Lect23 - Physics 212 Le cture23 50 40 30 20 10 0 Confused...

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Unformatted text preview: Physics 212 Le cture23 50 40 30 20 10 0 Confused Confident Avg = 3.0 Physics 212 Le cture23, S 1 lide Music Who is the Artist? A) B) C) D) E) Albert Collins Buddy Guy B. B. King John Lee Hooker Robert Cray BB Gre Album at Gre Due with: ts Due 1. All of thechoice s 2. Etta Jam s, e 2. I rm Thom a as, Koko Taylor, Koko KatieWe r, bste Ruth Brown…. Why? Why? I ke p saying BB e ry le e ve cture S .. hould play BB King ! Distinctiveguitar and voice … Physics 212 Le cture23, S 2 lide Physics 212 Le cture23 50 40 30 20 10 0 Confused Confident Avg = 3.0 Physics 212 Le cture23, S 3 lide PlaneWave fromLast Tim s e E and B arepe ndicular and in phase rpe Oscillatein tim and space e Dire ction of propagation give by E X B n E0 = cB0 Argum nt of sin/cos give dire e s ction of propagation Physics 212 Le cture23, S 4 lide Pre flight 2 BB No – moving in the minus z direction 40 30 20 10 0 Physics 212 Le cture23, S 5 lide Pre flight 6 BB c=3.0 x 108 m/s Wave ngth is e le qual to thespe d of light divide by thefre ncy. e d que Wave λ= c 300, 000, 000 1 = = f 900, 000, 000 3 60 50 40 30 Che ck: Che Look at sizeof ante on baseunit nna Look 20 10 0 Physics 212 Le cture23, S 6 lide Dopple S r hift Doppler Example Audio Doppler Example Visual TheBig I de a As sourceapproache s: Wave ngth de ase le cre s Fre ncy Incre s que ase Physics 212 Le cture23, S 7 lide Dopple S for e Wave r hift -m s What’s Diffe nt fromS re ound or Wate Wave ? r s S ound /Wate Wave : r s You can calculate(no re lativity ne de e d) You BUT Re is som what com sult e plicate is sourceor obse r m d: rve oving wrt m dium e ? Re Ele ctrom tic Wave : agne s Ele You ne d re e You e lativity (tim dilation) to calculate BUT Re is sim : only de nds on re sult ple pe lativem otion of source& obse r rve Re 1+ β f′= f 1− β 1 2 β = v/c v/c β > 0 if source& obse r areapproaching rve if β < 0 if source& obse r arese rve parating if Physics 212 Le cture23, S 8 lide Dopple S for e Wave r hift -m s f’ f v or f f’ v TheDopple S is the SAME for both cases ! r hift The f’/f ONLY DEPENDSON THE RELATI VE VELOC TY I 1+ β f′= f 1− β 1 2 Physics 212 Le cture23, S 9 lide Dopple S for e Wave r hift -m s A Noteon Approxim ations 1+ β f′= f 1− β 1 2 β << 1 f ′ ≈ f ( 1+ β ) WHY ?? Taylor S rie Expand e s: 1+ β F (β ) = 1− β 1/ 2 around β = 0 around F ( β ) = F ( 0) + Evaluate : F ′(0) F ′′(0) 2 β+ β + ... 1! 2! NOTE: F ( β ) = (1 + β )1 / 2 F (β ) ≈ 1 + 1 β 2 Physics 212 Le cture23, S 10 lide 10 F (0) = 1 F ′(0) = 1 F (β ) ≈ 1 + β Re S d hift Wave ngths shifte highe le d r wave ngth le Fre ncie shifte lowe que s d r S se tar parating fromus (Expanding Unive ) rse Our S un S in a distant tar galaxy galaxy Physics 212 Le cture23, S 11 lide 11 Exam ple Policeradars ge twicethee ct sincetheEM wave m a round trip: t ffe s ake f ′ ≈ f ( 1 + 2β ) If f = 24,000,000,000 Hz (k-band radar gun) If 24,000,000,000 c = 300,000,000 m/s v 30 m/s (67 mph) 31 m/s (69 mph) β 1.000 x 10-7 1.033 x 10-7 f’ 24,000,004,800 24,000,004,959 f’-f 4800 Hz 4959 Hz Physics 212 Le cture23, S 12 lide 12 Pre flight 7 BB A) B) C) f iclicker = 900 MHz Ne d to shift fre ncy UP e que How fast would you ne d to run to se the e e How i>clicke radiation? r i>clicke f ′ 1014 1 + β = 9 = 105 = f 10 1− β 1 + β 10 = 1− β 10 1/ 2 Ne d to approach i>clicke e r 60 50 40 30 20 10 0 (β > 0 ) 1010 − 1 1 − 10−10 β = 10 = 10 + 1 1 + 10−10 Approxim ation Exe : rcise β ≈ 1 − (2 × 10−10 ) Physics 212 Le cture23, S 13 lide 13 Wave Carry Ene s rgy Physics 212 Le cture23, S 14 lide 14 I nte nsity I nte nsity = Ave e rgy de re pe unit tim , pe unit are rage ne live d r er a I≡ 1 dU A dt Length = c dt Length dt Area = A Area dU = u ⋅ volume = u Acdt I =c u S unlight on Earth: I ~ 1000J/s/m 1000J/s/m Physics 212 Le cture23, S 15 lide 15 Wave Carry Ene s rgy Physics 212 Le cture23, S 16 lide 16 C m nt on Poynting Ve om e ctor Just anothe way to ke p track of all this r e - I ts m qual to I Its agnitudeis e – I ts dire ction is thedire ction of propagation of thewave Physics 212 Le cture23, S 17 lide 17 Light has Mom ntum e ! I f it has e rgy and its m ne oving, the it also has m e n om ntum : Analogy fromm chanics: e p2 E= 2m dE 2 p dp mv dp = = dt 2m dt m dt = vF v→c For E-M wave s: dE dU → = IA dt dt IA = cF IF = cA I P= c Radiation pre ssure pre ssure Physics 212 Le cture23, S 18 lide 18 Pre flight 4 70 60 50 40 30 20 10 0 BB But the again, what areweke ping constant he ? n e re WHAT ABOUT PHOTONS? Physics 212 Le cture23, S 19 lide 19 PHOTONS Webe vethee rgy in an e waveis carrie by photons lie ne -m d Que stion: What arePhotons? Answe Photons arePhotons. r: Photons posse both waveand particleprope s ss rtie Particle : Ene and Mom ntumlocalize rgy e d Ene Wave : Wave The havede y finitefre ncy & wave ngth (f λ = c) que le C ctions se n in e onne e quations: E = hf p = h/ λ Planck’s constant Planck’s h = 6.63e-34 J-s Que stion: How can som thing beboth a particleand a wave e ? Answe I t can’t (whe weobse it) r: n rve What wese de nds on how wechooseto m asureit ! e pe e Them ry of quantumm chanics: Moreon this in PHYS214 yste e Physics 212 Le cture23, S 20 lide 20 Exe rcise An e ctrom tic waveis de le agne scribe by: d ˆ whe re is theunit ve in the+y dire ctor ction. j r E = ˆ 0 cos(kz − ωt ) jE y x z Which of the following graphs represents the z-dependence of Bx at t = 0? X (A) (B) (C ) (D) X E and B are“in phase (or 180o out of phase ” ) Wavem s in +z dire ove ction y rr E E × B points in direction of propagation x B z Physics 212 Le cture23, S 21 lide 21 r E = ˆ 0 cos(kz − ωt ) jE BB r ˆ B = −iB0 cos(kz − ωt ) Exe rcise An e ctrom tic waveis de le agne scribe by: d r iˆ + ˆ j E= E0 cos(kz + ωt ) 2 y x z What is the form of B for this wave? (A) (B) ˆj r i+ˆ B= ( E0 / c) cos(kz + ωt ) 2 r iˆ − ˆ j B= ( E0 / c)cos(kz + ωt ) 2 (C) (D) ˆj r −i + ˆ B= ( E0 / c) cos(kz + ωt ) 2 ˆj r −i − ˆ B= ( E0 / c) cos(kz + ωt ) 2 BB r iˆ + ˆ j E= E0 cos(kz + ωt ) 2 Wavem s in –z dire ove ction +z points out of scre n e -z points into scre n e y E x rr E × B points in negative z-direction Physics 212 Le cture23, S 22 lide 22 B Exe rcise An e ctrom tic waveis de le agne scribe by: d r E = ˆ 0 sin( kz + ωt ) jE BB Which of the following plots represents Bx(z) at time t = π /2ω ? (A) Wavem s in ne ove gativez-dire ction y E B x (B) (C) (D) r ˆ B = i ( E0 / c)sin(kz + ωt ) Bx = ( E0 / c)sin(kz + π / 2) at ω t = π /2: +z points out of scre n e -z points into scre n e rr E × B points in negative z-direction Bx = ( E0 / c){sin kz cos(π / 2) + cos kz sin(π / 2)} Bx = ( E0 / c) cos(kz ) Physics 212 Le cture23, S 23 lide 23 Exe rcise A ce rtain unnam d physics profe was arre d for running a stoplight. Hesaid the e ssor ste light was gre n. A pe stian said it was re Theprofe the said: “Weareboth e de d. ssor n be truthful; you just ne d to account for theDopple e ct !” ing e r ffe BB Is it possible that the professor’s argument is correct? (λ green = 500 nm, λ red = 600 nm) (A) YES (B) NO ssor s que md • As profe approache stoplight, thefre ncy of its e itte light will be shifte UP d e s • Thespe d of light doe not change re , le d • The fore thewave ngth (c/f) would beshifte DOWN s nough, hecould obse a gre n light ! rve e • I f hegoe fast e Physics 212 Le cture23, S 24 lide 24 Follow-Up A ce rtain unnam d physics profe was arre d for running a stoplight. Hesaid the e ssor ste light was gre n. A pe stian said it was re Theprofe the said: “Weareboth e de d. ssor n be truthful; you just ne d to account for theDopple e ct !” ing e r ffe BB How fast would the professor have to go to see the light as green? (λ green = 500 nm, λ red = 600 nm) (A) 540 m/s (B) 5.4 X104 m/s (C) 5.4 X 107 m/s f′= f 1+ β 1− β (D) 5.4 X 108 m/s Re lativistic Dopple e ct: r ffe f ′ 600 1+ β = = f 500 1− β 36(1 − β ) = 25(1 + β ) f ′ = f (1 + β ) β= 11 = 0.18 61 Noteapproxim ation for sm β is not bad: all c = 3 X 108 m v = 5.4 X 107 m /s /s β= 1 = 0.2 5 C hangethechargeto S PEEDING! Physics 212 Le cture23, S 25 lide 25 ...
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This note was uploaded on 03/05/2011 for the course PHYS 212 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.

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