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Unformatted text preview: Husain, Zeena Homework 12 Due: Nov 18 2003, 4:00 am Inst: H L Berk 1 This printout should have 19 questions, check that it is complete. Multiplechoice questions may continue on the next column or page: find all choices before making your selection. The due time is Central time. 001 (part 1 of 2) 10 points The time interval indicated on this diagram is G . S G t S Which formula corresponds best to the di agram? 1. S ( t ) = S sin 2 t 3 G 2. S ( t ) = S sin 3 t 2 G 3. S ( t ) = S sin 2 t 3 G 4. S ( t ) = S sin 2 t G 5. S ( t ) = S sin t 3 G 6. S ( t ) = S sin 3 t G correct 7. S ( t ) = S sin 2 t 3 G 8. S ( t ) = S sin 3 t 2 G 9. S ( t ) = S sin t 2 G 10. S ( t ) = S sin 3 t 2 G Explanation: The equation of a wave with zero displace ment at the origin is given by S ( t ) = S sin( t ) = S sin 2 T t , since 2 T . From the figure, we see 1 3 G = 1 2 T which means T = 2 3 G . Since 2 T = 3 G , we have S ( t ) = S sin 3 G t . 002 (part 2 of 2) 10 points This wave has period T . S T t S Which formula corresponds best to the di agram? 1. S ( t ) = S sin 2 t T 2 2. S ( t ) = S sin 2 t T + 2 correct 3. S ( t ) = S sin t T 2 4. S ( t ) = S sin t T + 2 5. S ( t ) = S sin 2 t T 6. S ( t ) = S sin t T 7. S ( t ) = S sin 2 t T 8. S ( t ) = S sin  2 2 t T 9. S ( t ) = S sin  2 t T 10. S ( t ) = S sin  t T Explanation: First note that most of the incorrect solu tions can be eliminated immediately by check ing the value of the displacement at t = 0. The equation for a wave with period T and maximum displacement at the origin is S ( t ) = S cos 2 T t . Husain, Zeena Homework 12 Due: Nov 18 2003, 4:00 am Inst: H L Berk 2 Since cos( t ) = sin t + 2 we find S ( t ) = S sin 2 T t + 2 . 003 (part 1 of 5) 10 points The wave function for a linearly polarized wave on a taut string is y ( x,t ) = A sin( t k x + ) , where A = 0 . 34 m, = 9 . 1 s 1 , k = 6 . 2 m 1 , = 0 . 41, t is in seconds and x and y are in meters. What is the speed of the wave? Correct answer: 1 . 46774 m / s. Explanation: Basic Concepts: v = T k = 2 f = 2 Solution: For the propagation speed of a wave we have v = k = (9 . 1 s 1 ) (6 . 2 m 1 ) = 1 . 46774 m / s . 004 (part 2 of 5) 10 points What is the vertical displacement of the string at x = 0 . 07 m, t = 3 s? Correct answer: 0 . 285793 m. Explanation: We can obtain the result if we simply sub stitute the values for x and t into y ( x,t ) y ( x ,t ) = A sin[ t k x + ] = (0 . 34 m) sin h (9 . 1 s 1 ) (3 s) (6 . 2 m 1 ) (0 . 07 m) + (0 . 41) i = 0 . 285793 m ....
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