1Phy107 Fall 20061Wavelength, frequency, and velocity are all related.Waves can add up, either giving a wave of largeramplitude, or one of smaller amplitude.HW#4: Chapter 8: Conceptual: # 19, Problems: # 2, 7Chapter 9: Conceptual: # 4, 10 Problems: # 2, 4, 8From last time…Phy107 Fall 20062Interference 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 phase diff’Phy107 Fall 20063Superimposing sound waves• Depending on your relative distance fromtwo identical sound sources, the soundintensity can vary.• Important aspect is relative distance fromeach source in wavelengths!Destructive interference for 1 half wavelength, also for3 half wavelengths, 5 half-wavelengths, etc.Constructive interference also occurs at differences of2 whole wavelengths, 3 whole wavelengthsPhy107 Fall 20064Interference of 2 speakerscresttroughconstructiveinterference,loud tonedestructiveinterferencequit tonePhy107 Fall 20065InterferenceengineeringPhy107 Fall 20066Doppler Effect• A Doppler effect is experienced whenever there isrelative motion between a source of waves and anobserver.• For instance, a fire engine or train passing you.– When the source and the observer are moving toward eachother, the observer hears a higher frequency– When the source and the observer are moving away fromeach other, the observer hears a lower frequency• Although the Doppler Effect is commonlyexperienced with sound waves, it is a phenomenacommon to all waves2Phy107 Fall 20067Doppler Effect for a moving source• 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 lowerPhy107 Fall 20068Shock Waves and Sonic Booms• A shock waveresults when thesource velocityexceeds the speedof the wave itself• The circlesrepresent thewave frontsemitted by thesourcePhy107 Fall 20069Sonic Boom• Source of sound approaching the listener is equal to orfaster than the speed of sound• Each successive wave is superimposed on the previous one• Shock wave results as air compression in crest gets very largePhy107 Fall 200610Breaking the sound barrier• No sound received till after thesource passes the listener - then asonic boom - followed by normalsound from the source• Conical bow wake from condensedwater vapor at high pressure shockwave front.Phy107 Fall 200611Breaking the ‘sound’ barrier in a canoe!If the canoe moves faster thanthe water wave velocity, shockwave also builds up where allthe crests line up.For water wave velocity ~1 m/s,so Mach 2 is 2 m/s= 4.5 mph !!Phy107 Fall 200612Resonance• So far have been talking about waves traveling in media that extend in all directions.• In a finite object, the boundaries cause reflections.• The reflected wave interferes with rest of wave,causing destructive or constructive interference.• For destructive interference,the wave tends to die away.• But for constructive interference,the wave builds up.• Which one happens depends on wavelength.3Phy107 Fall 200613Most objects resonate• But even complicated objects havesome natural frequency of oscillation• Pendulum• Wine glass• Musical instruments• Natural frequency has to do with size andmaterials properties of object.Phy107 Fall 200614Closed tube resonancePhy107 Fall 200615Resonance on string• First three natural vibrationalmodes of a string fixed atboth ends (e.g. a guitarstring).• A normal pluck excitesprimarily the first vibrationalmode.Phy107 Fall 200616Wine glass resonancesHolographic interferometryshowing contour map ofvibration for differentmodes. Points of maximummotion appear as bull’seyes.Phy107 Fall 200617Driving at resonance• Can tune a speaker tothe fundamentalresonant frequency ofthe wine glass (here1210 Hz).• More and more energypoured into glass - theglass vibrates withlarger and largeramplitude.• The glass shatters asthe vibrationamplitude becomestoo large.Stroboscopic movie of fundamentalvibration mode of a wineglass.Phy107 Fall 200618Tacoma Narrows Bridge• Even a non-resonant drive cantransfer energy.• Driven by 40 mph wind• Causes vibration of bridge at itsnatural (resonant) frequency.Movie of bridgetorsional vibrations4Phy107 Fall 200619Electricity and Magnetism• Electric charge and electric forces• Magnetic forces• Unification of electric and magnetic forces– Understanding how they combine together– Electromagnetic wavesPhy107 Fall 200620Electrical Charge• Charge: intrinsic property of matter• Two types:– Positive Charge: Protons– Negative Charge: electrons– Opposites Attract! (likes repel)• Atoms are neutral– Positively charged central nucleus r~10-15 m– Negatively charged electrons orbit r~10-10 m• Charge is quantized(one electron or proton)Phy107 Fall 200621Electrical charge• Electrons carry electrical charge, and can bemoved from one material to another.• The electrons have a negative charge.• The unit of electric charge is the Coulomb• One electron carries only a tiny amount of chargeCharge on 1 electron = 1.6 x 10-19 CoulombTransferring 1 Coulomb of charge means that6,250,000,000,000,000,000 electrons have moved!Phy107 Fall 200622Positive and negative seperated• Triboelectric – friction• Conduction – contact• Induction– Proximity/ground• PolarizationPhy107 Fall 200623Separating charge• Positively charged rod can then be used totransfer electrons from other objects.Rod becomespositively chargedafter rubbing with fur.Electrons (negativecharges) have beentransferred from rodto fur.Phy107 Fall 200624Charge by conduction (touching)Neutralmetal+++++++++++++++++-----Positively charged rod(too few electrons)+++++++Less positively charged rod+++++Positivelychargedmetal+++++++++++++++++-----electron flowPith ball demo5Phy107 Fall 200625Interactions between chargesThe positively charged rod attracts negativecharges to the top of the electroscope.This leaves positive charges on the leaves.The like-charges on the leaves repel each other.attractive force between positive andnegative charges.repulsive force between two positiveor two negative chargeWhy did the electrons flow?Phy107 Fall 200626Force between chargesOpposite charges attractLike charges repel.• Other than the polarity, they interact
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