Consider a system of three connected strings, $$S_1$$, $$S_2$$ and $$S_3$$ with uniform linear mass densities $$\mu$$ kg/m, $$4\mu$$ kg/m and $$16\mu$$ kg/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 $$y = y_0 \cos(\omega t - kx)$$ cm, where $$y_0$$, $$\omega$$ and $$k$$ are constants of appropriate dimensions. Which of the following statements is/are correct:

When the wave reflects from $$P$$ for the first time, the reflected wave is represented by $$y = \alpha_1 y_0 \cos(\omega t + kx + \pi)$$ cm, where $$\alpha_1$$ is a positive constant.

When the wave transmits through $$P$$ for the first time, the transmitted wave is represented by $$y = \alpha_2 y_0 \cos(\omega t - kx)$$ cm, where $$\alpha_2$$ is a positive constant.

When the wave reflects from $$Q$$ for the first time, the reflected wave is represented by $$y = \alpha_3 y_0 \cos(\omega t - kx + \pi)$$ cm, where $$\alpha_3$$ is a positive constant.

When the wave transmits through $$Q$$ for the first time, the transmitted wave is represented by $$y = \alpha_4 y_0 \cos(\omega t - 4kx)$$ cm, where $$\alpha_4$$ is a positive constant.