So phase difference between then $\phi = \frac{{2\pi }}{\lambda } \times \frac{\lambda }{2} = \pi $
$(A)$ With a node at $O$, the minimum frequency of vibration of the composite string is $v_0$
$(B)$ With an antinode at $O$, the minimum frequency of vibration of the composite string is $2 v_0$
$(C)$ When the composite string vibrates at the minimum frequency with a node at $O$, it has $6$ nodes, including the end nodes
$(D)$ No vibrational mode with an antinode at $O$ is possible for the composite string
