Consider a system of three connected strings, $\mathrm{S}_1, \mathrm{~S}_2$ and $\mathrm{S}_3$ 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 $P_{\text {, }}$ 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 0 is connected to the free end of $\mathrm{S}_1$. The wave from the generator is represented by $y=y_0 \cos (\omega t-k x) c m$, where $y_0 \omega$ and k are constants of appropriate dimensions. Which of the following statements is/are correct:
Select ALL correct options:
A
When the wave reflects from P for the first time, the reflected wave is represented by $y=\alpha_1 y_0 \cos (\omega t+k x+\pi) c m$, where $\alpha_1$ is a positive constant.
B
When the wave transmits through P for the first time, the transmitted wave is represented by $y=\alpha_2 y_0 \cos (\omega t-k x) c m$, where $\alpha_2$ is a positive constant.
C
When the wave reflects from $Q$ for the first time, the reflected wave is represented by $y=\alpha_3 y_0 \cos (\omega t-k x+\pi) c m$, where $\alpha_3$ is a positive constant.
D
When the wave transmits through $Q$ for the first time, the transmitted wave is represented by $y=\alpha_4 y_0 \cos (\omega t-4 k x) c m$, where $\alpha_4$ is a positive constant.
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