Consider a system of three connected strings, S 1 , S 2 and S 3 with uniform linear mass…

Physics · JEE Advanced · NTA Exams — Oscillations and Waves

Consider a system of three connected strings, S₁, S₂ and S₃ with uniform linear mass densities μ kg/m, 4μ kg/m and 16μ kg/m, respectively, as shown in the figure. S₁ and S₂ are connected at the point P, whereas S₂ and S₃ are connected at the point Q, and the other end of S₃ is connected to a wall. A wave generator O is connected to the free end of S₁. The wave from the generator is represented by y = y₀ cos(ωt − kx) cm, where y₀, ω and k are constants of appropriate dimensions. Which of the following statements is/are correct?

1. When the wave reflects from P for the first time, the reflected wave is represented by
   y = a₁y₀ cos(wt + kx + p) cm, where a₁ is a positive constant.
2. When the wave transmits through P for the first time, the transmitted wave is represented by
   y = a₂y₀ cos(wt − kx) cm, where a₂ is a positive constant.
3. When the wave reflects from Q for the first time, the reflected wave is represented by
   y = a₃y₀ cos(wt − kx + p) cm , where a₃ is a positive constant.
4. When the wave transmits through Q for the first time, the transmitted wave is represented by
   y = a₄ y₀ cos(wt − 4kx) cm , where a₄ is a positive constant.