HW #13-solutions

# HW #13-solutions - wolz(cmw2833 HW#13 Antoniewicz(57420...

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wolz (cmw2833) – HW #13 – Antoniewicz – (57420) 1 This print-out should have 20 questions. Multiple-choice questions may continue on the next column or page – fnd all choices beFore answering. 001 10.0 points You are given two waves, a transverse wave that moves to the right f 1 ( x ) and a transverse wave that moves to the leFt f 2 ( x ), on a string. As the problem begins, the wave f 1 ( x ) is mov- ing to the right at v 1 = +1 m/s and the wave f 2 ( x ) is moving to the leFt at v 2 = - 1 m/s. v 1 v 2 0 1 2 3 4 5 6 7 8 9 10 -3 -2 -1 0 1 2 3 Amplitude (centimeter) Distance (meter) What is the shape oF the wave on the string aFter 3 s? 1. 0 1 2 3 4 5 6 7 8 9 10 -3 -2 -1 0 1 2 3 Distance (meter) 2. 0 1 2 3 4 5 6 7 8 9 10 -3 -2 -1 0 1 2 3 Distance (meter) 3. 0 1 2 3 4 5 6 7 8 9 10 -3 -2 -1 0 1 2 3 Distance (meter) 4. 0 1 2 3 4 5 6 7 8 9 10 -3 -2 -1 0 1 2 3 Distance (meter)

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wolz (cmw2833) – HW #13 – Antoniewicz – (57420) 2 5. 0 1 2 3 4 5 6 7 8 9 10 -3 -2 -1 0 1 2 3 Distance (meter) 6. 0 1 2 3 4 5 6 7 8 9 10 -3 -2 -1 0 1 2 3 Distance (meter) correct 7. 0 1 2 3 4 5 6 7 8 9 10 -3 -2 -1 0 1 2 3 Distance (meter) 8. 0 1 2 3 4 5 6 7 8 9 10 -3 -2 -1 0 1 2 3 Distance (meter) 9. 0 1 2 3 4 5 6 7 8 9 10 -3 -2 -1 0 1 2 3 Distance (meter) 10. 0 1 2 3 4 5 6 7 8 9 10 -3 -2 -1 0 1 2 3 Distance (meter) Explanation: The initial wave moving to the right is rep- resented with a dashed line and the eave mov- ing to the left is represented with a dotted line.
wolz (cmw2833) – HW #13 – Antoniewicz – (57420) 3 0 1 2 3 4 5 6 7 8 9 10 -3 -2 -1 0 1 2 3 Amplitude (centimeter) Distance (meter) Initial time, t = 0 s After 3 s the positions of the two waves are have both moved 3 meters in opposite directions. The sum of the two wave is the resultant wave, the light gray line. 0 1 2 3 4 5 6 7 8 9 10 -3 -2 -1 0 1 2 3 Distance (meter) Superpostion, at t = 3 s 0 1 2 3 4 5 6 7 8 9 10 -3 -2 -1 0 1 2 3 Distance (meter) Resultant, at t = 3 s 002 (part 1 of 4) 3.0 points A wave pulse on a string is described by the equation y 1 = A ( B x - C t ) 2 + D . A second wave pulse on the same string is described by y 2 = - A ( B x + C t - E ) 2 + D , where x is in meters and t in seconds, A = 9 . 67 m, B = 4 . 2 m 1 , C = 4 . 04 s 1 , D = 2 . 32, and E = 7 . 22. In which direction does each pulse y 1 travel? 1. - x direction 2. + x direction correct Explanation: For any function y ( B x + C t ) describing a wave, the sign of B C decides the direction of travel: B C < 0 = + x direction B C > 0 = ⇒ - x direction Another way to view this is to imagine view- ing the wave while traveling with the same speed and direction as the wave. In that case, the wave form would appear constant. We can then determine the direction of the wave by seeing how x , our position, must change to keep y constant as time progresses ( i.e. as t increases). For example, when y = (4 . 2 m 1 ) x - (4 . 04 s 1 ) t , we see that when t increases, x must increase in order to keep (4 . 2 m 1 ) x - (4 . 04 s 1 ) t , and hence y , constant. Hence the velocity must be in the direction of increasing x ( i.e. a positive x ve- locity). This means that y 1 is traveling in the + x direction and y 2 is traveling in the - x direction.

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HW #13-solutions - wolz(cmw2833 HW#13 Antoniewicz(57420...

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