PropertiesofWaves
OneofthemostelegantandgracefulOlympicsportsisrhythmicgymnastics.A
ribbondancerflicksastickattachedtoaribbon,makingwavestraveldownthe
ribbon.Someofthewavesarelong,whileothersareshorter.Therateatwhichthe
gymnastflicksherhandsaffectsthelengthandshapesofthewavesintheribbon.
Therearemanydifferentkindsofwaves.Wavescancarryalittleenergyora
lot.Theycanbeshortorlong.Theycanberareorfrequent.Theycantravelfastor
slow.Allwaves,however,sharecertainproperties.Thebasicpropertiesofwaves
areamplitude,wavelength,frequencyandspeed.
WaveDiagrams
Tounderstandthepropertiesofwaves,ithelpstorepresentawaveona
diagram.Transversewaveslikethoseonaropeareeasytodraw.Youcandrawa
transversewaveasshowninFigure5.Thinkofthehorizontallineasthepositionof
theropebeforeitisdisturbed.Thisisitsrestposition.Asthewavepasses,therope
goesaboveorbelowtherestposition.Rememberthatthecrestsandthetroughsare
thehighestandlowestpointsonthewave.
Todrawlongitudinalwaves,thinkofthecompressionsinthespringtoyasbeingsimilartothe
crestsofatransversewave.Therarefactionsinthespringtoyarelikethetroughsofatransversewave.
Bytreatingcompressionsascrestsandrarefactionsastroughs,youcandrawlongitudinalwavesinthe
samewayastransversewaves.
Amplitude
Somewavesareveryhigh,whileothersarebarelynoticeable.Thedistancethemediumraises
dependsontheamplitudeofthewavethatpassesthroughit.Amplitudeisthemaximumdistancethe
particlesofthemediumcarrythewavemoveawayfromtheirrestpositions.Theamplitudeisameasure
ofhowmuchaparticleinthemediummoveswhendisturbedbythewave.Theamplitudeofawater
waveisthemaximumdistanceawaterparticlemoves
aboveorbelowthesurfacelevelofcalmwater.
Youknowthatwavesareproducedbysomething
vibrating.Thefartherthemediummovesasitvibrates,
thelargertheamplitudeoftheresultingwaves.Youcan
increasetheamplitudeofthewavesonaropebymoving
yourhandupanddownagreaterdistance.Todothis,
youhavetousemoreenergy.Thisgreateramountof
energyisthentransferredtotherope.Thus,the
amplitudeofawaveisadirectmeasureofitsenergy.
AmplitudeofTransverseWaves
Comparethetwotransversewavesin
A
B
figure.YoucanseethatwaveBgoesupand
downagreaterdistancethanwaveA.The
amplitudeofatransversewaveisthemaximum
distancethemediummovesupordownfromits
restposition.Youcanfindtheamplitudeofa
transverswavebymeasuringthedistanceform
therestpositiontoacrestortoatrough.
AmplitudeofLongitudinalWaves
Theamplitudeofalongitudinalwaveisameasureofhowcompressedorrarefiedthemedium
becomes.High-energyvibrationscausethecompressionstobeverycrowded.Thismakesthe
rarefactionsquiteloose.Crowdedcompressionsanduncrownedrarefactionsarelikehighcrestsandlow
troughs.Thatmeansthatlongitudinalwaveshavelargeamplitude.
Wavelength
Awavetravelsacertaindistancebeforeitstartstorepeat.Thedistancebetweentwo
correspondingpartsofawaveisitswavelength.Youcanfindthewavelengthofatransversewaveby
measuringthedistancefromcresttocrestorfromtroughtotrough.Youfindthewavelengthofa
longitudinalwavebymeasuringthedistancefromcompressiontocompression.
Frequency
Wavefrequencyisthenumberofcompletewavesthatpassagivenpointinacertainamountof
time.Ifyoumakewavesonaropesothatonewavepassedbyeverysecond,thefrequencyis1waveper
second.Sincewavesarevibrationsofamedium,frequencycanalsobedescribedasthenumberof
vibrationspersecond.Toincreasethefrequencyofthewavesonarope,youcanmakemorevibrations
bymovingyourhandupanddownmoreoften,(perhapstwoorthreetimespersecond).Todecreasethe
frequency,youmoveyourhandlessoften,perhapsonceeverytwoorthreeseconds.
Frequencyismeasuredinunitscalledhertz(Hz).Awaveorvibrationthatoccurseverysecond
hasafrequencyof1Hz.Iftwowavespassyoueverysecond,thenthefrequencyofthewaveis2per
second,or2Hertz.ThehertzwasnamedaftertheGermanscientistHeinrichHertz,whofirstproduced
radiowavesinanexperimentalsituation.
Speed
Imaginewatchingadistantthunderstormonahotsummerday.Firstyouseetheflashof
lightning,thenafewsecondslateryouheartherollofthunder.Eventhoughthelightningandthunder
occurredatthesameinstant,theyreachyousecondsapart.Thishappensbecausesoundandlighttravel
atverydifferentspeeds.Lighttravelsmuchfasterthansound.Differentwavestravelatdifferentspeeds.
Thespeedofawaveishowfarthewavetravelsinoneunitoftime,ordistancedividedbytime.
Thespeed,wavelengthandfrequencyofawavearerelatedtoeachotherbyamathematical
formula:
Speed=WavelengthxFrequency
Ifyouknowanytwoofthequantitiesinthespeedformula–speed,wavelength,andfrequency–
youcancalculatethethirdquantity.Forexampleifyouknowthespeedandthewavelengthofawave,
youcancalculatethefrequency.Ifyouknowthespeedandthefrequency,youcancalculatethe
wavelength.
Wavesindifferentmediumstravelatdifferentspeeds.Inagivenmediumandunderthesame
conditionsthespeedofawaveisconstant.Forexample,allsoundwavestravelingthroughtheairatthe
samepressureandatthesametemperaturetravelatthesamespeed.Ifthetemperatureorpressure
changes,thesoundwaveswilltravelatadifferentspeed.
Ifonetypeofwavetravelsataconstantspeedinonemedium,whatdoyouthinkwill
happenifthefrequencychanges?Whenyoumultiplythewavelengthandfrequencyafterthechange,you
shouldgetthesamespeedasbeforethechange.Therefore,ifyouincreasethefrequencyofawavethe
wavelengthmustdecrease.