(Solution) - A wave traveling along a string in the x direction -(2025 Original AI-Free Solution)

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A wave traveling along a string in the + x-direction is given by y1 (x, t) = A cos (wt ? Bx), where x = 0 is the end of the string, which is tied rigidly to a wall, as shown in Fig. 1-21 (P1.6). When wave y1 (x, t) arrives at the wall, a reflected wave y2 (x, t) is generated. Hence, at any location on the string, the vertical displacement ys will be the sum of the incident and reflected waves: ys (x, t) = y1 (x, t) + y2(x, t).
(a) Write down an expression for y2(x, t), keeping in mind its direction of travel and the fact that the end of the string cannot move.
(b) Generate plots of y1 (x, t), y2 (x, t) and ys (x, t versus x over the range - 2? < x <0 at wt = ?/4 and at ?/2.