Two uniform strings of mass per unit length $$\mu$$ and $$4\mu$$, and length $$L$$ and $$2L$$, respectively, are joined at point $$O$$, and tied at two fixed ends $$P$$ and $$Q$$, as shown in the figure. The strings are under a uniform tension $$T$$. If we define the frequency $$\nu_0 = \frac{1}{2L}\sqrt{\frac{T}{\mu}}$$, which of the following statement(s) is(are) correct?

A

With a node at $$O$$, the minimum frequency of vibration of the composite string is $$\nu_0$$

B

With an antinode at $$O$$, the minimum frequency of vibration of the composite string is $$2\nu_0$$

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