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Quiz 2

Quiz 2. Physics 7C Fa 2008 Lecture 3: Waves. Quiz 2 Understanding Interference. Reviewing the Basics. Constructive Interference: total phase equivalent Destructive Interference: total phase separated by half cycle.

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Quiz 2

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  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

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