Major Concepts of Physics PHY102
Lecture #6
What are the quantitative aspects
about waves?
February 8th
Spring 2016
Prof. Liviu Movileanu
http://movileanulab.syr.edu/MajorConceptsPhysics2016.html
lmovilea@syr.edu
Room 211, Physics Bldg., 443-8078
Major Concepts of Physics PHY102 – Lecture #6
2016Syracuse University
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Lecture objectives
Hints on homework problems. Some examples
 Review quantitative description of waves
 Review quantitative description of interference
 Young’s double-slit experiment
Announcements
Major Concepts of Physics PHY102 – Lecture #6
2016Syracuse University
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Important relationships
Major Concepts of Physics PHY102 – Lecture #6
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A simple example of wave equation
A transverse sinusoidal wave is represented by the following
equation
y = 0.2sin(20t – 0.1x) m
Assuming that the units of the quantities in the equation are meters
and seconds, find:
a) the amplitude of the wave;
b) the wavelength;
c) the time period;
d) the velocity of propagation (state the direction of propagation);
Major Concepts of Physics PHY102 – Lecture #6
2016Syracuse University
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Answer
a) The amplitude of the wave is:
A = 0.2 m
b) The wavelength:
=2/k=2/(0.1)=20 m
c) the time period:
=2/T, then T=2/=2/20=/10 s
d) the velocity of propagation (state the direction of propagation);
v=/T=200 m/s
Major Concepts of Physics PHY102 – Lecture #6
2016Syracuse University
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First Example
We have two waves.
Suppose that the crest of the first wave overlaps
the crest of the second wave.
Then, the effect is that the net wave has increased
amplitude at this point and time.
This is constructive interference.
d sin  = m, m= 0, ±1, ± 2, ± 3, …
d=the distance between slits
Major Concepts of Physics PHY102 – Lecture #6
2016Syracuse University
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Second Example
Suppose the crest of the first wave overlaps the trough
of the second wave.
Then, the net wave has its amplitude reduced.
This is destructive interference.
d sin  = (m+1/2), m= 0, ±1, ± 2, ± 3, …
Major Concepts of Physics PHY102 – Lecture #6
2016Syracuse University
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Demonstration of Interference
The interference model.
Two sinusoidal waves superpose on each other.
When the waves are in-phase, we have
constructive interference.
When the waves are 180 degrees out-of-phase,
we have destructive interference.
Major Concepts of Physics PHY102 – Lecture #6
2016Syracuse University
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The Thomas Young double-slit experiment
The pattern consists of
a series of bright and
dark parallel bands
called fringes
Constructive
interference occurs
where a bright fringe
occurs
Destructive
interference results
in a dark fringe
Major Concepts of Physics PHY102 – Lecture #6
2016Syracuse University
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Interference Equations
• For a bright fringe, produced by constructive
interference, the path difference must be either
zero or an integral multiple of the wavelength
• δ = d sin θbright = m λ
– m = 0, ±1, ±2, …
– m is called the order number
• When m = 0, it is the zeroth order maximum
• When m = ±1, it is called the first order
maximum
Major Concepts of Physics PHY102 – Lecture #6
2016Syracuse University
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Interference Equations
• When destructive interference occurs, a dark fringe
is observed
• This needs a path difference of an odd number of
half wavelengths
• δ = d sin θdark = (m + ½) λ
– m = 0, ±1, ±2, …
Major Concepts of Physics PHY102 – Lecture #6
2016Syracuse University
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Interference Equations
• The positions of the
fringes can be
measured vertically
from the zeroth
order maximum
• y = L tan θ  L sin θ
• Assumptions
– L>>d
– d>>λ
– tan θ  sin θ
θ is small and therefore the
approximation tan θ  sin θ can
be used
Major Concepts of Physics PHY102 – Lecture #6
2016Syracuse University
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Interference Equations, Final
• For bright fringes (use sinθ bright=m λ /d)
y bright
L

m m  0,  1,  2 
d
• For dark fringes (use sinθ dark=λ (m + ½)λ /d)
y dark
L 
1

 m   m  0,  1,  2 
d 
2
Major Concepts of Physics PHY102 – Lecture #6
2016Syracuse University
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Example 25.5
Major Concepts of Physics PHY102 – Lecture #6
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Another Example (see Problem 32Textbook)
Light incident on a pair of slits produces an interference pattern on a screen 2.50 m
from the slits. If the slit separation is 0.0150 cm and the distance between adjacent
bright fringes in the pattern is 0.760 cm, what is the wavelength of the light? [Hint:
Is the small angle approximation justified?]
Strategy Show that the small-angle approximation is justified. Then, use the result for
the slit separation obtained in Example 25.4.
Solution Compare x and D.
D
2.50 m

 329, so x << D and the small angle approximation is justified.
x 0.760 102 m
Find the wavelength of the light.
dx (0.0150 102 m)(0.760 102 m)
d
, so  

 456 nm .
x
D
2.50 m
D
Major Concepts of Physics PHY102 – Lecture #6
2016Syracuse University
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Announcements
1. Homework #2 is due on this week’s laboratory session.
Homework #3 is due on week of Feb 22-26.
2. This week: Workshop #3, “Interference”
3. Do you want to be challenged? More MCAT preps #1? Work
problems throughout the sections 25.1, 25.4
4. Next lecture (Lecture #7), Wednesday, Feb 10, Review Meeting
for Exam #1
Major Concepts of Physics PHY102 – Lecture #6
2016Syracuse University
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