Major Concepts of Physics PHY102

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• Major Concepts of Physics PHY102

Lecture 4Quantitative aspects about
waves? January 26th Spring 2009 Prof. Liviu
Movileanu http//physics.syr.edu/courses/PHY102.07
Spring/index.html lmovilea_at_physics.syr.edu Room
211, Physics Bldg., 443-8078
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Major Concepts of Physics PHY102 Lecture 4
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Lecture objectives
Hints on homework problems. Some
examples ?Review quantitative description of
waves ?Review quantitative description of
interference ?Youngs double-slit experiment
Announcements
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Major Concepts of Physics PHY102 Lecture 4
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Important relationships

Review Lecture 2
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Major Concepts of Physics PHY102 Lecture 4
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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)
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Major Concepts of Physics PHY102 Lecture 4
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Answer
a) The amplitude of the wave is A 0.2 m b) The
wavelength ?2?/k2?/(0.1)20? m c) the time
period ?2?/T, then T2?/?2?/20?/10 s d) the
velocity of propagation (state the direction of
propagation) v?/T200 m/s
 
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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, dthe distance
between slits

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Major Concepts of Physics PHY102 Lecture 4
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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 ? (m1/2)?, m 0, 1, 2,
3,
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Major Concepts of Physics PHY102 Lecture 4
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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.
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Major Concepts of Physics PHY102 Lecture 4
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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

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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
• d d sin ?bright m ?
• 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

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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
• d d sin ?dark (m ½) ?
• m 0, 1, 2,

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Interference Equations

• The positions of the fringes can be measured
  vertically from the zeroth order maximum
• y L tan ? ? L sin ?
• Assumptions
• Lgtgtd
• dgtgt?
• tan ? ? sin ?

? is small and therefore the approximation tan ?
? sin ? can be used
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Major Concepts of Physics PHY102 Lecture 4
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Interference Equations, Final

• For bright fringes (use sin? brightm ? /d)
• For dark fringes (use sin? dark? (m ½)? /d)

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Example 25.5
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Announcements

• 1. This week Workshop 2 Interference
• 2. Homework 1 is due this week. News! 4 is a
  bonus problem.
• 3. Do you want to be challenged? More MCAT preps?
• Work problems throughout the sections 25.1, 25.4
• 4. Next lecture Diffractionis based on your
  knowledge about interference

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Quiz 1 (January 29th, 2007)
     
1. Is the light a wave or a particle? 2. What is
the period? 3. What is the wave speed? 4. What
is the interference? 5. What is the
wave-relation between speed and wavelength? 6
(demo). How many lasers did we use in the lecture
3s demonstration regarding interference?
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Major Concepts of Physics PHY102 Lecture 4
2009?Syracuse University