JEE Advanced · 2025 · 18 May 2025 · Paper 1 · Waves & Sound

Consider a system of three connected strings, $S_1,S_2$ and $S_3$ with uniform linear mass densities $\mu \mathrm{kg}/\mathrm{m}$, $4\mu \mathrm{kg}/\mathrm{m}$ and $16\mu \mathrm{kg}/\mathrm{m}$, respectively, as shown in the figure. $S_1$ and $S_2$ are connected at the point $P$, whereas $S_2$ and $S_3$ are connected at the point $Q$, and the other end of $S_3$ is connected to a wall. A wave generator O is connected to the free end of $S_1$. The wave from the generator is represented by $y=y_0$ $\cos (\omega t-kx)\mathrm{cm}$, where $y_0,\omega$ and $k$ are constants of appropriate dimensions. Which of the following statements is/are correct:

1. (A)When the wave reflects from $P$ for the first time, the reflected wave is represented by $y={\alpha }_1{\mathrm{y}}_0\cos (\omega t+kx+\pi )\mathrm{cm}$, where ${\alpha }_1$ is a positive constant.✓ Correct
2. (B)When the wave transmits through $P$ for the first time, the transmitted wave is represented by $y={\alpha }_2{\mathrm{y}}_0\cos (\omega t-kx)\mathrm{cm}$, where ${\alpha }_2$ is a positive constant.
3. (C)When the wave reflects from $Q$ for the first time, the reflected wave is represented by $y={\alpha }_3{\mathrm{y}}_0\cos (\omega t-kx+\pi )\mathrm{cm}$, where ${\alpha }_3$ is a positive constant.
4. (D)When the wave transmits through $Q$ for the first time, the transmitted wave is represented by $y={\alpha }_4{\mathrm{y}}_0\cos (\omega t-4kx)\mathrm{cm}$, where ${\alpha }_4$ is a positive constant.✓ Correct

Answer: (A), (D)

JEE Advanced · 2025 · 18 May 2025 · Paper 1 · One or more correct options