1. Today 1/17  Interference  HW:1/17 HW Handout “Interference” Due Thur, 1/23 (beginning of class)  Today’s goal: Predict locations where constructive and destructive interference occur.

2. This picture now includes the sources of the waves. Source 1Source 2 In this case the sources are in “sync” and produce waves of equal wavelength. The wave velocity depends only on the medium and so is the same for both. midpoint

3. This picture now includes the sources of the waves. Source 1Source 2 In this case the sources are in “sync” and produce waves of equal wavelength. The wave velocity depends only on the medium and so is the same for both. midpoint

4. This picture now includes the sources of the waves. Source 1Source 2 In this case the sources are in “sync” and produce waves of equal wavelength. The wave velocity depends only on the medium and so is the same for both. midpoint

5. This picture now includes the sources of the waves. Source 1Source 2 In this case the sources are in “sync” and produce waves of equal wavelength. The wave velocity depends only on the medium and so is the same for both. midpoint

6. This picture now includes the sources of the waves. Source 1Source 2 In this case the sources are in “sync” and produce waves of equal wavelength. The wave velocity depends only on the medium and so is the same for both. midpoint

7. This picture now includes the sources of the waves. Source 1Source 2 In this case the sources are in “sync” and produce waves of equal wavelength. The wave velocity depends only on the medium and so is the same for both. midpoint

8. This picture now includes the sources of the waves. Source 1Source 2 In this case the sources are in “sync” and produce waves of equal wavelength. The wave velocity depends only on the medium and so is the same for both. midpoint

9. This picture now includes the sources of the waves. Source 1Source 2 In this case the sources are in “sync” and produce waves of equal wavelength. The wave velocity depends only on the medium and so is the same for both. midpoint

10. This picture now includes the sources of the waves. Source 1Source 2 In this case the sources are in “sync” and produce waves of equal wavelength. The wave velocity depends only on the medium and so is the same for both. midpoint

11. This picture now includes the sources of the waves. Source 1Source 2 In this case the sources are in “sync” and produce waves of equal wavelength. The wave velocity depends only on the medium and so is the same for both. midpoint

12. This picture now includes the sources of the waves. Source 1Source 2 In this case the sources are in “sync” and produce waves of equal wavelength. The wave velocity depends only on the medium and so is the same for both. midpoint

13. This picture now includes the sources of the waves. Source 1Source 2 In this case the sources are in “sync” and produce waves of equal wavelength. The wave velocity depends only on the medium and so is the same for both. midpoint

14. This picture now includes the sources of the waves. Source 1Source 2 In this case the sources are in “sync” and produce waves of equal wavelength. The wave velocity depends only on the medium and so is the same for both. midpoint

15. This picture now includes the sources of the waves. Source 1Source 2 In this case the sources are in “sync” and produce waves of equal wavelength. The wave velocity depends only on the medium and so is the same for both. midpoint

16. This picture now includes the sources of the waves. Source 1Source 2 In this case the sources are in “sync” and produce waves of equal wavelength. The wave velocity depends only on the medium and so is the same for both. Where are the locations of constructive and destructive interference? cccdd How would your answer change if the sources were out of sync? midpoint

17. This picture now includes the sources of the waves. Source 1Source 2 Out of sync means that one produces a crest while the other produces a trough--it’s a timing thing. How would your answer change if the sources were out of sync? midpoint

18. This picture now includes the sources of the waves. Source 1Source 2 Out of sync means that one produces a crest while the other produces a trough--it’s a timing thing. How would your answer change if the sources were out of sync? midpoint

19. This picture now includes the sources of the waves. Source 1Source 2 Out of sync means that one produces a crest while the other produces a trough--it’s a timing thing. How would your answer change if the sources were out of sync? midpoint

20. This picture now includes the sources of the waves. Source 1Source 2 Out of sync means that one produces a crest while the other produces a trough--it’s a timing thing. How would your answer change if the sources were out of sync? midpoint

21. This picture now includes the sources of the waves. Source 1Source 2 Out of sync means that one produces a crest while the other produces a trough--it’s a timing thing. How would your answer change if the sources were out of sync? midpoint

22. This picture now includes the sources of the waves. Source 1Source 2 Out of sync means that one produces a crest while the other produces a trough--it’s a timing thing. How would your answer change if the sources were out of sync? midpoint

23. This picture now includes the sources of the waves. Source 1Source 2 Out of sync means that one produces a crest while the other produces a trough--it’s a timing thing. How would your answer change if the sources were out of sync? midpoint

24. This picture now includes the sources of the waves. Source 1Source 2 Out of sync means that one produces a crest while the other produces a trough--it’s a timing thing. How would your answer change if the sources were out of sync? midpoint

25. This picture now includes the sources of the waves. Source 1Source 2 Out of sync means that one produces a crest while the other produces a trough--it’s a timing thing. How would your answer change if the sources were out of sync? midpoint

26. This picture now includes the sources of the waves. Source 1Source 2 Out of sync means that one produces a crest while the other produces a trough--it’s a timing thing. How would your answer change if the sources were out of sync? midpoint

27. This picture now includes the sources of the waves. Source 1Source 2 Out of sync means that one produces a crest while the other produces a trough--it’s a timing thing. How would your answer change if the sources were out of sync? midpoint

28. This picture now includes the sources of the waves. Source 1Source 2 Out of sync means that one produces a crest while the other produces a trough--it’s a timing thing. How would your answer change if the sources were out of sync? midpoint

29. This picture now includes the sources of the waves. Source 1Source 2 Out of sync means that one produces a crest while the other produces a trough--it’s a timing thing. How would your answer change if the sources were out of sync? midpoint

30. This picture now includes the sources of the waves. Source 1Source 2 Out of sync means that one produces a crest while the other produces a trough--it’s a timing thing. How would your answer change if the sources were out of sync? midpoint

31. This picture now includes the sources of the waves. Source 1Source 2 Out of sync means that one produces a crest while the other produces a trough--it’s a timing thing. How would your answer change if the sources were out of sync? midpoint

32. This picture now includes the sources of the waves. Source 1Source 2 Out of sync means that one produces a crest while the other produces a trough--it’s a timing thing. How would your answer change if the sources were out of sync? midpoint

33. This picture now includes the sources of the waves. Source 1Source 2 Out of sync means that one produces a crest while the other produces a trough--it’s a timing thing. How would your answer change if the sources were out of sync? midpoint

34. This picture now includes the sources of the waves. Source 1Source 2 Out of sync means that one produces a crest while the other produces a trough--it’s a timing thing. ccdd How would your answer change if the sources were out of sync? Now the locations for constructive and destructive interference switch! d cccdd Sources in phase (in sync) Sources out of phase (out of sync)

35. Source 1Source 2 ccddd Sources out of phase (out of sync) cccdd Sources in phase (in sync) Source 1Source 2 In any case, the interference occurs in a pattern. The next job is to invent a rule so we can predict these locations.

36. Source 1Source 2 ccddd Sources out of phase (out of sync) cccdd Sources in phase (in sync) Source 1Source 2 What do you need to predict interference? 1. Whether the sources are in phase or not 2. Wavelength 3. Location

37. Source 1Source 2 ccddd Sources out of phase (out of sync) cccdd Sources in phase (in sync) Source 1Source 2 We want one thing we can say about all these places for “in phase and constructive.” The difference in distance from each source to constructive locations is given by... PL 2 - PL 1 = Path Length Difference = PLD = n, n = 0,1,2,3... PLD = 0 PL 1 PL 2 2 2

38. Source 1Source 2 ccddd Sources out of phase (out of sync) cccdd Sources in phase (in sync) Source 1Source 2 Now what can we can say about the places for “in phase and destructive.” The difference in distance from each source to destructive locations is given by... Path Length Difference = PLD = (n + 1 / 2 ), n = 0,1,2,3... 1 / 2 3 / 2 1 / 2 3 / 2

39. Source 1Source 2 ccddd Sources out of phase (out of sync) cccdd Sources in phase (in sync) Source 1Source 2 What about the places for “out of phase and constructive.” The difference in distance from each source to constructive locations is... Path Length Difference = PLD = (n + 1 / 2 ), n = 0,1,2,3... 1 / 2 3 / 2 1 / 2 3 / 2

40. Source 1Source 2 ccddd Sources out of phase (out of sync) cccdd Sources in phase (in sync) Source 1Source 2 What about the places for “out of phase and destructive.” The difference in distance from each source to destructive locations is... Path Length Difference = PLD = n, n = 0,1,2,3... PLD = 0 2 2 0

41. Source 1Source 2 ccddd Sources out of phase (out of sync) cccdd Sources in phase (in sync) Source 1Source 2 PLD = (n + 1 / 2 ), n = 0,1,2,3... PLD = 0 Summary: In phase, constructive In phase, destructive Out of phase, constructive Out of phase, destructive PLD = (n + 1 / 2 ), n = 0,1,2,3... PLD = n, n = 0,1,2,3...

42. Interference in 2-D Sources “in phase” Crest meets crest and trough meets trough, constructive, loud sound or bright light Crest meets trough and trough meets crest, destructive, no sound or dark Crest Trough

43. Interference in 2-D Sources “in phase” Constructive at a point if it is the same distance from each source Destructive at a point if it is 1 / 2 farther away from one source Crest Trough

44. Interference in 2D Sources “out of phase” Crest meets trough and trough meets crest, destructive, no sound or dark Crest meets crest and trough meets trough, constructive, loud sound or bright Crest Trough

45. Interference in 2-D Sources “out of phase” Destructive at a point if the point is the same distance from each source Constructive at a point if the point is 1 / 2 farther away from one source Crest Trough