A string is vibrating in its fifth overtone between two rigid supports $2.4 \mathrm{~m}$ apart. The distance…
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
$0.8 \mathrm{~m}$
$0.2 \mathrm{~m}$
$0.1 \mathrm{~m}$
$0.6 \mathrm{~m}$
Solution
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, $\frac{\mathrm{L}}{12}=\frac{2.4 \mathrm{~m}}{12}=0.2 \mathrm{~m}$