interference of waves the amplitude and phase of resultant wave coherent waves

1. interference of waves • the amplitude and phase of resultant wave • coherent waves • standing waves, πphase shift • the standing waves on the string • interference, constructive and destructive • interference

2. E.g. 7-3 The wave equation of one wave propagating along x axis can be written as: The reflection occurs at x = 0 and the reflection point is one node. Find: 1) the wave equation of the reflected wave. 2) the wave equation of the superposition of these two waves. 3)the position of the nodes and antinodes.

4. The Doppler Effect （多普勒效应） When the wave source and the observer move relatively, the measured frequency by the observer is different from the true frequency (the frequency of the wave source). This phenomena is called Doppler effect. （观察者相对于波源运动，观察者测量波的频率得到的结果将和波源 的频率不同，这种现象称为多普勒效应）

5. 1. Observer moving toward source The frequency measured by the observer reads: 2. Source moving toward observer ） The frequency measured by the observer reads: Both the source and the observer are in motion：

6. E.g. 7-4

7. Outline of Part 2 Oscillations and Mechanical Waves • Simple Harmonic Motions • Simple Pendulum • Damped and Forced oscillations • Vertical and Compound Oscillators • Superposition of Oscillations • Rotating Vector Approach to be continued

8. Continue • Mechanical Waves: Definition and Properties • Wave Function and Its Physical Implications • Simple Harmonic Wave • Wave Number, Wave Speed, Wave Length, etc • Wave Lines, Wave Surfaces, Wave Front • The Huygens’ Principle to be continued

9. Continue • Energy Density and Energy Flow Density • Diffraction, Reflection, and Refraction • The Principle of Superposition • Coherent Waves and Interference • Standing Waves • The Doppler Effect The End

10. Part III Wave Optics 10 Periods

11. The Nature of Light （光的本性） particle ？ Yes，Newton, etc Light wave ？ Yes，Huygens, etc Light behaves like a wave. Thomas Young, Augustin Fresnel, etc Light is a form of high-frequency electromagnetic wave. James Clerk Maxwell Wave-particle Duality !!! Quantum Theory （波粒二象性）

12. Particle-Wave Duality of Light 光的波粒二象性 Light behaves as a wave sometime, and behaves like a particle in other cases, as is called particle-wave duality. photoelectric effect 光电效应 Compton effect 康普顿效应

13. Light as an Electro-magnetic Wave light: transverse wave the speed of light in vacuum: the speed of light in medium: relative permeability refraction index relative permittivity See Fig. 24.6 in P904 for representation of EMW.

14. electromagnetic spectrum: 电磁波谱 millimeter：毫米

15. reflection refraction imaging prism Geometric Optics ray model, path reversible interference diffraction polarization Wave Optics: Wave model electromagnetic waves, Huygens’ principle Optics Photoelectric effect Compton effect Blackbody radiation Quantum Theory: particle-wave duality, etc

16. Interference of Light （光的干涉） Conditions for Interference （干涉条件） • identical wavelengths • constant phase difference • vibrating in parallel direction coherent Yes Conditions for interference fulfilled? incoherent No Again, to observe obvious interference effects, the intensity difference between the individual waves can’t be too large .

17. Interference of Waves Review

18. Review interfere constructively interfere destructively

19. If two waves are in phase everywhere, we get: interfere constructively interfere destructively path length （程长） path difference （波程差）

20. Optical Path Length （光程） f light Path length: