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Unformatted text preview: homework 13 FRENNEA, KYLE Due: Apr 28 2007, 4:00 am 1 Question 1 part 1 of 2 10 points Two pulses traveling on the same string are described by y 1 = 5 ( a x b t ) 2 + 2 and y 2 = 5 ( a x + b t 6) 2 + 2 where a = 2 . 9 m 1 and b = 2 . 5 s 1 . At what time do the two cancel? Correct answer: 1 . 2 s (tolerance 1 %). Explanation: y 1 travels in the positive x direction, and y 2 travels in the negative x direction. To cancel each other , we require y 1 + y 2 = 0 which is 5 ( a x b t ) 2 + 2 = 5 ( a x + b t 6) 2 + 2 ( a x b t ) 2 = ( a x + b t 6) 2 a x b t = ( a x + b t 6) . (1) Using the positive square root in Eq. (1), t = 3 b = 1 . 2 s. Question 2 part 2 of 2 10 points At what point do the two waves always cancel? Correct answer: 1 . 03448 m (tolerance 1 %). Explanation: Using the negative square root in Eq. (1), x = 3 a = 1 . 03448 m. Question 3 part 1 of 1 10 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 10321 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 10321 1 2 3 Distance (meter) 2. 1 2 3 4 5 6 7 8 9 10321 1 2 3 Distance (meter) 3. 1 2 3 4 5 6 7 8 9 10321 1 2 3 Distance (meter) homework 13 FRENNEA, KYLE Due: Apr 28 2007, 4:00 am 2 4. 1 2 3 4 5 6 7 8 9 10321 1 2 3 Distance (meter) 5. 1 2 3 4 5 6 7 8 9 10321 1 2 3 Distance (meter) 6. 1 2 3 4 5 6 7 8 9 10321 1 2 3 Distance (meter) 7. 1 2 3 4 5 6 7 8 9 10321 1 2 3 Distance (meter) 8. 1 2 3 4 5 6 7 8 9 10321 1 2 3 Distance (meter) 9. 1 2 3 4 5 6 7 8 9 10321 1 2 3 Distance (meter) 10. 1 2 3 4 5 6 7 8 9 10321 1 2 3 Distance (meter) correct 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. homework 13 FRENNEA, KYLE Due: Apr 28 2007, 4:00 am 3 1 2 3 4 5 6 7 8 9 10321 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 10321 1 2 3 Amplitude(centimeter) Distance (meter) Superpostion, at t = 3 s 1 2 3 4 5 6 7 8 9 10321 1 2 3 Amplitude(centimeter) Distance (meter) Resultant, at t = 3 s Question 4 part 1 of 1 10 points Two sound sources oscillate in phase with the same amplitude A . They are separated in space by 7 4 ....
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