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# Lect23 - Physics 212 40 30 20 10 0 Confused Confident Avg =...

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Unformatted text preview: Physics 212 Lecture 23 50 40 30 20 10 0 Confused Confident Avg = 3.0 Physics 212 Lecture 23, Slide 1 Music Who is the Artist? BB A) B) C) D) E) Albert Collins Buddy Guy B. B. King John Lee Hooker Robert Cray Great Album Duets with: 1. All of the choices 2. Etta James, 2. Irma Thomas, Koko Taylor, Koko Katie Webster, Ruth Brown…. Why? I keep saying BB every lecture.. Should play BB King ! Distinctive guitar and voice… Physics 212 Lecture 23, Slide 2 Physics 212 Lecture 23 50 40 30 20 10 0 Confused Confident Avg = 3.0 Physics 212 Lecture 23, Slide 3 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 Preflight 2 BB No – moving in the minus z direction No No – has Ey rather than Ex No has 40 30 20 10 0 Physics 212 Lecture 23, Slide 5 Preflight 6 BB c=3.0 x 108 m/s Wavelength is equal to the speed of light divided by the frequency. cy. λ= c 300, 000, 000 1 = = 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 6 Doppler Shift Doppler Example Audio Doppler Example Visual The Big Idea As source approaches: Wavelength decreases Frequency Increases Physics 212 Lecture 23, Slide 7 Doppler Shift for e-m Waves Doppler 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? Result wrt 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 v/c β > 0 if source & observer are approaching if β < 0 if source & observer are separating if Physics 212 Lecture 23, Slide 8 Doppler Shift for e-m Waves Doppler 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 9 Doppler Shift for e-m Waves Doppler 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 10 10 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 11 11 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 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 12 12 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 13 13 Waves Carry Energy Physics 212 Lecture 23, Slide 14 14 Intensity Intensity = Average energy delivered per unit time, per unit area I≡ Length = c dt Length Area = A Area 1 dU A dt dU = u ⋅ volume = u Acdt I =c u Sunlight on Earth: I ~ 1000J/s/m2 ~ 1 kW/m2 Physics 212 Lecture 23, Slide 15 15 Waves Carry Energy Physics 212 Lecture 23, Slide 16 16 Comment on Poynting Vector Comment Poynting 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 17 17 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 18 18 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 19 19 PHOTONS We believe the energy in an e-m wave is carried by photons We 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 hf p = h/λ h/ Planck’s constant Planck 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 20 20 Exercise y x E = ˆ 0 cos(kz − ωt ) jE An electromagnetic wave is described by: 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) E = ˆ 0 cos(kz − ωt ) jE Wave moves in +z direction y E E × B points in direction of propagation x B BB ˆ B = −iB0 cos(kz − ωt ) z hysics 212 P Lecture 23, Slide 21 21 Exercise An electromagnetic wave is described by: y ˆj i+ˆ E= E0 cos(kz + ωt ) 2 x z What is the form of B for this wave? ˆj −i + ˆ ( E0 / c) cos(kz + ωt ) 2 (A) ˆj i+ˆ B= ( E0 / c) cos(kz + ωt ) 2 (C) B= (B) ˆj i−ˆ B= ( E0 / c) cos(kz + ωt ) 2 (D) ˆj −i − ˆ B= ( E0 / c)cos(kz + ωt ) 2 E= ˆj i+ˆ E0 cos(kz + ωt ) 2 BB Wave moves in –z direction y E x +z points out of screen -z points into screen B E × B points in negative z-direction Physics 212 Lecture 23, Slide 22 22 Exercise An electromagnetic wave is described by: 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 E × B points in negative z-direction (C) (D) 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 23 23 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 24 24 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 5 β = = 0.2 Change the charge to SPEEDING! Physics 212 Lecture 23, Slide 25 25 ...
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