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Waves

Wavestransferenergywithouttransferringma3erTwocategoriesofwaves:

Mechanicalwaves:requireamediumfortheirtransfer e.g.waterwavesorsoundwaves(air)

Electromagne8cwaves:consistofelectricandmagnecfieldsoscillangatrightanglestoeachother

e.g.radiaon,lightTwoformsofwaves:

Transversewaves:oscillaonsareperpendiculartothedireconofthewave

Longitudinalwaves:oscillaonsareparalleltothedireconofthewave 1

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Waves

TransverseWave

LongitudinalWave

crest

trough

compression rarefacon

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De(initions

Frequencyf:thenumberofcrestsorcompressionspassingthroughagivenposionpersecond(Hz)

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De(initions


PeriodT=1/f:themetakenbetweenbetweentwosuccessivewavecrests(orcompressions)arrivingata

parcularposion(seconds)

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De(initions




AmplitudeA:themaximumdisplacementfromthemeanposion

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De(initions




AmplitudeA:themaximumdisplacementfromthemeanposion(isameasureoftheenergycarriedbythewave)

Wavelength:thedistancebetweentwosuccessivecrestsortroughs(meters)

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De(initions




AmplitudeA:themaximumdisplacementfromthemeanposion(isameasureoftheenergycarriedbythewave)

Wavelength:thedistancebetweentwosuccessivecrestsortroughs(meters)

Phase:describesalocaonwithinasinglewavelengthA

B

C

D

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Phasedifference

0 180 360

Thephasedifferencebetweentwopointsalongawaveisthefracon

ofacyclebywhichonelagsbehindtheother

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Phasedifference

Wecanalsotalkaboutthephasedifferencebetween

twowaves

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Phasedifferenceand

wavelength Onecyclecorrespondsto2radians=onefullwavelength

Phasedifference=2x/ Bothtransverseandlongitudinalwavesareprogressivewaves:thewaveprofilemovesalongwiththespeedofthe

wave,andthewaverepeatsitselfatequaldistances

Wavespeedc=/T=f

A

B

x

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ProgressiveWaveequation

Angularfrequencyofoscillaon:=2/T=2f

Displacement whereistheamplitude

PhasedifferencebetweenOandA:=2x/

Displacementatdistancex:

Adisplacement

wavedirecon

x

yO

y =sint=sin(2 ft)

y =sin(t) =sin(2 tT

2 x) =sin2 t

T x

"#$ %

&'

(thevesignisbecausethewaveis

movingfromle\torightsoAlags

behindO)y =sin2

t

T+

x

!

"#

$

%&

Forawavetravellingintheopposite

direcon: 11

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PrincipleofSuperposition

Whentwowavesaretravellingthroughthesamemedium,thedisplacementatanypointcanbefoundbyaddingupthe

separatedisplacementsduetothetwowaves

y = y1 +y2 =sin(t)+sin(t)12

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Stationarywaves

Asta8onary(orstanding)waveisawavethatappearstoremaininaconstantposion

Nodes:posionsofzerodisplacement An8-nodes:posionsofmaximumdisplacement

nodean-node

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Stationarywaves

Principleofsuperposionapplies Displacementatdistancex

Wavetravellingtotheright

Wavetravellingtothele\

Resultantwave

y 1=

sin(t)

=

sin(t

2x

)

y2 =

sin(t+) =sin(t+2x

)

y = y1 +y 2 =sin(t2x

)+sin(t+

2x

) =

= 2sin(t)cos(2x

) = Asin(t)where

A = 2cos(2x

)

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Example

Twowaveswhosedisplacementequaonsare

arepropagangthroughthesameelascmaterialinopposite

direcons.Thedistancesxandyareincm,andthemetin

seconds.

a)Whatistheequaonoftheresulngstaonarywave?

b)Whatistheamplitudeofthevibraonofthewaveatthe

pointx=3.025cm?

y1= 8sin2

t

0.3 5x

"

#$

%

&' y2 = 8sin2

t

0.3+5x

!

"#

$

%&and

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HarmonicsandOvertones

=LEtc

=2L

=?

nthharmonic:

=2

nL

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Example

Thestringshownis6.0meterslongandisvibrangasthethirdharmonic.Thestringvibratesupanddownwith45

completevibraonalcyclesin10seconds.Determinethe

frequency,period,wavelengthandspeedforthiswave.

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Propertiesofwaves

Reflec8on:waveschangedireconwhentheybounceoffabarrier.angle

ofincidence=angleofreflecon

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Propertiesofwaves



Refrac8on:waveschangedireconastheypassfromonemediumto

another(thespeedofthewavealso

changes)

i

r

Air

Water

Incidentray

Refractedray

Angleofrefracon

Angleofincidence

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Propertiesofwaves





changes)

sin i

sinr= SnellsLaw.iscalledtherefrac8veindex

=WavespeedinsubstanceA

WavespeedinsubstanceB 20

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Propertiesofwaves





changes)

Dispersion:wavespreadsoutintocomponentfrequencies(through

refracon)

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Propertiesofwaves





changes)


refracon)

Diffrac8on:wavebendswhenpassingthroughagaporaroundan

obstacle

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Propertiesofwaves





changes)


refracon)


obstacle

Interference:coherentwavessuperimpose

Wave1

Wave2

Resultant

wave

Construcveinterference

Wave1

Wave2

Resultant

wave

Destrucveinterference

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Propertiesofwaves





changes)


refracon)


obstacle


Polariza8on:wavesthatareallowedtooscillateinasingle

direconarecalledpolarized

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Propertiesofwaves





changes)


refracon)


obstacle


Polariza8on:wavesthatareallowedtooscillateinasingle

direconarecalledpolarized

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ToDo

Readsecon16fromthebook[p.304-p.318Wavemoon] HomeworkAssignmentwk6:quesons16.2,16.,16.5,16.6,16.11

Handitinnolaterthan4:00pmontheWednesdayaVerthereadingweek-LATEWORKWILLNOTBEACCEPTED

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Documents

Waves - P2, week 6