A wave traveling along a string in the +x-direction is given bywhere x = 0 is the end of t...

A wave traveling along a string in the +x-direction is given by

where x = 0 is the end of the string which is tied rigidly to a wall, as shown in Fig.P1.7. 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 is the sum of the incident and reflected waves:

ys(x,1) = y1 (x,t) + y2(x,t).

(a) Write an expression for y2(x,t) keeping in mind its direction of travel and the fact that the end of the string cannot move.

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(b) Generate plots of y1(x,t), y2(x,t) and ys(x,t) versus x over the range –2λ ≤ x ≤ 0 at ωt;π/4 and at ωt = π/2.

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Figure P1.7 Wave on a string tied to a wall at x = 0 Problem (1.7)