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CALC A string that lies along the +x-axis has a free end
Chapter 15, Problem 75P(choose chapter or problem)
CALC ?A string that lies along the +x-axis has a free end at x= 0. (a) By using steps similar to those used to derive Eq. (15.28), show that an incident traveling wave y1(x, t) = gives rise to a standing wave y(x, t) = (b) Show that the standing wave has an antinode at its free end (x= 0). (c) Find the maximum displacement, maximum speed, and maximum acceleration of the free end of the string.
Questions & Answers
QUESTION:
CALC ?A string that lies along the +x-axis has a free end at x= 0. (a) By using steps similar to those used to derive Eq. (15.28), show that an incident traveling wave y1(x, t) = gives rise to a standing wave y(x, t) = (b) Show that the standing wave has an antinode at its free end (x= 0). (c) Find the maximum displacement, maximum speed, and maximum acceleration of the free end of the string.
ANSWER:Solution 75P Step 1: a) rovided, incident wave, y (x,t) = A cos (kx + t) 1 So, the reflected wave will move in the negative x - direction. Therefore, the reflected wave will be, y (x,t)2 A cos (-kx + t) So, we can represent the total displacement for the wave as, y (x,t) = y1x,t) + y2x,t) That is, y (x,t) = A cos (kx + t) + A cos (-kx + t)