Chapter 7 The superposition of waves

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Chapter 7 The superposition of waves November 10
Addition of waves of the same frequency Introduct
ion Principle of superposition the total
disturbance at any point of the medium is the
algebraic sum of the constituent individual waves.
7.1 The addition of waves of the same
frequency I) Algebraic method
E0
y
a
x
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Phase difference
If the two disturbances are from the same source
but travel different routes
Terms coherent light (e1-e2 constant),
incoherent light constructive interference (d
0, 2p, ...), destructive interference (d p,
3p, ...). A special (simple) case
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Superposition of many waves
The interference of coherent waves only
redistributes the energy in space, it cannot
change the total amount of energy.
II) Complex method
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III) Phasor method
7.1.4 Standing waves
Two harmonic waves of the same frequency
propagating in opposite directions
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Partial standing and partial traveling waves
Question What is the speed of a partial standing
wave?
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Read Ch7 1 Homework Ch7 (1-14)
2,6,9,13,14 Due November 21
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November 12 Beats and group velocity 7.2 The
addition of waves of different frequency Addition
of two waves of close frequency
Define average w, average k, modulation w,
modulation k as
Carrier
Envelope
Beat frequency
When two waves with close frequency but different
amplitude overlap, they produce beats with less
contrast.
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Group velocity
Phase velocity of carrier wave
Group velocity the velocity at which the
modulation envelope advances.
when Dw is small,
In terms of ,
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In general, for a laser pulse
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Read Ch7 2 Homework Ch7 (15-31)
17(Optional),19,21,23,25,27,30(Optional) Due
November 21
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November 14 Anharmonic periodic waves 7.3
Anharmonic periodic waves Goal Resolving a real
wave into component sine waves finding the
frequency, amplitude, and phase. Fouriers
theorem Any function having a spatial period l
can be synthesized by a sum of harmonic functions
whose wavelengths are integral submultiples of l.

Representing f(x) in the frequency domain
frequency spectrum and phase
Fourier analysis finding A0, Am and
Bm Orthogonality of sinusoidal functions
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Symmetry conditions 1) f(-x) f(x), even ,
Fourier series contain only cosine terms. 2)
f(-x) - f(x), odd, Fourier series contain only
sine terms.
Example
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Read Ch7 3 Homework Ch7 (32-36) 35,36 Due
November 21
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November 17 Nonperiodic waves 7.4 Nonperiodic
waves Transition from periodic to nonperiodic
functions
As l ? ?, Fourier series is replaced by Fourier
integrals
Introducing negative frequency useful for
describing symmetric systems.
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Pulses and wave packets Example 1 square pulse
Example 2 cosine wave train
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• Frequency bandwidth Dk or Dw
• Product of the widths of the wave packet in
  k-space and in x-space
• For cosine wave train,
• For square wave,
• Generally, for any pulse .

7.4.3 Coherent length Spectral line A colored
band of the spectral component of
light. Linewidths 1) Nature linewidth (10-9-10-8
s), 2) Doppler linewidth, 3) Collisions
(interruption of wavetrains). Coherent time Dtc
1/Dn Coherent length Dlc c Dtc Example White
light Dl 300 nm, Dn 31014 Hz, Dtc 3 fs,
Dlc 900 nm 1.6 l. He-Ne laser Dl 10-6 nm,
Dlc ? 400 m.
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Read Ch7 4 Homework Ch7 (37-)
38,42,44,46 Due December 3
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Pulses and wave packets Example 3 Gaussian pulse