Thursday, Sep. 3Phy208 Lecture 2 1 Physics 208, Fall 2009 Waves: Interference and Diffraction (Chap....
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Transcript of Thursday, Sep. 3Phy208 Lecture 2 1 Physics 208, Fall 2009 Waves: Interference and Diffraction (Chap....
![Page 1: Thursday, Sep. 3Phy208 Lecture 2 1 Physics 208, Fall 2009 Waves: Interference and Diffraction (Chap. 20-22) Colors in soap films, CDs, and butterfly wings.](https://reader036.fdocuments.in/reader036/viewer/2022081516/56649d745503460f94a537a6/html5/thumbnails/1.jpg)
Thursday, Sep. 3 Phy208 Lecture 2 1
Physics 208, Fall 2009
Waves: Interference and Diffraction (Chap. 20-22) Colors in soap films, CDs, and butterfly wings
Refraction of Light, and Optics (Chap. 23-24) Telescopes, microscopes, and eyes
Electricity (Chap. 26-32) Capacitors & cell membranes, battery-less flashlights
Magnetism (Chap. 33-34) Electromagnetic Waves (Chap. 35)
Light and polarization Modern Physics (Chap. 37-42)
Radiation and matter, radioactivity, nuclear fission
www.physics.wisc.edu/undergrads/courses/fall09/208
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Thursday, Sep. 3 Phy208 Lecture 2 2
Your Professor and TAs
TA consultation hours are in 2331 Chamberlin. Hours will be posted.
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Thursday, Sep. 3 Phy208 Lecture 2 3
Lectures Tuesday, Thursday 12:05-12:55
2103 Chamberlin Includes
Demonstrations Examples Quick questions
Honors section Friday 12:05-12:55, 2103 Chamberlin First meeting Sep. 11 (next week) Required for those signed up for honors
(B or better course grade also required for honors)
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Thursday, Sep. 3 Phy208 Lecture 2 4
Discussions and LabsDiscussions
Monday and Wednesday (begin Wed, Sep. 9)
Weekly Q&A, group problem, quiz.
Labs
- start week of Sep 14 (3254 Chamberlin).
- No lab notebook: question sheets distributed.
- 8 of 9 labs must be completed to pass the course.
- Complete only 8 -> lab grade reduced by 30%.
• If you must miss a lab:• Immediately contact your TA• Try to arrange for a different lab section that week• If not possible, lab missed (for a good reason) can be made up
only during the immediately following exam week.
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Thursday, Sep. 3 Phy208 Lecture 2 5
Homework: (Mastering Physics)
Should be able to use your login from Physics 207
– Follow email instructions for registering (as soon as possible)
– Course ID: PHYSICS208FALL2009
• Assigned each Thursday – Week2HW available now. Due 8 days later Friday at midnight.
Text: (Same as Physics 207 last semester)
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Thursday, Sep. 3 Phy208 Lecture 2 6
Exams
Exam 1: Tue. Sep. 29 5:30-7 pm Exam 2: Tue. Oct. 27 5:30-7 pm Exam 3: Thur. Dec. 3 5:30-7 pm Cumulative Final Exam: Mon. Dec 21, 5:05 pm -7:05 pm
Exams make up most of your grade (70%)
Three midterm exams, 1 hr 30 min eachTypically 5-6 problems (old exams at web site)
Multiple choiceShort answerLonger calculation
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Thursday, Sep. 3 Phy208 Lecture 2 7
Grading
Weight Comments
Labs 10% 8 of the 9 labs required to pass the courseLab grade reduced 30% if only 9 labs completed
Discussion 10% Mon & Wed
Homework 10% Mastering Physics
Exams:Exam2Exam2Exam3Final
15 %
15%
15%
25%
1:30 hrs1:30 hrs1:30 hrs2:00 hrs
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Thursday, Sep. 3 Phy208 Lecture 2 8
Last semester: mechanical waves Examples
Sound waves Water waves Earthquake waves
Medium required Wave describes
displacement of medium
This semester: electromagnetic waves Examples
Light wavesRadio wavesMicrowavesX-rays
No medium requiredCan propagate in vacuum
Wave describes local electric and magnetic fields
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Thursday, Sep. 3 Phy208 Lecture 2 9
Common wave properties
ReflectionSuperposition
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Thursday, Sep. 3 Phy208 Lecture 2 10
Wave properties
• Wave has both space and time dependence
Shows constant time intervals
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Thursday, Sep. 3 Phy208 Lecture 2 11
crest
Periodic wave• Repeats continuously, moves in space• Wavelength : distance to complete one
cycle• Period T: time to complete one cycle• Frequency f: 1/Period
trough
€
Asin2π
λx −
2π
Tt
⎛
⎝ ⎜
⎞
⎠ ⎟Mathematically:
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Thursday, Sep. 3 Phy208 Lecture 2 12
Moving wave crests
• Period = 1 second• Propagation speed = v
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Thursday, Sep. 3 Phy208 Lecture 2 13
Same period, slower wave velocity
• Period = 1 second• Propagation speed = v/2
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Thursday, Sep. 3 Phy208 Lecture 2 14
Freq., wavelength, velocity are related
• Source emits a crest once every period T.
• This crest propagates at velocity v.
• By the time the source emits another crest T seconds later, the first crest has moved vT.
• So the distance between crests is vT.
– This is the wavelength of the wave
• Wavelength = velocity period
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Thursday, Sep. 3 Phy208 Lecture 2 15
Wave relations• Velocity = Wavelength / Period• v = / T, or v = f• f = Frequency = 1 / Period = 1/T
€
Asin2π
λx −
2π
Tt
⎛
⎝ ⎜
⎞
⎠ ⎟Sinusoidal traveling wave:
€
Asin kx − ωt ( )or
€
k = 2π /λ ω = 2π f = 2π /T
Wavenumber( m-1 )
Angular frequency(rad/s)
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Phase difference between waves
Thursday, Sep. 3 Phy208 Lecture 2 16
Phase difference
Here the phase difference is
λ
• Waves of same amplitude, wavelength, frequency, can still be “different”.
Can be phase difference between waves
180˚π radians“1/2 wavelength”
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Mathematical expression for phase
• Phase is the argument of the sin function• Phase shift is extra displacement of wave
along propagation direction.• Rigidly moves the positions of the crests,
troughs, and zeroes
Thursday, Sep. 3 Phy208 Lecture 2 17
€
Asin k x − ω t + ϕ ( )
Wavenumber Angular frequency
Phase Shift
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Thursday, Sep. 3 Phy208 Lecture 2 18
Interference
• Water drop is a source of circular waves (two-dimensions here)
• When the waves overlap, they superimpose.
• In some areas they cancel, in others they reinforce.
• Depends on phase difference.
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Thursday, Sep. 3 Phy208 Lecture 2 19
Destructive Interference in a String
• Two pulses are traveling in opposite directions
• Net displacement = sum of individual displacements
• Pulses unchanged after interference
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Thursday, Sep. 3 Phy208 Lecture 2 20
Destructive interference in a continuous wave
• Two waves, a and b, have the same amplitude and frequency
• They are 1/2 wavelength out of phase
• When they combine, the waveforms cancel
+
=
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Thursday, Sep. 3 Phy208 Lecture 2 21
Setting up destructive interference
• Sound takes two paths to arrive at ear• One path 1/2 wavelength longer than other• Results in destructive interference
Destructive
Destructive interference for frequencies such that path length difference is 1/2 wavelength.
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Thursday, Sep. 3 Phy208 Lecture 2 22
Interference of 2 speakers
cresttrough
constructive interference,loud tone
destructive interferencequit tone
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Thursday, Sep. 3 Phy208 Lecture 2 23
A little more detail
Same distance, same phase
Path 1Path 2
Path-length difference = (Path 2) - (Path 1) = 0
d
Path 1
Path 2
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Thursday, Sep. 3 Phy208 Lecture 2 24
Other angles?
Interference: Constructive: =
= Extra path length
d
€
/d = sinθ
δ = d sinθ
Path 1Path 2
Path-length difference 0
Destructive: = €
mλ
€
2m +1
2λ
€
=0, λ , 2λ , 3λK
€
=1
2λ ,
3
2λ ,
5
2λK