Two uniform strings of mass per unit length μ and 4μ, and length L and 2 L …

Physics · JEE Advanced · NTA Exams — Oscillations and Waves

Two uniform strings of mass per unit length μ and 4μ, 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 \(v_{0}=\frac{1}{2 L} \sqrt{\frac{T}{\mu}},\) , which of the following statement(s) is(are) correct?

1. With a node at O, the minimum frequency of vibration of the composite string is v₀.
2. With an antinode at O, the minimum frequency of vibration of the composite string is 2v₀.
3. When the composite string vibrates at the minimum frequency with a node at O, it has 6 nodes, including the end nodes.
4. No vibrational mode with an antinode at O is possible for the composite string.