1. 1 Chapter 16 Waves-I

2. 2  Mechanical Wave Sound (f: 20Hz ~ 20KHz) Water wave, Ultrasound (f: 1MHz ~ 10MHz) Wave on a vibrating string  Electromagnetic Wave Radio wave Micro Wave (0.1 ~ 30cm) Light (400 ~700nm) X-ray (0.01 ~ 1nm)  Wave  Matter Wave

3. 3 Waves  Wave Characteristics  Mathematical Expression of Traveling Wave  Pulse Wave  Harmonic Wave  Speed of a transverse wave on a string longitudinal (sound) in a fluid  Energy Transport  Superposition of Waves  Reflection and Transmission (Boundary Problem)

4. 4 Wave Characteristics 1) Definite speed (v w ) A: Amplitude  : Wave length T: Period 2) Transport Energy (Not matter) 3) Particles of the medium moves back and forth “or” up and down about their equilibrium point (For Mechanical Wave only)

5. 5 In a transverse wave, the displacement of every such oscillating element along the wave is perpendicular to the direction of travel of the wave, as indicated in Fig. 16-1. In a longitudinal wave the motion of the oscillating particles is parallel to the direction of the wave’s travel, as shown in Fig. 16-2. 16.3 Transverse and Longitudinal Waves

6. 6 如何描述波函數 (Wave Function)

7. 7 Traveling Pulse x0x0 -v-v The shape of the Pulse does not change with time.

8. 8 如何描述 Harmonic Wave ( 諧波 ) 函數

9. 9 Harmonic Wave

10. 10

11. 11 16.4 Wave variables

12. 12 16.4 The Speed of a Traveling Wave If point A retains its displacement as it moves, the phase giving it that displacement must remain a constant:

13. 13 Proof : Velocity of a particle of the medium

14. 14  Which of the following functions represent traveling waves ?

15. 15 y(x,t) x t=0 t=2 t=5

16. 16 t=0 t=1 t=2 y(x,t) x t x=0

17. 17 t=0y(x,t) x t=1t=2

18. 18 利用牛頓定律推導波動方程式 The Wave Equation Wave Speed on a Stretched String

19. 19 x y Wave Speed on a Stretched String

20. 20 Θ

21. 21 x y x dx x+dx y+dy y F=|F 1 | F=|F 2 | dy Θ(x+dx) Θ(x) F 2y =FsinΘ(x+dx) F 1y =FsinΘ(x) a y =d 2 y/dt 2

22. 22 dx dy Θ(x)

23. 23 The Wave Equation

24. 24 Proof : Velocity of a particle of the medium

25. 25 16.6: Energy and Power of a Wave Traveling along a String The average power, which is the average rate at which energy of both kinds (kinetic energy and elastic potential energy) is transmitted by the wave, is:

26. 26 15.2 Simple Harmonic Motion In the figure snapshots of a simple oscillatory system is shown. A particle repeatedly moves back and forth about the point x=0. The time taken for one complete oscillation is the period, T. In the time of one T, the system travels from x=+x m, to –x m, and then back to its original position x m. The velocity vector arrows are scaled to indicate the magnitude of the speed of the system at different times. At x=±x m, the velocity is zero.

27. 27 Elastic potential energy If the disturbance is small,

28. 28

29. 29

30. 30 Energy Transmitted by Harmonic Wave on string

31. 31 16.6: Energy and Power of a Wave Traveling along a String The average power, which is the average rate at which energy of both kinds (kinetic energy and elastic potential energy) is transmitted by the wave, is:

32. 32 Homework  Chapter 16 ( page 438 ) 9, 21, 24, 25, 29, 31, 34, 46, 58, 59 9, 21, 24, 25, 29, 31, 34, 46, 58, 59

33. 33 16.9: The Superposition of Waves Overlapping waves algebraically add to produce a resultant wave (or net wave). Overlapping waves do not in any way alter the travel of each other.

34. 34 16.9: Interference of Waves If two sinusoidal waves of the same amplitude and wavelength travel in the same direction along a stretched string, they interfere to produce a resultant sinusoidal wave traveling in that direction.

35. 35 16.9: Interference of Waves

36. 36 16.9: Interference of Waves

37. 37 Superposition of two Harmonic Wave

38. 38

39. 39 16.12: Standing Waves, Reflections at a Boundary

40. 40 例：例：例：例：

41. 41

42. 42

43. 43 16.12: Standing Waves

44. 44 16.13: Standing Waves and Resonance Fig. 16-19 Stroboscopic photographs reveal (imperfect) standing wave patterns on a string being made to oscillate by an oscillator at the left end. The patterns occur at certain frequencies of oscillation. (Richard Megna/Fundamental Photographs) For certain frequencies, the interference produces a standing wave pattern (or oscillation mode) with nodes and large antinodes like those in Fig. 16-19. Such a standing wave is said to be produced at resonance, and the string is said to resonate at these certain frequencies, called resonant frequencies.