# Lect23 - Physics 212 Lecture 23 Physics 212 Lecture 23,...

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Unformatted text preview: Physics 212 Lecture 23 Physics 212 Lecture 23, Slide 1 Physics BB Music Who is the Artist? A) B) C) D) E) Oscar Peterson Kenny Barron Dave Brubeck Thelonius Monk Marcus Roberts Why? Time to return to classic jazz Most unique piano player?? Most Check out the Jazz Biography CD (couldn’t find a Check find picture) great recordings from 40’s and 50’s picture) Physics 212 Lecture 23, Slide 2 Physics Your Comments “the whole E-M wave graph, I still don't understand what it is trying wave to tell us and where the sin(kz-wt) even comes from or how I'm even to wt) supposed to use it” supposed It certainly can be confusing.. It We will try to make it clear !! We “The doppler thingy ma bobber.” We’ll work an example & discuss approximations 40 30 “all of it,really. Is it just me, or is it a tad all to perfect that some guy named "Poynting" has a vector named after him?” "Poynting" 05 20 10 It’s a formal thing… 0 Confused Confident Physics 212 Lecture 23, Slide 3 Physics Plane Waves from Last Time E and B are perpendicular and in phase Oscillate in time and space Direction of propagation given by E X B E0 = cB0 Argument of sin/cos gives direction of propagation Physics 212 Lecture 23, Slide 4 Physics Understanding the speed and direction of the wave Ex = Eosin(kz-ωt) Ex t=0 z Ex sin( kz − π ) = − cos( kz) z 2 t = π/2ω What has happened to the wave form in this time interval? It has MOVED TO THE RIGHT by λ/4 λ/4 ω speed = c = =λ = λf π / 2ω 2π Physics 212 Lecture 23, Slide 5 Physics Preflight 2 BB No – moving in the minus z direction No No – has Ey rather than Ex No 40 30 20 10 0 Physics 212 Lecture 23, Slide 6 Physics Preflight 6 BB c=3.0 x 108 m/s Wavelength is equal to the speed of light divided by the frequency. cy. c 300, 000, 000 1 λ= = = f 900, 000, 000 3 60 50 40 Check: Check: Look at size of antenna on base unit Look 30 20 10 0 Physics 212 Lecture 23, Slide 7 Physics Doppler Shift The Big Idea The As source approaches: Wavelength decreases Frequency Increases Physics 212 Lecture 23, Slide 8 Physics Doppler Shift for e-m Waves What’s Different from Sound or Water Waves ? Sound /Water Waves : You can calculate (no relativity needed) BUT Result is somewhat complicated: is source or observer moving wrt medium? medium? Electromagnetic Waves : Electromagnetic You need relativity (time dilation) to calculate BUT Result is simple: only depends on relative motion of source & observer bserver 1+ β f′= f 1− β 1 2 β = v/c β > 0 if source & observer are approaching if β < 0 if source & observer are separating if Physics 212 Lecture 23, Slide 9 Physics Doppler Shift for e-m Waves f f’ v or f f’ v The Doppler Shift is the SAME for both cases ! f’/f ONLY DEPENDS ON THE RELATIVE VELOCITY 1+ β f′= f 1− β 1 2 Physics 212 Lecture 23, Slide 10 Physics Doppler Shift for e-m Waves A Note on Approximations 1+ β f′= f 1− β 1 2 f ′ ≈ f (1 + β ) β << 1 WHY ?? 1/ 2 1 + β Taylor Series: Expand F ( β ) = 1− β F ( β ) = F (0) + around β = 0 around F ′(0) F ′′(0) 2 β+ β + ... 1! 2! Evaluate: F ( 0) = 1 F ′(0) = 1 F (β ) ≈ 1 + β NOTE: F ( β ) = (1 + β )1 / 2 F (β ) ≈ 1 + 1 β 2 Physics 212 Lecture 23, Slide 11 Physics Red Shift Wavelengths shifted higher wavelength Frequencies shifted lower Star separating from us (Expanding Universe) Our Sun Star in a Star distant galaxy distant Physics 212 Lecture 23, Slide 12 Physics Example Police radars get twice the effect since the EM waves make a round trip: 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 β f’ f’-f 30 m/s (67 mph) 1.000 x 10-7 24,000,004,800 4800 Hz 31 m/s (69 mph) 1.033 x 10-7 24,000,004,959 4959 Hz Physics 212 Lecture 23, Slide 13 Physics Preflight 7 BB ficlicker = 900 MHz A) B) C) Need to approach i>clicker Need to shift frequency UP How fast would you need to run to How see the i>clicker radiation? see 1/ 2 f ′ 1014 1 + β = 9 = 105 = f 10 1− β (β > 0) 60 50 40 30 20 10 0 1+ β 10 = 1− β 10 1010 − 1 1 − 10 −10 β = 10 = 10 + 1 1 + 10 −10 Approximation Exercise: β ≈ 1 − (2 × 10−10 ) Physics 212 Lecture 23, Slide 14 Physics Waves Carry Energy Physics 212 Lecture 23, Slide 15 Physics Intensity Intensity = Average energy delivered per unit time, per unit area 1 dU I≡ A dt Length = c dt Length Area = A Area dU = u ⋅ volume = u Acdt I =c u Sunlight on Earth: I ~ 1000J/s/m2 ~ 1 kW/m2 Physics 212 Lecture 23, Slide 16 Physics Waves Carry Energy Physics 212 Lecture 23, Slide 17 Physics Comment on Poynting Vector Just another way to keep track of all this - Its magnitude is equal to I Its – Its direction is the direction of propagation of the wave Physics 212 Lecture 23, Slide 18 Physics Light has Momentum! If it has energy and its moving, then it also has momentum: Analogy from mechanics: p2 E= 2m dE 2 p dp mv dp = = dt 2m dt m dt dE dU → = IA dt dt For E-M waves: I P= c Radiation pressure = vF v→c IA = cF IF = pressure cA Physics 212 Lecture 23, Slide 19 Physics Preflight 4 70 60 BB 50 40 30 20 10 0 But then again, what are we keeping constant here? WHAT ABOUT PHOTONS? Physics 212 Lecture 23, Slide 20 Physics PHOTONS We believe the energy in an e-m wave is carried by photons Question: What are Photons? Answer: Photons are Photons. Photons possess both wave and particle properties Particle: Energy and Momentum localized Energy Wave: Wave: They have definite frequency & wavelength (fλ = c) Connections seen in equations: E = hf p = h/λ Planck’s constant h = 6.63e-34 J-s Question: How can something be both a particle and a wave? Answer: It can’t (when we observe it) What we see depends on how we choose to measure it ! The mystery of quantum mechanics: More on this in PHYS 214 Physics 212 Lecture 23, Slide 21 Physics Exercise y x r An electromagnetic wave is described by: E = ˆ 0 cos(kz − ωt ) jE where ˆ is the unit vector in the +y direction. j z Which of the following graphs represents the z-dependence of Bx at t = 0? X (A) X (B) (C) (D) E and B are “in phase” (or 180o out of phase) r E = ˆ 0 cos(kz − ωt ) jE Wave moves in +z direction y rr E E × B points in direction of propagation x r BB ˆ B = −iB0 cos(kz − ωt ) B zhysics 212 Physics P Lecture 23, Slide 22 Exercise y r i+ˆ ˆj E= E0 cos(kz + ωt ) 2 An electromagnetic wave is described by: x z What is the form of B for this wave? ˆj r −i + ˆ B= ( E0 / c) cos(kz + ωt ) 2 (A) r i+ˆ ˆj B= ( E0 / c)cos(kz + ωt ) 2 (C) (B) r i−ˆ ˆj B= ( E0 / c)cos(kz + ωt ) 2 (D) B = −i − j ( E0 / c) cos(kz + ωt ) r i+ˆ ˆj E= E0 cos(kz + ωt ) 2 r ˆ ˆ BB 2 Wave moves in –z direction y E x +z points out of screen -z points into screen B rr E × B points in negative z-direction Physics 212 Lecture 23, Slide 23 Physics Exercise An electromagnetic wave is described by: r E = ˆ 0 sin(kz + ωt ) jE BB Which of the following plots represents Bx(z) at time t = π/2ω ? (A) (B) Wave moves in negative z-direction y +z points out of screen E -z points into screen B x rr E × B points in negative z-direction (C) (D) r ˆ B = i ( E0 / c)sin(kz + ωt ) at ωt = π/2: Bx = ( E0 / c)sin(kz + π / 2) Bx = ( E0 / c){sin kz cos(π / 2) + cos kz sin(π / 2)} Bx = ( E0 / c) cos(kz ) Physics 212 Lecture 23, Slide 24 Physics Exercise A certain unnamed physics professor was arrested for running a stoplight. He said the light was green. A pedestian said it was red. The professor then said: “We are both being truthful; you just need to account for the Doppler effect !” BB Is it possible that the professor’s argument is correct? (λgreen = 500 nm, λred = 600 nm) (A) YES (B) NO • As professor approaches stoplight, the frequency of its emitted light will be shifted UP • The speed of light does not change • Therefore, the wavelength (c/f) would be shifted DOWN • If he goes fast enough, he could observe a green light ! Physics 212 Lecture 23, Slide 25 Physics Follow-Up A certain unnamed physics professor was arrested for running a stoplight. He said the light was green. A pedestian said it was red. The professor then said: “We are both being truthful; you just need to account for the Doppler effect !” BB How fast would the professor have to go to see the light as green? (λgreen = 500 nm, λred = 600 nm) (A) 540 m/s (B) 5.4 X104 m/s (C) 5.4 X 107 m/s Relativistic Doppler effect: f ′ = f f ′ 600 1+ β = = f 500 1− β 1+ β 1− β 36(1 − β ) = 25(1 + β ) Note approximation for small β is not bad: c = 3 X 108 m/s ﬂ v = 5.4 X 107 m/s (D) 5.4 X 108 m/s β= f ′ = f (1 + β ) 11 = 0.18 61 1 β = = 0.2 5 Change the charge to SPEEDING! Physics 212 Lecture 23, Slide 26 Physics ...
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## This note was uploaded on 02/09/2012 for the course PHYSICS 212 taught by Professor Mestre during the Spring '11 term at University of Illinois at Urbana–Champaign.

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