Physics 208, Fall 2009

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


Your Professor and TAs

TA consultation hours are in 2331 Chamberlin. Hours will be posted.


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)


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.


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)


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


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

http://www.masteringphysics.com/


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


Common wave properties

ReflectionSuperposition


Wave properties

• Wave has both space and time dependence

Shows constant time intervals


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:


Moving wave crests

• Period = 1 second• Propagation speed = v


Same period, slower wave velocity

• Period = 1 second• Propagation speed = v/2


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


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)

Phase difference between waves


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”

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


€

Asin k x − ω t + ϕ ( )

Wavenumber Angular frequency

Phase Shift


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.


Destructive Interference in a String

• Two pulses are traveling in opposite directions

• Net displacement = sum of individual displacements

• Pulses unchanged after interference


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

+

=


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.


Interference of 2 speakers

cresttrough

constructive interference,loud tone

destructive interferencequit tone


A little more detail

Same distance, same phase

Path 1Path 2

Path-length difference = (Path 2) - (Path 1) = 0

d

Path 1

Path 2


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

Physics 208, Fall 2009

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