Consider a system of three connected strings, S 1 , S 2 and S 3 with uniform linear mass densities μ kg / m , 4 μ kg / m and 16 μ kg / m , respectively, as shown in the figure. S 1 and S 2 a

Question

Consider a system of three connected strings, $S_{1}, S_{2}$ and $S_{3}$ with uniform linear mass densities $μ kg / m$ , $4 μ kg / m$ and $16 μ kg / m$ , 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 $y = y_{0}$ $cos (ω t - k x) cm$ , where $y_{0}, ω$ and $k$ are constants of appropriate dimensions. Which of the following statements is/are correct:

TestHub · Accepted Answer

(A) y 1 ​ = y 0 ​ cos ( ω t − k x ) when wave going from Rarer to Denser, ​ y r ​ = A r ​ cos ( ω t + k x + π ) y r ​ = a 1 ​ y 0 ​ cos ( ω t + k x + π ) ​ option (A) correct (B) For transmitted from point P ​ y t ​ = A t ​ cos [ ω t − k 1 ​ x ] k k 1 ​ ​ = μ μ 1 ​ ​ ​ = k k 1 ​ ​ = μ 4 μ ​ ​ k 1 ​ = 2 k y t ​ = a 2 ​ y 0 ​ cos [ ω t − 2 kx ] ​ option (B) incorrect (C) when reflected from Q ​ y i ​ = a 2 ​ y 0 ​ cos [ ω t − 2 k x ] y r ​ = a 3 ​ y 0 ​ cos [ ω t + 2 k x + π ] ​ option (C) incorrect (D) when transmitted from Q ​ y t ​ = a 4 ​ y 0 ​ cos [ ω t = k 2 ​ x ] 2 k k 2 ​ ​ = 4 μ 16 μ ​ ​ ⇒ k 2 ​ = 4 k y t ​ = a 4 ​ y 0 ​ cos [ ω t − 4 kx ] ​ option (D) correct

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Options:(select one or more)

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