With a node at $O$ , the minimum frequency of vibration of the composite string is $v_0$
With an antinode at $O$ , the minimum frequency of vibration of the composite string is $2 v_0$
When the composite string vibrates at the minimum frequency with a node at $O$ , it has 6 nodes, including the end nodes
No vibrational mode with an antinode at $O$ is possible for the composite string

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