Consider a system of three connected strings, $ S_1, S_2 $ and $ S_3 $ with uniform linear mass densities $ \mu \, \text{kg/m}, 4\mu \, \text{kg/m} $ and $ 16\mu \, \text{kg/m} $, respectively, as shown in the figure. $ S_1 $ and $ S_2 $ are connected at 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:
A sub-atomic particle of mass \( 10^{-30} \) kg is moving with a velocity of \( 2.21 \times 10^6 \) m/s. Under the matter wave consideration, the particle will behave closely like (h = \( 6.63 \times 10^{-34} \) J.s)