1Wednesday, Jan. 23 Phy208 Lecture 11Physics 208, Spring 2008 Waves: Interference and Diffraction (Chap. 20-22) Colors in soap films, CDs, and butterfly wings Refraction of Light, and Optics (Chap. 23) Telescopes, microscopes, and eyes Electricity and Magnetism (Chap. 25-32) Capacitors & cell membranes, battery-less flashlights Electromagnetic Waves (Chap. 33-34) Light and polarization Modern Physics (Chap. 37-42) Radiation and matter, radioactivity, nuclear fission http://www.physics.wisc. edu/undergrads/courses/sp ring08/208Wednesday, Jan. 23 Phy208 Lecture 12Your Profs and TAsWednesday, Jan. 23 Phy208 Lecture 13Lectures Monday, Wednesday 8:50-9:40 am,2103 Chamberlin Includes Demonstrations Examples Quick questions Honors lecture / discussion Friday 8:50-9:30, 2103 Chamberlin All welcome, but required for those signed up for honors(B or better course grade also required for honors)Wednesday, Jan. 23 Phy208 Lecture 14Discussions and LabsDiscussionsTuesday and Thursday (begin tomorrow, Jan. 24)Weekly Q&A, group problem, quiz.Labs - start next week (3254 Chamberlin). - No lab notebook: question sheets distributed. - 10 of 11 labs must be completed to pass the course. - Complete only 10 -> 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 uponly during the immediately following exam week.Wednesday, Jan. 23 Phy208 Lecture 15 Homework: (Mastering Physics)Should be able to use your login from Physics 207– Follow email instructions for registering• Assigned each Thursday,due the following Thursday at midnight.• First assignment:HW1 on Jan. 24 due on Jan. 31 at midnightText: (Same as Physics 207 last semester)Wednesday, Jan. 23 Phy208 Lecture 16ExamsExam 1: Wed. Feb. 20 5:30-7 pmExam 2: Wed. Mar. 26 5:30-7 pmExam 3: Wed. Apr. 23 5:30-7 pmCumulative Final Exam: Mon. May 12 12:25-2:25 pmExams make up most of your grade (70%) 1 1/2 hour midterm exams Typically 5-6 problems (old exams at web site) Multiple choice Short answer Longer calculation2Wednesday, Jan. 23 Phy208 Lecture 17GradingTue & Thurs10%Discussion1:30 hrs1:30 hrs1:30 hrs2:00 hrs15 %15%15%25%Exams:MTE1MTE2MTE3FinalMastering Physics10%Homework10 of the 11 labs requiredto pass the courseLab grade reduced 30% ifonly 10 labs completed10%LabsCommentsWeightWednesday, Jan. 23 Phy208 Lecture 18Last semester:mechanical waves Examples Sound waves Water waves Earthquake waves Medium required Wave describesdisplacement of mediumThis semester:electromagnetic waves Examples Light waves Radio waves Microwaves X-rays No medium required Can propagate in vacuum Wave describes local electricand magnetic fieldsWednesday, Jan. 23 Phy208 Lecture 19Common wave propertiesReflectionSuperpositionWednesday, Jan. 23 Phy208 Lecture 110Wave properties• Wave has both space and time dependenceShows constant time intervalsWednesday, Jan. 23 Phy208 Lecture 111crestPeriodic wave• Repeats continuously, moves in space• Wavelength λ: distance to complete one cycle• Period T: time to complete one cycle• Frequency f: 1/Periodtrough! A sin2"#x $2"Tt% & ' ( ) * Mathematically:Wednesday, Jan. 23 Phy208 Lecture 112Moving wave crests• Period = 1 second• Propagation speed = v3Wednesday, Jan. 23 Phy208 Lecture 113Same period, slower wave velocity• Period = 1 second• Propagation speed = v/2Wednesday, Jan. 23 Phy208 Lecture 114Freq., wavelength, velocity are related• Period:– Time interval between crests at some location, or– Time for source to emit once cycle of the wave.• Wavelength:– Spatial distance between crests.• Source emits a crest once every period T.• This crest propagates at velocity v.• By the time the source emits another crest T secondslater, the first crest has moved vT.• So the distance between crests is vT.– This is the wavelength of the wave• Wavelength = velocity × periodWednesday, Jan. 23 Phy208 Lecture 115Equation form• Velocity = Wavelength / Period• v = λ / T, or v = λf• f = Frequency = 1 / Period = 1/TWednesday, Jan. 23 Phy208 Lecture 116Interference• Water drop is a source ofcircular waves (two-dimensions here)• When the waves overlap,they superimpose.• In some areas they cancel,in others they reinforce.• This is called interferenceWednesday, Jan. 23 Phy208 Lecture 117Destructive Interference in aString• Two pulses are traveling inopposite directions• The net displacement whenthey overlap thedisplacements of the pulsessubtract• Note that the pulses areunchanged after theinterferenceWednesday, Jan. 23 Phy208 Lecture 118Destructive interference in acontinuous wave• Two waves, a and b, havethe same amplitude andfrequency• They are 1/2 wavelengthout of phase• When they combine, thewaveforms cancel+=4Wednesday, Jan. 23 Phy208 Lecture 119Setting up destructive interference• Sound takes two paths to arrive at ear• One path 1/2 wavelength longer than other• Results in destructive interferenceDestructiveDestructiveinterference forfrequencies such thatpath lengthdifference is 1/2wavelength.Wednesday, Jan. 23 Phy208 Lecture 120QuestionTwo speakers each emit a 340 Hz sound wave.At what separation of these speakers wouldyou hear a quieter sound by turning on oneof the speakers? (sound velocity = 340 m/s)A. 0.1 mB. 0.25 mC. 0.5 mD. 1.0 mE. 2.0 mWednesday, Jan. 23 Phy208 Lecture 121Interference of 2 speakerscresttroughconstructiveinterference,loud tonedestructiveinterferencequit toneWednesday, Jan. 23 Phy208 Lecture 122A little more detailSame distance,same phasePath 1Path 2Path-length differenceδ = (Path 2) - (Path 1) = 0dPath 1Path 2Wednesday, Jan. 23 Phy208 Lecture 123Other angles?Interference:Constructive: δ=δ = Extra path lengthd! "/ d = sin#"= d sin#θPath 1Path 2Path-length difference δ≠0Destructive: δ=! m"! 2m + 12" ! "= 0, #, 2#, 3#K ! "=12#, 32#, 52#KWednesday, Jan. 23 Phy208 Lecture 124Interferenceengineering5Wednesday, Jan. 23 Phy208 Lecture 125Line array works by interference• Off-axis sound canceled by interference on thevertical axis.• Horizontal plane unaffected• Total sound intensity drops off more slowlyWednesday, Jan. 23 Phy208 Lecture 126QuestionIn your room you have two speakers in differentcorners. At your desk you are exactly 1 meter fromeach, so that there is no
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