1Mon, Mar. 6 2006 Phy107 HE2 review1Hour Exam 2: Wednesday, March 8• In-class, covering waves, electromagnetism, and relativity• Twenty multiple-choice questions• Will cover: March Chap 6-7,9-12Griffith Chap 12,15,16All lecture material• You should bring– 1 page notes, written double sided– #2 Pencil and a Calculator– Review Monday March 6– Review questions online under “Review Quizzes” linkMon, Mar. 6 2006 Phy107 HE2 review2Topics covered in Exam 2• Waves, interference, resonance, andelectromagnetism• EM radiation, light, color• Special Relativity time & space• Special Rel. energy, & General RelativityMon, Mar. 6 2006 Phy107 HE2 review3Wave properties• Amplitude is the maximum displacement ofstring above the equilibrium position• Wavelength, λ, is the distance between twosuccessive points that behave identically• Period: time required to complete one cycle• Frequency = 1/Period = rate at which cyclesare completed• Velocity = Wavelength/Period,v = λ / T, or v = λfMon, Mar. 6 2006 Phy107 HE2 review4Types of wave motion• Longitudinal wave– Vibrations are in the direction of motion• Transverse wave– Vibrations are perpendicular to the direction ofmotion.Mon, Mar. 6 2006 Phy107 HE2 review5Waves QuestionsWhen both transverse and longitudinal waves arepresent (such as p and s seismic waves in the Earth),the longitudinal wave usually travels faster.If the longitudinal wave travels twice as fast as thetransverse wave of the same frequency, how aretheir wavelengths related?A. Longitudinal wavelength twice as longB. Longitudinal wavelength half as longC. Both same.Mon, Mar. 6 2006 Phy107 HE2 review6Superposition & interference• Superposition of waves• Interference of waves on a string• Interference of sound waves– Constructive interference– Destructive interference• Doppler effect– Change in apparent frequency due to motionof source or observer2Mon, Mar. 6 2006 Phy107 HE2 review7Interference of sound waves• Interference arises when waves change their‘phase relationship’.• Can vary phase relationship of two waves bychanging physical location of speaker.ConstructiveDestructive‘in-phase’‘1/2 λ phase diff’Mon, Mar. 6 2006 Phy107 HE2 review8Interference of 2 speakerscresttroughconstructiveinterference,loud tonedestructiveinterferencequit toneMon, Mar. 6 2006 Phy107 HE2 review9Interference questionYou are standing at a point where the signals from tworadio antennas cancel exactly.The towers broadcast at 1000 kHz.You walk around with a constant distance from tower 1.How much closer to tower 2 do you need to go to getfull constructive interference (strong radio signal)?A. 300 metersB. 150 metersC. 75 metersMon, Mar. 6 2006 Phy107 HE2 review10Interference summary• Important quantity is distance differencein number of wavelengths.• A distance difference of a half wavelengthleads to destructive interference.• Whole wavelength differenceslead to constructive interference.But destructive interference also for3 half wavelengths, 5 half-wavelengths, etc.Constructive interference also occurs at differences of2 whole wavelengths, 3 whole wavelengthsMon, Mar. 6 2006 Phy107 HE2 review11Doppler Effect• As the source movestoward the observer (A),the wavelength appearsshorter and the frequencyincreases• As the source moves awayfrom the observer (B),the wavelength appearslonger and the frequencyappears to be lowerMon, Mar. 6 2006 Phy107 HE2 review123Mon, Mar. 6 2006 Phy107 HE2 review13Resonance• Vibrational modes are accurately shown by means ofholographic interferometry, which displays a contour map ofthe vibration. Several modes of vibration of a wine glass areshown in the photo below. Points of maximum motion, whichoccur around the rim, appear as "bull's eyes." The vibrationalamplitude changes by half a wavelength of light (316 nm) inmoving from one bright fringe to the next one. Thefundamental mode, designated as the (2,0) mode, has foursuch regions, with the glass moving in alternate directions as itvibrates.Vibrational resonances of the wineglassStroboscopic movie offundamental vibrationmode of a wineglass.Mon, Mar. 6 2006 Phy107 HE2 review14Electrcity and magnetism• Coulomb force between charged particles– Same form as gravitational force• Electric field lines: path followed by charged particle• Electric current: flow of charged particles• Magnetic field:– arises from electric currents (moving charges)– also results in force on an electric current• Faraday effect:– changing magnetic field induces electric current– Magnetic field from induced currents opposes change inapplied fieldMon, Mar. 6 2006 Phy107 HE2 review15Electrical Charge• Only the negative charge moves around.These are the electrons.• The positive charges are protons.Protons and electrons form a ‘planetary’ atom.• Electrons orbit around a nucleus containing the protons.Compare planets orbiting around a sun.• Atoms are bound together, forming solid materials.Electrons can be torn from atoms,transferred to other materials.Mon, Mar. 6 2006 Phy107 HE2 review16Force between chargesOpposite charges attractLike charges repel.• Other than the polarity, they interact much likemasses interact gravitationally.• Force is along the line joining the particles.Gravitational force: FG=GM1M2/ r2G=6.7x10-11 Nm2/kg2Electrostatic force: FE = k Q1 Q2 /r2k = 9x109 Nm2/C2+—Force on positive particledue to negative particleMon, Mar. 6 2006 Phy107 HE2 review17Coulomb force questionIf the distance between two positive charges isincreased by a factor of two, the forcebetween themA. Increases by a factor of 2B. Decreases by factor of 2C. Decreases by a factor of 4Mon, Mar. 6 2006 Phy107 HE2 review18The idea of electric fields• EM wave made up ofoscillating electric and magnetic fields.• But what is an electric field?• Electric field is a way to describe the forceon a charged particle due to other chargesaround it.• Force = charge × electric field• The direction of the force is the direction ofthe electric field.4Mon, Mar. 6 2006 Phy107 HE2 review19Magnetic forces• North Pole and South Pole• This is the elementarymagnetic particle• Called magnetic dipole(North poleand south pole)• There are no magnetic‘monoples’ (magnetic charges)NSNSNSSNUnlikesattractLikesrepelMon, Mar. 6 2006 Phy107 HE2 review20Source of magnetic field• Current in wire produces magnetic field.• That magnetic field aligns compass
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