental overtone separation between successive nodes is \(\mathrm{L}\).
For the first overtone separation between successive nodes is \(\frac{L}{2}\).
For the second overtone the separation between successive nodes will be \(\frac{L}{3}\).
So, for nth overtone the separation between successive nodes will be \(\frac{\mathrm{L}}{(\mathrm{n}+1)}\).
Therefore, for the fifth over separation between successive nodes will be \(\frac{\mathrm{L}}{6}\).
In the separation between successive node and antinode is half of the separation between two successive nodes.
So, \(\frac{\mathrm{L}}{12}=\frac{2.4 \mathrm{~m}}{12}=0.2 \mathrm{~m}\)