2. Physics 102: Lecture 14, Slide 1 Resonance Electromagnetic Waves Physics 102: Lecture 14

3. Physics 102: Lecture 14, Slide 2 Review: Impedance Triangle and Resonance R (X L -X C ) Z  X L and X C point opposite. When adding, they tend to cancel! When X L = X C they completely cancel and Z = R. This is resonance! V max,gen = I max Z I max (X L -X C ) I max X L I max X C I max R V gen,max 

4. Physics 102: Lecture 14, Slide 3 Resonance R is independent of f R

5. Physics 102: Lecture 14, Slide 4

6. Physics 102: Lecture 14, Slide 5 Resonance R is independent of f X L increases with f R XLXL

7. Physics 102: Lecture 14, Slide 6 Resonance R is independent of f X L increases with f X C increases with 1/f R XCXC XLXL

8. Physics 102: Lecture 14, Slide 7 Resonance R is independent of f X L increases with f X C increases with 1/f Z: X L and X C subtract R XCXC Z Resonance: X L = X C XLXL f0f0 Z is minimum at resonance frequency!

9. Physics 102: Lecture 14, Slide 8

10. Physics 102: Lecture 14, Slide 9 Resonance R is independent of f X L increases with f X C increases with 1/f Z: X L and X C subtractCurrentZ f0f0 Resonance: X L = X C Current is maximum at resonance frequency! I max = V gen,max /Z

11. Physics 102: Lecture 14, Slide 10 Preflight 14.1 As the frequency of the circuit is either raised above or lowered below the resonant frequency, the impedance of the circuit: L R C Always increases Only increases for lowering the frequency Only increases for raising the frequency f0f0 Z

12. Physics 102: Lecture 14, Slide 11 ACT: Resonance The AC circuit to the right is being driven at its resonance frequency. Compare the maximum voltage across the capacitor with the maximum voltage across the inductor. 1)V C > V L 2)V C = V L 3)V C < V L 4)Depends on R L R C

13. Physics 102: Lecture 14, Slide 12

14. Physics 102: Lecture 14, Slide 13 Preflight 14.3 At the resonant frequency, which of the following is true? I is in phase with V generator I leads V generator I lags V generator VLVL VCVC VRVR V gen 

15. Physics 102: Lecture 14, Slide 14 Resonance in Radios L R C An AC circuit with R= 2 , L = 0.30  H and variable capacitance is connected to an antenna to receive radio signals at the resonance frequency. If you want to listen to music broadcasted at 96.1 MHz, what value of C should be used?

16. Physics 102: Lecture 14, Slide 15 ACT: Radios Your radio is tuned to FM 96.1 MHz and want to change it to FM 105.9 MHz, which of the following will work. 1.Increase Capacitance 2.Decrease Capacitance 3.Neither, you need to change L

17. Physics 102: Lecture 14, Slide 16

18. Physics 102: Lecture 14, Slide 17 Summary of Resonance At resonance –Z is minimum (=R) –I max is maximum (=V gen,max /R) –V gen is in phase with I –X L = X C V L = -V C At lower frequencies –X C > X L V gen lags I At higher frequencies –X C < X L V gen lead I I max (X L -X C ) I max X L I max X C I max R V gen,max 

19. Physics 102: Lecture 14, Slide 18 Electromagnetic Waves Light, Radio, TV, Microwaves, Satellites, X-Rays

20. Physics 102: Lecture 14, Slide 19 Electromagnetic Waves -+ -+ Direction wave travels Generator creates E field up and down.

21. Physics 102: Lecture 14, Slide 20

22. Physics 102: Lecture 14, Slide 21 Electromagnetic Waves --++--++ Direction wave travels Generator creates E field up and down.

23. Physics 102: Lecture 14, Slide 22 Electromagnetic Waves -+ -+ Direction wave travels Generator creates E field up and down.

24. Physics 102: Lecture 14, Slide 23 Electromagnetic Waves Direction wave travels Generator creates E field up and down.

25. Physics 102: Lecture 14, Slide 24

26. Physics 102: Lecture 14, Slide 25 Electromagnetic Waves +-+- Direction wave travels Generator creates E field up and down.

27. Physics 102: Lecture 14, Slide 26 Electromagnetic Waves ++--++-- Direction wave travels Generator creates E field up and down.

28. Physics 102: Lecture 14, Slide 27 Electromagnetic Waves +-+- Direction wave travels Generator creates E field up and down. http://www.colorado.edu/physics/2000/waves_particles/wavpart4.html

29. Physics 102: Lecture 14, Slide 28

30. Physics 102: Lecture 14, Slide 29 ACT: EM Waves Which direction should I orient my antenna to receive a signal from a vertical transmission tower? 1) Vertical2) Horizontal 3) 45 Degrees +-+- Direction wave travels

31. Physics 102: Lecture 14, Slide 30 Electromagnetic Waves (Preflight 14.5) Generator also creates B field into and out of the page! x z y +-+-

32. Physics 102: Lecture 14, Slide 31 Electromagnetic Waves x z y Transverse (vs. sound waves – longitudinal) E perpendicular to B and always in phase E & B increase and decrease at same times Can travel in empty space (sound waves can’t!) “Speed of light”: v = c = 1/ √ (  0  0 ) = 3 x 10 8 m/s (186,000 miles/second!) Frequency: f = v/  = c/  Period: T = 1/f wave travels one wavelength  in one period T

33. Physics 102: Lecture 14, Slide 32

34. Physics 102: Lecture 14, Slide 33 Preflight 14.6 – 14.12 Which of the following are transverse waves? sound light radio X-ray microwave water waves “The Wave” (i.e. at football games)

35. Physics 102: Lecture 14, Slide 34 EM Waves Practice E x Shown below is the E field of an EM wave broadcast at 96.1 MHz and traveling to the right. (1) What is the direction of the magnetic field? (2) Label the two tic marks on the x axis (in meters). 3.16.2

36. Physics 102: Lecture 14, Slide 35 Doppler Effect Doppler Example Audio Doppler Example Visual f o = f e (1 + u/c) moving toward each other f o = f e (1 - u/c) moving away from each other Notes: These are easier than equations for sound! If f increases then decreases (and vice versa), since speed is always c (c= f) Finding relative velocity: u = v 1 + v 2 moving in opposite directions u = v 1 – v 2 moving in same direction observed frequency emitted frequency

37. Physics 102: Lecture 14, Slide 36

38. Physics 102: Lecture 14, Slide 37 ACT: Doppler Practice V = 32 m/sV = 50 m/s In the jeep, the frequency of the light from the troopers car will appear: (1) higher (more blue)(2) Lower (more red) What value should you use for u in the equation? (1) 32(2) 50(3) 50+32(4) 50-32

39. Physics 102: Lecture 14, Slide 38