Download Interference of Waves

1. interference of waves
2. the amplitude and phase of resultant wave
3. coherent waves
4. standing waves, π phase shift
5. the standing waves on the string
6. interference, constructive and destructive
interference
1
E.g. 7-3
The wave equation of one wave propagating along x axis
can be written as:
t x
y1  A cos 2 (  )
T 
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.
2
Solution: (1) From the problem,  phase shift occurs at x =0.
That is the wave is inverted after reflection, and the reflected
t x
wave reads: y2  A cos 2 (    ) .
T 
(2) From the principle of superposition, the resultant wave is
x
t
y  y1  y2  2 A sin(2 ) sin(2 )

T
(3) From the wave equation, it is easily to find the antinodes
1 
locate at xa  ( k  ) , and the nodes locate at
2 2
k
xn  
, k  0,1, 2
2
.
3
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）
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1. Observer moving toward source
The frequency measured by the observer reads:
f '
v'


v  vO

 v  vO 

f
 v 
2. Source moving toward observer ）
The frequency measured by the observer reads:
 v 
f ' 
f
 '  v  vS 
v
Both the source and the
observer are in motion：
v '  v  vO 
f ' 
f
 '  v  vS 
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E.g. 7-4
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Outline of Part 2
Oscillations and Mechanical Waves
1. Simple Harmonic Motions
2. Simple Pendulum
3. Damped and Forced oscillations
4. Vertical and Compound Oscillators
5. Superposition of Oscillations
6. Rotating Vector Approach
to be continued
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Continue
7. Mechanical Waves: Definition and Properties
8. Wave Function and Its Physical Implications
9. Simple Harmonic Wave
10.Wave Number, Wave Speed, Wave Length, etc
11.Wave Lines, Wave Surfaces, Wave Front
12.The Huygens’ Principle
to be continued
8
Continue
13. Energy Density and Energy Flow Density
14. Diffraction, Reflection, and Refraction
15. The Principle of Superposition
16. Coherent Waves and Interference
17.Standing Waves
18.The Doppler Effect
The End
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Part III Wave Optics
10 Periods
10
The Nature of Light
（光的本性）
particle ？
Yes，Newton, etc
wave ？
Yes，Huygens, etc
Light
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 !!!
（波粒二象性）
Quantum Theory
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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.
wave-like properties:
interference
diffraction
particle-like properties:
photoelectric effect
the Compton effect
photoelectric effect 光电效应
Compton effect 康普顿效应
12
Light as an Electro-magnetic Wave
light: transverse wave
the speed of light in vacuum:
c  2.99792458 10 m / s
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the speed of light in medium:
c
c
v 
n
 r r
refraction index
relative permeability
relative permittivity
See Fig. 24.6 in P904 for representation of EMW.
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400  760 nm
electromagnetic spectrum: 电磁波谱 millimeter：毫米
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Geometric Optics
ray model, path reversible
Optics
Wave Optics: Wave model
electromagnetic waves,
Huygens’ principle
Quantum Theory:
particle-wave duality, etc
reflection
refraction
imaging
prism
interference
diffraction
polarization
Photoelectric effect
Compton effect
Blackbody radiation
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Interference of Light
（光的干涉）
Conditions for Interference （干涉条件）
① identical wavelengths
② constant phase difference
③ vibrating in parallel direction
Yes
coherent
Conditions for interference fulfilled?
No
incoherent
Again, to observe obvious interference effects, the intensity
difference between the individual waves can’t be too large .
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Interference of Waves
Review
y1  A1 cos(t  1 
2
r1 )

2
y2  A2 cos(t  2 
r2 )

y  y1  y2  A cos(t   )
A
A  A  2 A1 A2 cos ；  2  1 
2
1
2
2
2

(r2  r1 )
I av  I1  I 2  2 I1I 2 cos 
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Review
A
A  A  2 A1 A2 cos ；  2  1 
2
1
2
2
2

(r2  r1 )
interfere constructively
  2k , A  A1  A2
  (2k  1) , A  A1  A2
interfere destructively
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If two waves are in phase everywhere, we get:
interfere constructively
  r2  r1  k  , A  A1  A2

  r2  r1  (2k  1) , A  A1  A2
2
interfere destructively
path length （程长）
path difference
（波程差）


2
 

 2
    ; 

4
 

2
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Optical Path Length
（光程）
f
light
Path length:
r   ni ri
i


0 2
r
0 is the wavelength of light in vacuum.
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