1. Quiz 2

2. Physics 7C Fa 2008 Lecture 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. 12345 What type of interference occurs at each point?

5. Interference for differing frequencies: Beats 12345

6. 12345 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. d Two slits create two overlapping wave fronts 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. d Two slits create two overlapping wave fronts Crest Trough

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

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

16. x2x2 Two slits create two overlapping wave fronts Crest Trough Why? a)  x=0 b)  x= /2 c)  x  d) None of the above x1x1 x 1 =x 2 so  x=0!

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

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

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

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

21. d Two slits create two overlapping wave fronts Crest Trough Why? a)  x=0 b)  x= /2 c)  x  d) None of the above x2x2 x1x1 x 1 >x 2 now… x 1 =2 x 2 =1.5

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? a b d c e

24. a b 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? a)Constructive b)Destructive c)Time-dependent d)Depends which antinode

31. Standing Waves 2nd Harmonic 3rd Harmonic What type of interference occurs at an antinode? a)Constructive b)Destructive c)Time-dependent d)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