Homework 21 Solutions

Homework 21 Solutions - lim(kl9356 – Homework 21 –...

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Unformatted text preview: lim (kl9356) – Homework 21 – Weathers – (17104) 1 This print-out should have 10 questions. Multiple-choice questions may continue on the next column or page – find 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 1 2 3 4 5 6 7 8 9 10-3-2-1 1 2 3 Amplitude(centimeter) Distance (meter) What is the shape of the wave on the string after 3 s? 1. 1 2 3 4 5 6 7 8 9 10-3-2-1 1 2 3 Distance (meter) 2. 1 2 3 4 5 6 7 8 9 10-3-2-1 1 2 3 Distance (meter) 3. 1 2 3 4 5 6 7 8 9 10-3-2-1 1 2 3 Distance (meter) correct 4. 1 2 3 4 5 6 7 8 9 10-3-2-1 1 2 3 Distance (meter) 5. 1 2 3 4 5 6 7 8 9 10-3-2-1 1 2 3 Distance (meter) 6. lim (kl9356) – Homework 21 – Weathers – (17104) 2 1 2 3 4 5 6 7 8 9 10-3-2-1 1 2 3 Distance (meter) 7. 1 2 3 4 5 6 7 8 9 10-3-2-1 1 2 3 Distance (meter) 8. 1 2 3 4 5 6 7 8 9 10-3-2-1 1 2 3 Distance (meter) 9. 1 2 3 4 5 6 7 8 9 10-3-2-1 1 2 3 Distance (meter) 10. 1 2 3 4 5 6 7 8 9 10-3-2-1 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. 1 2 3 4 5 6 7 8 9 10-3-2-1 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. 1 2 3 4 5 6 7 8 9 10-3-2-1 1 2 3 Amplitude(centimeter) Distance (meter) Superpostion, at t = 3 s lim (kl9356) – Homework 21 – Weathers – (17104) 3 1 2 3 4 5 6 7 8 9 10-3-2-1 1 2 3 Amplitude(centimeter) Distance (meter) Resultant, at t = 3 s keywords: 002 (part 1 of 4) 10.0 points Hint: Recall a basic trigonometric relation sin θ 1 + sin θ 2 = 2 cos parenleftbigg θ 1- θ 2 2 parenrightbigg × sin parenleftbigg θ 1 + θ 2 2 parenrightbigg . Two harmonic waves are described by y 1 = A sin( k x- ω t- φ 1 ) and y 2 = A sin( k x- ω t- φ 2 ) , where A = 3 . 9 m , k = 7 . 2 rad / m , ω = 3 . 7 rad / s , φ 1 = 5 . 3 rad , and φ 2 =- 4 . 7 rad . The following questions concern the resultant wave, y 1+2 = y 1 + y 2 ....
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Homework 21 Solutions - lim(kl9356 – Homework 21 –...

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