Physics 212 Lecture 23 Physics 212 Lecture 23, Slide 1
Music Who is the Artist? A) Soul Rebels Brass Band B) John Boutte C) New Orleans Nightcrawlers D) Paul Sanchez & Shammar Allen E) Alex McMurray and Matt Perrine Why? Threadhead Records Beats Shazam!! Fan-funded and volunteer run record company Wonderful music from New Orleans Hint: Thursday s artists also did a great set at Lagniappe stage last Jazzfest Physics 212 Lecture 27
Your Comments i wish every lecture was this straightforward I thought the prelecture was confusing. It will present an equation and then declare that the rms variable should be used instead. I don t completely understand the difference and what root mean square is used for. Thanks! We ll mention this again pls chk back to Lec. 21 Not too bad, but clarify all the stuff on energy. Energy density and total energy are confusing. The first part of the pre-lecture was awesome. Then the energy was just so much material in so little time. Please go over energy but slower and with more examples please We ll do another example of power in e.m. waves Is pointing vector really spelled poynting ; vector??? Why did the electromagnetic field give away all its energy? Because there was no poynt in keeping it. Why is the electromagnetic wave insecure about his looks? Because he s a plain wave. I hope you enjoyed this LIGHT humor... 05 you don t read lecture thoughts after midnight right? ;( 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 E 0 = cb 0 Argument of sin/cos gives direction of propagation Physics 212 Lecture 23, Slide 4
Understanding the speed and direction of the wave E x = E o sin(kz-wt) E x z t = 0 E x sin( kz 2 ) cos( kz) z t = /2w What has happened to the waveform in this time interval? It has MOVED TO THE RIGHT by l/4 speed c l / 4 / 2w w l 2 lf Physics 212 Lecture 23, Slide 5
Checkpoint 1a since the electomagnetic wave is in the x direction it will be Ex e is in the y direction and since k and t are different signs, the wave it moving in the positive direction B field propagates in the positive z direction and lies in the yz-plane. Physics 212 Lecture 23, Slide 6
Checkpoint 1a No moving in the minus z direction No has E y rather than E x Physics 212 Lecture 23, Slide 7
Checkpoint 2a c=3.0 x 10 8 m/s Wavelength is equal to the speed of light divided by the frequency. c 300, 000, 000 1 l f 900, 000, 000 3 Check: Look at size of antenna on base unit Physics 212 Lecture 23, Slide 8
Doppler Shift The Big Idea As source approaches: Wavelength decreases Frequency Increases Physics 212 Lecture 23, Slide 9
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? Electromagnetic Waves : You need relativity (time dilation) to calculate BUT Result is simple: only depends on relative motion of source & observer f 1 f 1 1 2 = v/c > 0 if source & observer are approaching < 0 if source & observer are separating Physics 212 Lecture 23, Slide 10
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 f f 1 1 2 Physics 212 Lecture 23, Slide 11
Doppler Shift for e-m Waves A Note on Approximations f 1 f 1 1 2 Taylor Series: Expand << 1 WHY?? f 1/ 2 f 1 1 F ( ) around = 0 1 Remember > 0 for approach < 0 for separation Evaluate: F ( 0) 1 F ( ) F (0) F(0) 1! F ( ) F(0) 2! 2 1... NOTE: F( ) (1 ) n F ( 0) 1 F( ) 1 n Physics 212 Lecture 23, Slide 12
wavelength Red Shift (for Astronomical Objects) Wavelengths shifted higher Frequencies shifted lower Star separating from us (Expanding Universe) Our Sun Star in a distant galaxy Physics 212 Lecture 23, Slide 13
Example Police radars get twice the effect since the EM waves make a round trip: f f 12 v f f -f 30 m/s (67 mph) 31 m/s (69 mph) If f = 24,000,000,000 Hz (k-band radar gun) c = 300,000,000 m/s 1.000 x 10-7 24,000,004,800 4800 Hz 1.033 x 10-7 24,000,004,959 4959 Hz Physics 212 Lecture 23, Slide 15
Checkpoint 2b A) B) C) f iclicker = 900 MHz Running away from an iclicker will decrease the frequency which may let you see something. You need to increase the frequency at which the waves reach you, so you should run towards the iclicker Whether you move or the clicker moves, no visible wave will be availableency. Physics 212 Lecture 23, Slide 16
Checkpoint 2b A) B) C) f iclicker = 900 MHz Need to shift frequency UP Need to approach i>clicker ( > 0) How fast would you need to run to see the i>clicker radiation? f f 10 10 14 9 10 5 1 1 1/ 2 1 1 10 10 10 10 10 1 110 10 10 10 1 110 10 Approximation Exercise: 1 (2 10 ) Physics 212 Lecture 23, Slide 17
Waves Carry Energy Physics 212 Lecture 23, Slide 18
Intensity Intensity = Average energy delivered per unit time, per unit area I 1 A du dt Length = c dt Area = A du u volume u Acdt I c u Sunlight on Earth: I ~ 1000J/s/m 2 ~ 1 kw/m 2 Physics 212 Lecture 23, Slide 19
Waves Carry Energy Physics 212 Lecture 23, Slide 20
Comment on Poynting Vector Just another way to keep track of all this - Its magnitude is equal to I Its direction is the direction of propagation of the wave Physics 212 Lecture 23, Slide 21
Power in EM Waves: Example A cell phone tower has a transmitter with a power of 100 W. What is the magnitude of the peak electric field a distance 1500 m (~ 1 mile) from the tower? Assume the transmitter is a point source. What is the intensity of the wave 1500 m from the tower? A) 1.5 nw/m 2 B) 3.5 W/m 2 C) 6 mw/m 2 I P 100 W W 3.5 4r 2 4 1500 m 2 m 2 E B 2 E E 1 E0 I S E0 20cI c c 2 E 0 0 0 0 7 8 6 1/2 mv 24 10 310 3.510 51 m Physics 212 Lecture 23, Slide 22
Checkpoint 1b Which of the following actions will increase the energy carried by an electromagnetic wave? A. Increase E keeping w constant B. Increase w keeping E constant C. Both of the above will increase the energy D. Neither of the above will increase the energy increasing E will increase amplitude, therefore engergy By increasing the frequency, we will increase the energy. Increasing the frequency or the field would increase the energy carried both dont effect because energy isnt dependant Physics 212 Lecture 23, Slide 26
Checkpoint 1b Which of the following actions will increase the energy carried by an electromagnetic wave? A. Increase E keeping w constant B. Increase w keeping E constant C. Both of the above will increase the energy D. Neither of the above will increase the energy But then again, what are we keeping constant here? WHAT ABOUT PHOTONS? The energy of one photon is E photon = hf = hw/2 U wave = N photons E photon = 1/2 e 0 E 0 2 Physics 212 Lecture 23, Slide 27
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 Wave: They have definite frequency & wavelength (fl = c) Connections seen in equations: E = hf p = h/l 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 28
Calculation 1 An electromagnetic wave is described by: where is the unit vector in the +y direction. E ˆjE 0 cos( kz wt) ĵ y x z Which of the following graphs represents the z-dependence of B x at t = 0? X X (A) (B) (C) (D) E and B are in phase (or 180 o out of phase) E ˆjE 0 cos( kz wt) Wave moves in +z direction y E B points in direction of propagation E x B z B ib ˆ cos( kz wt) 0 Physics 212 Lecture 23, Slide 29
Calculation 2 An electromagnetic wave is described by: iˆ ˆj E E0 cos( kz wt) 2 y x z What is the form of B for this wave? iˆ j B ˆ( E / c )cos( kz wt ) 2 (A) 0 (C) iˆ j B ˆ( E0 / c ) cos( kz wt ) 2 (B) iˆ j B ˆ( E0 / c )cos( kz wt ) 2 (D) iˆ j B ˆ( E0 / c )cos( kz wt ) 2 iˆ ˆj E E0 cos( kz wt) 2 y E x Wave moves in z direction +z points out of screen -z points into screen E B B points in negative z-direction Physics 212 Lecture 23, Slide 30
Calculation 3 An electromagnetic wave is described by: E ˆjE sin( kz wt) Which of the following plots represents B x (z) at time t = /2w? 0 (A) (B) (C) (D) Wave moves in negative z-direction y E B x E B points in negative z-direction +z points out of screen -z points into screen 0 B iˆ( E / c)sin( kz wt) 0 at wt = /2: B ( E / c)sin( kz / 2) x 0 B ( E / c){sin kz cos( / 2) cos kz sin( / 2)} x B ( E / c) cos( kz) x 0 Physics 212 Lecture 23, Slide 31
Calculation 4 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! Is it possible that the professor s argument is correct? (l green = 500 nm, l red = 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 to a smaller value If he goes fast enough, he could observe a green light! Physics 212 Lecture 23, Slide 32
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! How fast would the professor have to go to see the light as green? (l green = 500 nm, l red = 600 nm) (A) 540 m/s (B) 5.4 X10 4 m/s (C) 5.4 X 10 7 m/s (D) 5.4 X 10 8 m/s Relativistic Doppler effect: f f 1 1 f f 600 1 500 1 36(1 ) 25(1 ) Note approximation for small is not bad: f f (1 ) 11 61 0.18 1 5 0.2 c = 3 X 10 8 m/s v = 5.4 X 10 7 m/s Change the charge to SPEEDING! Physics 212 Lecture 23, Slide 33