View
215
Download
0
Category
Preview:
Citation preview
7/29/2019 Waves - P2, week 6
1/26
Waves
Wavestransferenergywithouttransferringma3erTwocategoriesofwaves:
Mechanicalwaves:requireamediumfortheirtransfer e.g.waterwavesorsoundwaves(air)
Electromagne8cwaves:consistofelectricandmagnecfieldsoscillangatrightanglestoeachother
e.g.radiaon,lightTwoformsofwaves:
Transversewaves:oscillaonsareperpendiculartothedireconofthewave
Longitudinalwaves:oscillaonsareparalleltothedireconofthewave 1
7/29/2019 Waves - P2, week 6
2/26
Waves
TransverseWave
LongitudinalWave
crest
trough
compression rarefacon
2
7/29/2019 Waves - P2, week 6
3/26
De(initions
Frequencyf:thenumberofcrestsorcompressionspassingthroughagivenposionpersecond(Hz)
3
7/29/2019 Waves - P2, week 6
4/26
De(initions
Frequencyf:thenumberofcrestsorcompressionspassingthroughagivenposionpersecond(Hz)
PeriodT=1/f:themetakenbetweenbetweentwosuccessivewavecrests(orcompressions)arrivingata
parcularposion(seconds)
4
7/29/2019 Waves - P2, week 6
5/26
De(initions
Frequencyf:thenumberofcrestsorcompressionspassingthroughagivenposionpersecond(Hz)
PeriodT=1/f:themetakenbetweenbetweentwosuccessivewavecrests(orcompressions)arrivingata
parcularposion(seconds)
AmplitudeA:themaximumdisplacementfromthemeanposion
5
7/29/2019 Waves - P2, week 6
6/26
De(initions
Frequencyf:thenumberofcrestsorcompressionspassingthroughagivenposionpersecond(Hz)
PeriodT=1/f:themetakenbetweenbetweentwosuccessivewavecrests(orcompressions)arrivingata
parcularposion(seconds)
AmplitudeA:themaximumdisplacementfromthemeanposion(isameasureoftheenergycarriedbythewave)
Wavelength:thedistancebetweentwosuccessivecrestsortroughs(meters)
6
7/29/2019 Waves - P2, week 6
7/26
De(initions
Frequencyf:thenumberofcrestsorcompressionspassingthroughagivenposionpersecond(Hz)
PeriodT=1/f:themetakenbetweenbetweentwosuccessivewavecrests(orcompressions)arrivingata
parcularposion(seconds)
AmplitudeA:themaximumdisplacementfromthemeanposion(isameasureoftheenergycarriedbythewave)
Wavelength:thedistancebetweentwosuccessivecrestsortroughs(meters)
Phase:describesalocaonwithinasinglewavelengthA
B
C
D
7
7/29/2019 Waves - P2, week 6
8/26
Phasedifference
0 180 360
Thephasedifferencebetweentwopointsalongawaveisthefracon
ofacyclebywhichonelagsbehindtheother
8
7/29/2019 Waves - P2, week 6
9/26
Phasedifference
Wecanalsotalkaboutthephasedifferencebetween
twowaves
9
7/29/2019 Waves - P2, week 6
10/26
Phasedifferenceand
wavelength Onecyclecorrespondsto2radians=onefullwavelength
Phasedifference=2x/ Bothtransverseandlongitudinalwavesareprogressivewaves:thewaveprofilemovesalongwiththespeedofthe
wave,andthewaverepeatsitselfatequaldistances
Wavespeedc=/T=f
A
B
x
10
7/29/2019 Waves - P2, week 6
11/26
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
7/29/2019 Waves - P2, week 6
12/26
PrincipleofSuperposition
Whentwowavesaretravellingthroughthesamemedium,thedisplacementatanypointcanbefoundbyaddingupthe
separatedisplacementsduetothetwowaves
y = y1 +y2 =sin(t)+sin(t)12
7/29/2019 Waves - P2, week 6
13/26
Stationarywaves
Asta8onary(orstanding)waveisawavethatappearstoremaininaconstantposion
Nodes:posionsofzerodisplacement An8-nodes:posionsofmaximumdisplacement
nodean-node
13
7/29/2019 Waves - P2, week 6
14/26
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
)
14
7/29/2019 Waves - P2, week 6
15/26
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
15
7/29/2019 Waves - P2, week 6
16/26
HarmonicsandOvertones
=LEtc
=2L
=?
nthharmonic:
=2
nL
16
7/29/2019 Waves - P2, week 6
17/26
Example
Thestringshownis6.0meterslongandisvibrangasthethirdharmonic.Thestringvibratesupanddownwith45
completevibraonalcyclesin10seconds.Determinethe
frequency,period,wavelengthandspeedforthiswave.
17
7/29/2019 Waves - P2, week 6
18/26
Propertiesofwaves
Reflec8on:waveschangedireconwhentheybounceoffabarrier.angle
ofincidence=angleofreflecon
18
7/29/2019 Waves - P2, week 6
19/26
Propertiesofwaves
Reflec8on:waveschangedireconwhentheybounceoffabarrier.angle
ofincidence=angleofreflecon
Refrac8on:waveschangedireconastheypassfromonemediumto
another(thespeedofthewavealso
changes)
i
r
Air
Water
Incidentray
Refractedray
Angleofrefracon
Angleofincidence
19
7/29/2019 Waves - P2, week 6
20/26
Propertiesofwaves
Reflec8on:waveschangedireconwhentheybounceoffabarrier.angle
ofincidence=angleofreflecon
Refrac8on:waveschangedireconastheypassfromonemediumto
another(thespeedofthewavealso
changes)
sin i
sinr= SnellsLaw.iscalledtherefrac8veindex
=WavespeedinsubstanceA
WavespeedinsubstanceB 20
7/29/2019 Waves - P2, week 6
21/26
Propertiesofwaves
Reflec8on:waveschangedireconwhentheybounceoffabarrier.angle
ofincidence=angleofreflecon
Refrac8on:waveschangedireconastheypassfromonemediumto
another(thespeedofthewavealso
changes)
Dispersion:wavespreadsoutintocomponentfrequencies(through
refracon)
21
7/29/2019 Waves - P2, week 6
22/26
Propertiesofwaves
Reflec8on:waveschangedireconwhentheybounceoffabarrier.angle
ofincidence=angleofreflecon
Refrac8on:waveschangedireconastheypassfromonemediumto
another(thespeedofthewavealso
changes)
Dispersion:wavespreadsoutintocomponentfrequencies(through
refracon)
Diffrac8on:wavebendswhenpassingthroughagaporaroundan
obstacle
22
7/29/2019 Waves - P2, week 6
23/26
Propertiesofwaves
Reflec8on:waveschangedireconwhentheybounceoffabarrier.angle
ofincidence=angleofreflecon
Refrac8on:waveschangedireconastheypassfromonemediumto
another(thespeedofthewavealso
changes)
Dispersion:wavespreadsoutintocomponentfrequencies(through
refracon)
Diffrac8on:wavebendswhenpassingthroughagaporaroundan
obstacle
Interference:coherentwavessuperimpose
Wave1
Wave2
Resultant
wave
Construcveinterference
Wave1
Wave2
Resultant
wave
Destrucveinterference
23
7/29/2019 Waves - P2, week 6
24/26
Propertiesofwaves
Reflec8on:waveschangedireconwhentheybounceoffabarrier.angle
ofincidence=angleofreflecon
Refrac8on:waveschangedireconastheypassfromonemediumto
another(thespeedofthewavealso
changes)
Dispersion:wavespreadsoutintocomponentfrequencies(through
refracon)
Diffrac8on:wavebendswhenpassingthroughagaporaroundan
obstacle
Interference:coherentwavessuperimpose
Polariza8on:wavesthatareallowedtooscillateinasingle
direconarecalledpolarized
24
7/29/2019 Waves - P2, week 6
25/26
Propertiesofwaves
Reflec8on:waveschangedireconwhentheybounceoffabarrier.angle
ofincidence=angleofreflecon
Refrac8on:waveschangedireconastheypassfromonemediumto
another(thespeedofthewavealso
changes)
Dispersion:wavespreadsoutintocomponentfrequencies(through
refracon)
Diffrac8on:wavebendswhenpassingthroughagaporaroundan
obstacle
Interference:coherentwavessuperimpose
Polariza8on:wavesthatareallowedtooscillateinasingle
direconarecalledpolarized
25
7/29/2019 Waves - P2, week 6
26/26
ToDo
Readsecon16fromthebook[p.304-p.318Wavemoon] HomeworkAssignmentwk6:quesons16.2,16.,16.5,16.6,16.11
Handitinnolaterthan4:00pmontheWednesdayaVerthereadingweek-LATEWORKWILLNOTBEACCEPTED
26
Recommended