MCQ
Two uniform strings of mass per unit length $\mu$ and $4 \mu$, and length $L$ and $2 L$, 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 $v_0=\frac{1}{2 L} \sqrt{\frac{T}{\mu}}$, 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 $v_0$
$(B)$ 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
- ✓$A,C,D$
- B$A,C$
- C$A,B,C$
- D$A,B,D$
