Mastering Wave Interference: Concepts and Applications

1. Quiz 2

2. Physics 7C Fa 2008Lecture 3: Waves Quiz 2 Understanding Interference

3. Reviewing the Basics • Constructive Interference: • total phase equivalent • Destructive Interference: • total phase separated by half cycle Note: these waves have identical periods and wavelengths, but that is not always the case!

4. Interference for differing frequencies: Beats. 1 2 3 4 5 What type of interference occurs at each point?

5. Interference for differing frequencies: Beats 1 2 3 4 5

6. Interference for differing frequencies: Beats 1 2 3 4 5 The carrier frequency The beat frequency

7. Interference for differing frequencies: Beats • What’s happening at the gold arrows? • What’s happening at the black arrows?

8. Checking 1D interference • Two speakers are wired into different function generators with slightly different frequencies. They have identical wiring, and are placed face-to-face. What type of interference results? • A) Constructive • B) Destructive • C) Partial • D) Depends on what time you choose • E) Insufficient information to decide

9. Checking 1D interference • Two speakers are wired into different function generators with slightly different frequencies. They have identical wiring, and are placed face-to-face. What type of interference results? • A) Constructive • B) Destructive • C) Partial • D) Depends on what time you choose • E) Insufficient information to decide

10. Introducing 2D Interference:The Ripple Tank • Try to spot… • Places that are very deep • Places that are very shallow • Places that are “normal” depth • Places two crest combine • Places two troughs combine • Places a crest meets a trough

11. Two slits create two overlapping wave fronts d Crest Trough

12. 2D Interference • Conceptually, nothing new! • Temporal contribution if frequencies differ • Typically same medium & same source • Pathlength difference contribution • How far has each wave traveled? • Phase constant contribution • By how much do phases differ? (Typically same phase difference, though not always!) • Summary: Just like 1D interference, but typically you only need to think about pathlength difference!

13. Two slits create two overlapping wave fronts d Crest Trough

14. Two slits create two overlapping wave fronts d What type of interference occurs at the marked spot? Constructive Destructive Partial Time-dependent Crest Trough

15. Two slits create two overlapping wave fronts d • Why? • x=0 • x=/2 • x • None of the above Crest Trough

16. Two slits create two overlapping wave fronts x1 x2 • Why? • x=0 • x=/2 • x • None of the above x1=x2 so x=0! Crest Trough

17. Two slits create two overlapping wave fronts d What type of interference occurs at the marked spot? Constructive Destructive Partial Time-dependent Crest Trough

18. Two slits create two overlapping wave fronts d • Why? • x=0 • x=/2 • x • None of the above Crest Trough

19. Two slits create two overlapping wave fronts d What type of interference occurs at the marked spot? Constructive Destructive Partial Time-dependent Crest Trough

20. Two slits create two overlapping wave fronts d • Why? • x=0 • x=/2 • x • None of the above Crest Trough

21. Two slits create two overlapping wave fronts d x2 x1 • Why? • x=0 • x=/2 • x • None of the above x1>x2 now… x1=2 x2=1.5 Crest Trough

22. Another interesting phenomenon • What are you seeing? Look carefully • A) Constructive Interference Only • B) Destructive Interference Only • C) Beats • D) Pathlength-dependent Interference: both constructive & destructive depending on position • E) Partial Interference

23. What is x? b a d c e

24. What is x? b a d c e

25. Laser Interference In DL you will use a shortcut to calculate pathlength difference: d sin = x

26. Review: 2D Interference • Why calculate d sin  ? • d sin estimates the pathlength difference (x). That is, how much further does the wave travel from slit 1 compared to from slit 2. • When the wave splits through the slits, frequency and  don’t change, so only pathlength matters! • Constructive interference occurs if one wave travels a whole number of wavelengths further than the other • if x=n=0 or 2, 4, 6, etc. • Destructive interference occurs if one wave travels a half number of wavelengths further than the other • if x=(n/2)(for n odd)= or 3, 5, 7, etc. • …so d sin  = m determines type: constructive, destructive, or partial

27. Standing Waves • Fundamental

28. Standing Waves • 2nd Harmonic • 3rd Harmonic N = “node” A = “antinode”

29. Standing Waves • 2nd Harmonic • 3rd Harmonic • What type of interference occurs at a node? • a) Constructive • b) Destructive • c) Time-dependent • d) Depends which node

30. Standing Waves • 2nd Harmonic • 3rd Harmonic • What type of interference occurs at an antinode? • Constructive • Destructive • Time-dependent • Depends which antinode

31. Standing Waves • 2nd Harmonic • 3rd Harmonic • What type of interference occurs at an antinode? • Constructive • Destructive • Time-dependent • Depends which antinode

32. Superposition of 2 traveling harmonic waves • The period and wavelength are exactly the same. • One wave travels to the right, one to the left.

33. Checking 1D interference • Two speakers are connected to the same function generator with reversed wiring. One speaker is placed a half wavelength in front. What type of interference results? • A) Constructive • B) Destructive • C) Partial • D) Depends on what time you choose • E) Insufficient information to decide

34. Checking 1D interference • Two speakers are wired to the same function generator. The phase constants differ by /2. One speaker is placed a quarter wavelength in front. What type of interference results? • A) Constructive • B) Destructive • C) Partial • D) Depends on what time you choose • E) Insufficient information to decide