《物理双语教学课件》Chapter 10 Waves 波动.docx

《物理双语教学课件》Chapter 10 Waves 波动.docx

《《物理双语教学课件》Chapter 10 Waves 波动.docx》由会员分享，可在线阅读，更多相关《《物理双语教学课件》Chapter 10 Waves 波动.docx（15页珍藏版）》请在冰豆网上搜索。

《物理双语教学课件》Chapter10Waves波动

Chapter10Waves

10.1TypesofWaves

1.Mechanicalwaves:

Thesewavesaremostfamiliarbecauseweencounterthemalmostconstantly;commonexamplesincludewaterwaves,soundwaves,andseismicwaves.Allthesewaveshavecertaincentralfeatures:

theyaregovernedbyNewton’slaws,andtheycanexistonlywithinamaterialmedium,suchaswater,air,androck.

2.Electromagneticwaves:

Thesewavesarelessfamiliar,butyouusethemconstantly;commonexamplesincludevisibleandultravioletlight,radioandtelevisionwaves,microwaves,x-rays,andradarwaves.Thesewavesrequirenomaterialmediumtoexist.Lightwavesfromstars,forexample,travelthroughthevacuumofspacetoreachus.Allelectromagneticwavestravelthroughavacuumatthesamespeedc,givenbyc=299,792,458m/s.

3.Matterwaves:

Althoughthesewavesarecommonlyusedinmoderntechnology,theirtypeisprobablyveryunfamiliartoyou.Electrons,protons,andotherfundamentalparticles,andevenatomsandmolecules,travelaswaves.Becausewecommonlythinkofthesethingsasconstitutingmatter,thesewavesarecalledmatterwaves.

4.Muchofwhatwediscussinthischapterappliestowavesofallkinds.However,forspecificexamplesweshallrefertomechanicalwaves.

10.2TransverseandLongitudinalWaves

1.Transversewave

（1）.Awavesentalongastretched,tautstringisthesimplestmechanicalwave.Ifyougiveoneendofastretchedstringasingleup-and-downjerk,awaveintheformofasinglepulsetravelsalongthestring,asinthefigure.Thispulseanditsmotioncanoccurbecausethestringisundertension.Whenyoupullyourendofthestringupward,itbeginstopullupwardontheadjacentsectionofthestringviatensionbetweenthetwosections.Astheadjacentsectionmovesupward,itbeginstopullthenextsectionupward,andsoon.Meanwhile,youhavepulleddownonyourendofthestring.So,aseachsectionmovesupwardinturn,itbeginstobepulledbackdownwardbyneighboringsectionsthatalreadyonthewaydown.Thenetresultisthatadistortioninthestring’sshape（thepulse）movesalongthestringatsomevelocityv.

（2）.Ifyoumoveyourhandupanddownincontinuoussimpleharmonicmotion,acontinuouswavetravelsalongthestringatvelocityv.Becausethemotionofyourhandisasinusoidalfunctionoftime,thewavehasasinusoidalshapeatanygiveninstant,asinthefigure（b）.Thatis,thewavehastheshapeofasinecurveoracosinecurve.

（3）.Weconsiderhereonlyan“ideal”string,inwhichnofriction-likeforceswithincausethewavetodieoutasittravelsalongthestring.Inaddition,weassumethatthestringissolongthatweneednotconsiderawavereboundingfromthefarend.

（4）.Onewaytostudythewavesofthefigureistomonitorthewave’sform（shapeofwave）asitmovestotheright.Alternatively,wecanmonitorthemotionofanelementofthestringastheelementoscillatesupanddownwhilethewavepassesthroughit.Wewouldfindthatthedisplacementofeverysuchoscillatingstringelementisperpendiculartothedirectionoftravelofthewave,asindicatedinthefigure.Thismotionissaidtobetransverse,andthewaveissaidtobeatransversewave.

2.Longitudinalwave:

（1）.Therightfigureshowshowasoundwavecanbeproducedbyapistoninalong,airfilledpipe.Ifyousuddenlymovethepistonrightwardandthenleftward,youcansendapulseofsoundalongthepipe.Therightwardmotionofthepistonmovestheelementsofairnexttoitrightward,changingtheairpressurethere.Theincreasedairpressurethenpushesrightwardontheelementofairsomewhatfartheralongthepipe.Oncetheyhavemovedrightward,theelementsmovebackleftward.Thusthemotionoftheairandthechangeinairpressuretravelrightwardalongthepipeasapulse.

（2）.Ifyoupushandpullonthepistoninsimpleharmonicmotion,asisbeingdoneinthefigure,asinusoidalwavetravelsalongthepipe.Becausethemotionoftheelementsofairisparalleltothedirectionofthewave’stravel.Themotionissaidtobelongitudinalwave.

3.Bothatransversewaveandalongitudinalwavearesaidtobetravelingwavesbecausethewavetravelsfromonepointtoanother,asfromoneendofthestringtotheotherendorfromoneendofthepipetotheotherend.Notethatitisthewavethatmovesbetweenthetwopointsandnotthematerial（stringorair）throughwhichthewavemoves.

10.3WavelengthandFrequency

1.Introduction

（1）.Tocompletelydescribeawaveonastring,weneedafunctionthatgivestheshapeofthewave.Thismeansthatweneedarelationintheform

inwhichyisthetransversedisplacementofanystringelementasafunctionhofthetimetandthepositionxoftheelementalongthestring.Ingeneral,asinusoidalshapelikethewavecanbedescribedwithhbeingeitherasinefunctionoracosinefunction;bothgivethesamegeneralshapeforthewave.Inthischapterweusethesinefunction.

（2）.Forasinusoidalwave,travelingtowardincreasingvaluesofx,thetransversedisplacementyofastringelementatpositionxattimeisgivenby

here

istheamplitudeofthewave;thesubscriptmstandsformaximum,becausetheamplitudeisthemagnitudeofthemaximumdisplacementofthestringelementineitherdirectionparalleltotheyaxis.Thequantitieskand

areconstantswhosemeaningsareabouttodiscuss.Thequantity

iscalledthephaseofthewave.

2.

WavelengthandangularWaveNumber

（1）.Thefigureshowshowthetransversedisplacementyvarieswithpositionxataninstant,arbitrarilycalledt=0.Thatis,thefigureisa“snapshot”ofthewaveatthatinstant.Witht=0,thewaveequationbecomes

.TheFigure（a）isaplotofthisequation;itshowstheshapeoftheactualwaveattimet=0.

（2）.Thewavelength

ofawaveisthedistancebetweenrepetitionsofthewaveshape.Atypicalwavelengthismarkedinfigure（a）.Bydefinition,thedisplacementyisthesameatbothendsofthiswavelength,thatis,at

and

.Thus

.

（3）.Asinefunctionbeginstorepeatitselfwhenitsangleisincreasedby

rad;sowehave

.Wecallktheangularwavenumberofthewave;itsSIunitistheradianpermeter.

3.Period,angularfrequency,andfrequency:

（1）.Thefigure（b）showshowthedisplacementyvarieswithtimetatafixedposition,takentobex=0.Ifyouweretomonitorthestring,youwouldseethatthesingleelementofthestringatthatpositionmovesupanddowninsimpleharmonicmotionwithx=0:

.Thefigure（b）isaplotofthisequation;itdoesnotshowtheshapeofthewave.

（2）.WedefinetheperiodofoscillationsTofawavetobethetimeintervalbetweenrepetitionsofthemotionofanoscillatingstringelement.Atypicalperiodismarkedinthefigure（b）.Wehave

.

（3）.Thiscanbetrueonlyif

.Wecall

theangularfrequencyofthewave;itsSIunitistheradianpersecond.

（4）.Thefrequencyfofthewaveisdefinedas1/Tandisrelatedtotheangularfrequencyby

.Thisfrequencyfisanumberofoscillationsperunittime-madebyastringelementasthewavemovesthroughit,andfisusuallymeasuredinhertzoritsmultiples.

10.4TheSpeedofaTravelingwave

1.Thefigureshowstwosnapshotsofthewavetakenasmalltimeinterval

apart.Thewaveistravelinginthedirectionofincreasingx,theentirewavepatternmovingadistance

inthatdirectionduringtheinterval

.Theratio

（or,inthedifferentiallimit,dx/dt）isthewavespeedv.Howcanwefinditsvalue?

2.Asthewavemoves,eachpointofthemovingwaveformretainsitsdisplacementy.Foreachsuchpoint,theargumentofthesinefunctionmustbeaconstant:

.

3.Tofindwavespeedv,wetakethederivativeoftheequation,get

.Theequationtellsusthatthewavespeedisonewavelengthperperiod.

4.Thewaveequation

describesawavemovinginthedirectionofincreasingx.

（1）.Wecanfindtheequationofawavetravelingintheoppositedirectionbyreplacingtwith–t.

（2）.Thiscorrespondstothecondition

.（3）.Thusawavetravelingtowarddecreasingxisdescribedbytheequation

.（4）.Itsvelocityis

.

5.Considernowawaveofgeneralizedshape,givenby

wherehrepresentsanyfunction,thesinefunctionbeingonepossibility.Ouranalysisaboveshowsthatallwavesinwhichthevariablesxandtenterinthecombination

aretravelingwaves.Furthermore,alltravelingwavesmustbetheformabove.Thus

representsapossibletravelingwave.Thefunction

ontheotherhand,doesnotrepresentatravelingwave.

6.WaveSpeedonaStretchedString

（1）.Thespeedofawaveisrelatedtothewave’swavelengthandfrequency,butitissetbythemedium.Ifawaveisthroughamediumsuchaswater,air,steel,orastretchedstring,itmustcausetheparticlesofthatmediumtooscillateasitpasses.Forthathappen,themediummustpossessbothinertiaandelasticity.Thesetwopropertiesdeterminehowfastthewavecantravelinthemedium.Andconversely,itshouldbepossibletocalculatethespeedofthewavethroughthemediumintermsoftheseproperties.

（2）.WecanderivethespeedfromNewton’ssecondlawas

where

isthelineardensityofthestring,and

thetensioninthestring.

（3）.Theequationtellsusthatthespeedofawavealongastretchedidealstringdependsonlyonthecharacteristicsofthestringandnotonthefrequencyofthewave.

10.5EnergyandPowerofaTravelingStringWave

Whenwesetupawaveonastretchedstring,weprovideenergyforthemotionofthestring.Asthewavemovesawayfromus,ittransportsthatenergyasbothkineticenergyandelasticpotentialenergy.Letusconsidereachformin