Consider a system of three connected strings, S_1, S_2 and S_3 with uniform linear mass densities kg / m , 4 ~kg / m and 16 ~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 connecte

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

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Correct answer: D. When the wave transmits through Q for the first time, the transmitted wave is represented by y= _4 y_0 ( t-4 k x) cm , where _4 is a positive constant.

(A) y_1=y_0 ( t-k x) when wave going from Rarer to Denser, aligned & y_r=A_r ( t+k x+ ) \ & y_r=a_1 y_0 ( t+k x+ ) aligned option (A) correct (B) For transmitted from point P aligned & y _ t = A _ t [ t - k _1 x ] \ & k _1 k = _1 = k _1 k = 4 \ & k _1=2 k \ & y _ t = a _2 y _0 [ t -2 kx ] aligned option (B) incorrect (C) when reflected from Q aligned & y_i=a_2 y_0 [ t-2 k x] \ & y_r=a_3 y_0 [ t+2 k x+ ] aligned option (C) incorrect (D) when transmitted from Q aligned & y_ t =a_4 y_0 [ t =k_2 x ] \ & k_2 2 k = 16 4 k_2=4 k \ & y_ t =a_4 y_0 [ t -4 kx ] aligned option (D) correct

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