Thursday, Sep. 3Phy208 Lecture 2 1 Physics 208, Fall 2009 Waves: Interference and Diffraction (Chap ) Colors in soap films, CDs, and butterfly wings Refraction of Light, and Optics (Chap ) Telescopes, microscopes, and eyes Electricity (Chap ) Capacitors & cell membranes, battery-less flashlights Magnetism (Chap ) Electromagnetic Waves (Chap. 35) Light and polarization Modern Physics (Chap ) Radiation and matter, radioactivity, nuclear fission

Thursday, Sep. 3Phy208 Lecture 2 2 Your Professor and TAs TA consultation hours are in 2331 Chamberlin. Hours will be posted.

Thursday, Sep. 3Phy208 Lecture 2 3 Lectures Tuesday, Thursday 12:05-12: 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)

Thursday, Sep. 3Phy208 Lecture 2 4 Discussions and Labs Discussions 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.

Thursday, Sep. 3Phy208 Lecture 2 5 Homework: (Mastering Physics) Should be able to use your login from Physics 207 –Follow 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)

Thursday, Sep. 3Phy208 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 each Typically 5-6 problems (old exams at web site) Multiple choice Short answer Longer calculation

Thursday, Sep. 3Phy208 Lecture 2 7 Grading WeightComments Labs10%8 of the 9 labs required to pass the course Lab grade reduced 30% if only 9 labs completed Discussion10% Mon & Wed Homework10% Mastering Physics Exams: Exam2 Exam3 Final 15 % 25% 1:30 hrs 2:00 hrs

Thursday, Sep. 3Phy208 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 waves Radio waves Microwaves X-rays No medium required Can propagate in vacuum Wave describes local electric and magnetic fields

Thursday, Sep. 3Phy208 Lecture 2 9 Common wave properties Reflection Superposition

Thursday, Sep. 3Phy208 Lecture 2 10 Wave properties Wave has both space and time dependence Shows constant time intervals

Thursday, Sep. 3Phy208 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 Mathematically:

Thursday, Sep. 3Phy208 Lecture 2 12 Moving wave crests Period = 1 second Propagation speed = v

Thursday, Sep. 3Phy208 Lecture 2 13 Same period, slower wave velocity Period = 1 second Propagation speed = v/2

Thursday, Sep. 3Phy208 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

Thursday, Sep. 3Phy208 Lecture 2 15 Wave relations Velocity = Wavelength / Period v = / T, or v = f f = Frequency = 1 / Period = 1/T Sinusoidal traveling wave: or Wavenumber ( m -1 ) Angular frequency (rad/s)

Phase difference between waves Thursday, Sep. 3Phy208 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˚  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 Thursday, Sep. 3Phy208 Lecture 2 17 Wavenumber Angular frequency Phase Shift

Thursday, Sep. 3Phy208 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.

Thursday, Sep. 3Phy208 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

Thursday, Sep. 3Phy208 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 + =

Thursday, Sep. 3Phy208 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.

Thursday, Sep. 3Phy208 Lecture 2 22 Interference of 2 speakers crest trough constructive interference,loud tone destructive interference quit tone

Thursday, Sep. 3Phy208 Lecture 2 23 A little more detail Same distance, same phase Path 1 Path 2 Path-length difference  = (Path 2) - (Path 1) = 0 d Path 1 Path 2

Thursday, Sep. 3Phy208 Lecture 2 24 Other angles? Interference: Constructive:  =  = Extra path length d  Path 1 Path 2 Path-length difference  0 Destructive:  =