Physics 214 Lecture 1

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Physics 214
Waves and Quantum Physics
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Welcome to Physics 214

• Content Waves and Quantum Physics
• Format Active Learning (Learn from
  Participation)
• Textbook Young and Freedman -- Assignments on
  Syllabus page
• Lectures (presentations, demonstrations, ACTs)
• Discussion Sections (group problem solving) --
  start this week
• Labs (hands-on interactions with the phenomena)
  Submit Prelab to instructor at 1st session
  (next week)

Bring your calculator!
Ask the Professor (from the Homepage) An
opportunity for you to get answers in lecture to
your questions. This Thursday only 2 bonus
points for filling in the Ask the Professor
survey.
James Scholar Students Email Prof. Kwiat within
1 week. Note Make sure you do not have a lab
or discussion section before your Tuesday
lecture.
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WWW and Grading Policy

• This course makes extensive use of the
  World-Wide-Web
• http//online.physics.uiuc.edu/courses/phys214
• Here you will find general course announcements,
  the course syllabus, the course description
  information, the lecture slides, lab information,
  the homework assignments (which you will actually
  submit to be graded on the Web), sample exams,
  and the official gradebook.
• Faculty Lectures A,B Paul Kwiat Lectures
  C,D Bob Clegg
• Discussion Benjamin Lev Labs T.-C. Chiang
• Grading Policy
• see Course Description on Web for CAREFUL
  STATEMENT!!
• Your final grade for Physics 214 will be based on
  your total score
• final exam (350 pts),
• midterm exam (200 pts),
• four labs (145 pts total), Begin in Week 2.
  Prelabs due then.
• six homeworks (145 pts total), and
• five quizzes (highest four 150 pts total)
• Clicker participation (10 pts total one per
  class)
• Rough guidelines for letter grade ranges are
• A(960) A(935) A-(910)
• B(885) B(855) B-(830)
• C(800) C(770) C-(740)
• D(700) D(660) D-(620) F(lt620)

Slight change
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i-Clickers

• Why?
• reduce inhibitions on answering questions
• interactive class, shown to improve learning by
  up to 4x
• How?
• turn your clicker ON (last button)
• wait until timer is activated
• submit/change answer before timer stops
• Register online at 214 homepage, or
  http//www.iclicker.com/ (use your netid)
• points awarded retroactively, but register soon
  anyway (but not in class!)
• Why, revisited
• well award a point for every lecture attended
  (out of 1000 total in principle you can exceed
  1000!)
• attended ? responded to ?1/2 of questions
• You can attend at most one lecture per day it
  doesnt matter which one
• Misc.
• batteries if the battery-low indicator flashes,
  you still have several lectures worth of energy,
  i.e., NO EXCUSE
• at 1 of the final grade, kvetching and whining
  isnt worth it
• old I-Clickers (with 8-digit ID number) should
  work

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Clickers Example

• Whats your major
• A. Engineering
• B. Physics
• C. Chemistry
• D. Other science
• E. Something else

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What is 214 all about?(1)

• Many physical phenomena of great practical
  interest to engineers, chemists, biologists,
  physicists, etc. were not in Physic 211212.
• Wave phenomena
• Classical waves (brief review)
• Sound, electromagnetic waves, waves on a string,
  etc.
• Traveling waves, standing waves
• Interference and the principle of superposition
• Constructive and destructive interference
• Amplitudes and intensities

Interference!

• Interferometers
• Colors of a soap bubble, . . .
• Precise measurements, e.g., Michelson
  Interferometer

• Diffraction
• Optical Spectroscopy - diffraction gratings
  (butterfly wings!)
• Optical Resolution - diffraction-limited
  resolution of lenses,

• Quantum Physics - See next slide.
• Particles act like waves -- Waves act like
  particles
• Completely different from classical physics!

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What is 214 all about? (2)

• Quantum Physics
• Particles act like waves!
• Particles (electrons, protons, nuclei, atoms, . .
  . ) interfere like classical waves, i.e.,
  wave-like behavior
• Particles have only certain allowed energies
  like waves on a piano

• Explains nature of chemical bonds, structure of
  molecules, solids, metals, semiconductors, . . .
• One equation (the Schrodinger equation)
  forelectron waves explains all these effects

• Lasers, Superconductors, . . .

• Quantum tunneling
• Particles can tunnel through walls!

• Waves act like particles!
• When you observe (detect) a wave, you find
  quanta, i.e., particle-like behavior
• Instead of a continuous intensity, the result is
  a probabilityof finding quanta!

• Probability and uncertainty are part of nature!

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Today

• Examples of Waves
• Wave Equations
• Equations that describe waves key point is that
  solutions of linear wave equations obey the
  superposition principle
• Superposition
• Holds exactly for electromagnetic waves in vacuum
  and quantum waves
• Very good approximation for sound, waves on a
  string, etc.
• Amplitude and intensity
• Start interference continued next time

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Waves are all around us

• Familiar examples of waves

Earth
Light from stars that has traveled billions of
years traversing the universe and observed on
earth
Sound waves travelingthrough the air

• Pressure waves in the air
• Characterized by
• Frequency (pitch)
• Wavelength
• Speed 330 m/s (approx)

• Electromagnetic waves in vacuum
• Characterized by
• Frequency (pitch)
• Wavelength
• Speed c (constant of nature)

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The Harmonic Waveform (in 1-D)
y(x,t) for a fixed time t
x
Review from Physics 211/212. For more detail see
Lectures 26 and 27 in the 211 website.
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Wave Properties

• Period The time T for a point on the wave to
  undergo one complete oscillation.

Period T
For a fixed position x
Amplitude A
t
Movie (twave)

• Speed The wave moves one wavelength ? in one
  period T so its speed is v ??/ T.

• Frequency f 1/T cycles/second.
• Angular frequency w 2p f radians/second

Movie (tspeed)
Careful Remember the factor of 2p
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Example 1

• What is the amplitude, A, of this wave?

• What is the period, T, of this wave?

• If this wave moves with a velocity v 18 m/s,
  what is the wavelength, l, of the wave?

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Example 1

• What is the amplitude, A, of this wave?

T 0.1 s

• What is the period, T, of this wave?

v fl l/T

• If this wave moves with a velocity v 18 m/s,
  what is the wavelength, l, of the wave?

l vT 1.8 m
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Act 1
A harmonic wave moving in the positive x
direction can be described by the equation
y(x,t) A cos ( kx - wt ). Which of the
following equations describes a harmonic wave
moving in the negative x direction?
(a) y(x,t) A sin (kx - wt) (b) y(x,t) A cos
(kx wt) (c) y(x,t) A cos (-kx wt)
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Act 1 - Solution
A harmonic wave moving in the positive x
direction can be described by the equation
y(x,t) A cos ( kx - wt ). Which of the
following equations describes a harmonic wave
moving in the negative x direction?
(a) y(x,t) A sin (kx - wt) (b) y(x,t) A cos
(kx wt) (c) y(x,t) A cos (-kx wt)
In order to keep the argument zero, if t
increases, x must decrease.
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The Wave Equation...

• We will assume waves of the form y(x,t) f(x
  vt) and cos(kx - wt)
• What is the origin of these functional forms?
• These are solutions to a wave equation
• Example Sound waves pressure waves

See appendix for definition of apartial
derivativedenoted by ?h/ ?x, ?h2/ ?x2, etc.
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Act 2
The speed of sound in air is a bit over 300 m/s,
and the speed of light in air is about
300,000,000 m/s. Suppose we make a sound wave
and a light wave that both have a wavelength of 3
meters. 1. What is the ratio of the frequency of
the light wave to that of the sound wave?
(a) About 1,000,000 (b) About 0.000001 (c)
About 1000
2. What happens to the frequency if the light
passes under water?
(a) Increases (b) Decreases (c) Stays
the same
3. What happens to the wavelength if the light
passes under water?
(a) Increases (b) Decreases (c) Stays
the same
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Act 2 - Solution
The speed of sound in air is a bit over 300 m/s,
and the speed of light in air is about
300,000,000 m/s. Suppose we make a sound wave
and a light wave that both have a wavelength of 3
meters. 1. What is the ratio of the frequency of
the light wave to that of the sound wave?
(a) About 1,000,000 (b) About 0.000001 (c)
About 1000
2. What happens to the frequency if the light
passes under water?
(a) Increases (b) Decreases (c) Stays
the same
3. What happens to the wavelength if the light
passes under water?
(a) Increases (b) Decreases (c) Stays
the same
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Act 2 - Solution
The speed of sound in air is a bit over 300 m/s,
and the speed of light in air is about
300,000,000 m/s. Suppose we make a sound wave
and a light wave that both have a wavelength of 3
meters.
2. What happens to the frequency if the light
passes under water?
(a) Increases (b) Decreases (c) Stays
the same
3. What happens to the wavelength if the light
passes under water?
(a) Increases (b) Decreases (c) Stays
the same
Why does the wavelength change but not the
frequency?
The frequency does not change because the time
dependence of the wave is the same everywhere.
In the water the speed decreases, so the
wavelength must also.
Question Do we see frequency or wavelength?
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Wave Summary

• The formula
  describes a harmonic plane wave of amplitude A
  moving in the x direction.

• For a wave on a string, each point on the wave
  oscillates in the y direction with simple
  harmonic motion of angular frequency ?.

• The wavelength is

• The speed is

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Electron Waves in a Quantum Corral
Iron walls on Copper
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Superposition
Key point for this course!
See appendix fordefinition of apartial
derivativedenoted by ?h/ ?x, ?h2/ ?x2, etc.
If h1 and h2 are solutions, then c1h1c2h2 is a
solution!
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We can have all sorts of waveforms, but thanks to
superposition, if we find a nice simple set of
solutions, easy to analyze, we can just write
more complicated solutions as sums of simple
ones.
Wave Forms

• pulses caused by a brief disturbance of the
  medium

• various wavepackets

But we focus on harmonic waves simple
sinusoidal waves extending forever
These harmonic waves are useful ingredients
because they have the simplest behavior in
prisms, filters, diffraction gratings. It is a
mathematical fact that any reasonable waveform
can be represented as a combination of various
harmonic waves, i.e., sines and cosines. This is
the topic of Fourier Analysis (and very useful
for signal processing!)
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Mathematical Form of Constant-Speed Waves
y

• Suppose we have some function y f(x)

x
0

• Let d vt Then
• f(x - vt) will describe the same shape
  moving to the right with speed v.
• f(x vt) will describe the same shape moving
  to the left with speed v.

v
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Superposition of Waves

• Q What happens when two waves of the same type
  collide?
• A Because of superposition,
• the two waves just pass through each other
  unchanged! The wave at the end is just the sum
  of whatever would have become of the two parts at
  the beginning
• Superposition is an exact property for
• Electromagnetic waves in vacuum
• Matter waves in quantum mechanics (later)
• Established by experiment
• Many (but not all) other waves obey the principle
  of superposition to a high degree, e.g., sound,
  guitar string, etc.

Sum of waves 1 and 2
Movie (super_pulse)
Movie (super_pulse2)
Movie (super_pulse)
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Act 3

• If you added the two sinusoidal waves shown in
  the top plot, what would the result look like ?

(a)
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Act 3 - Solution

• The correct answer is (b) The sum of two or more
  sines or cosines having the same frequency is
  just another sine or cosine with the same
  frequency.

How do we know? Add graphically or use trig
identities
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Adding Waves with Different Phases

• Example Suppose we have two waves with the same
  amplitude A1 and angular frequency ?. Then their
  wave numbers k are also the same. Suppose that
  one starts at phase ? after the other

y1 A1 cos(k x - ? t) and y2 A1
cos(k x - ? t ?)
Spatial dependence of 2 waves at t
0 Resultant wave
Trig identity
Amplitude Oscillation
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Standing waves

• The formula y()(x,t) Acos(kx - wt) describes
  a wave of amplitude A moving in the x direction.

• The formula y(-)(x,t) Acos(kx wt) describes a
  wave of amplitude A moving in the -x direction.

• The sum of two waves with equal wavelength and
  amplitude traveling in x and x directions is a
  standing wave. If each traveling wave has
  amplitude A1, then y()(x,t) y(-)(x,t)
  A1cos(kx - wt) A1cos(kx wt) 2A1cos(kx)
  cos(wt)

where we used the identity
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Boundary conditions ? Standing waves

• A standing wave is the solution for a wave
  confined to a region
• Boundary condition Constraints on a wave where
  the potential changes
• Displacement 0 for wave on string E 0 at
  surface of a conductor

E 0

• If both ends are constrained (e.g., for a cavity
  of length L), then only certain wavelengths l are
  possible

• n l f
• 2L v/2L
• L v/L
• 2L/3 3v/2L
• L/2 2v/L
• n 2L/n nv/2L

nl 2L
n 1, 2, 3 mode index
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Amplitude and Intensity

• Initially in 214 we will deal primarily with
  sound waves and electromagnetic waves (radio
  frequency, microwaves, light).
• How bright is the light? How loud is the sound?

Amplitude, A Intensity, I
SOUND WAVE peak differential pressure, po
power transmitted/area (loudness) EM WAVE
peak electric field, Eo power
transmitted/area (brightness)
Transmitted power per unit area (W/m2)

• We will rarely (if ever) calculate the magnitudes
  of p or E, and we will generally calculate ratios
  of intensities, so we can simplify our analysis
  and write

Intensity Amplitude
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Superposition of Waves

• Q What happens when two waves collide?
• A They ADD together!
• We say the waves are in a superposition

Movie (super_pulse)
Movie (super_pulse2)
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Act 4
Pulses 1 and 2 pass through the same place at the
same time.. Pulse 2 has four times the peak
intensity of pulse 1, i.e., I2 4 I1.
1. What is the maximum possible total combined
intensity, Imax?
(a) 4 I1 (b) 5 I1 (c) 9 I1
2. What is the minimum possible intensity, Imin?
(a) 0 (b) I1 (c) 3 I1
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Act 4 - Solution
Pulses 1 and 2 pass through the same place at the
same time.. Pulse 2 has four times the peak
intensity of pulse 1, i.e., I2 4 I1.
1. What is the maximum possible total combined
intensity, Imax?
(a) 4 I1 (b) 5 I1 (c) 9 I1
2. What is the minimum possible intensity, Imin?
(a) 0 (b) I1 (c) 3 I1
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Act 4 - Solution
Pulses 1 and 2 pass through the same place at the
same time.. Pulse 2 has four times the peak
intensity of pulse 1, i.e., I2 4 I1.
1. What is the maximum possible total combined
intensity, Imax?
(a) 4 I1 (b) 5 I1 (c) 9 I1
2. What is the minimum possible intensity, Imin?
(a) 0 (b) I1 (c) 3 I1
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Interference of Waves

• What happens when two waves are present at the
  same point in space and time? (single w)
• Always add amplitudes (pressures or electric
  fields).
• What we observe however is Intensity (absorbed
  power).
• I A2

Example
Stereo speakers Listener
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Act 5 Changing phase of the Source

• Each speaker alone produces an intensity of I1
  1 W/m2 at the listener

I I1 1 W/m2
Drive the speakers in phase. What is the
intensity I at the listener?
I
Now shift phase of one speaker by 90o.What is the
intensity I at the listener?
I
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Act 5 Solution

• Each speaker alone produces an intensity of I1
  1 W/m2 at the listener

I A12 I1 1 W/m2
Drive the speakers in phase. What is the
intensity I at the listener?
I
Now shift phase of one speaker by 90o.What is the
intensity I at the listener?
I
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Act 5 Solution

• Each speaker alone produces an intensity of I1
  1 W/m2 at the listener

I A12 I1 1 W/m2
Drive the speakers in phase. What is the
intensity I at the listener?
I (2A1)2 4I1 4 W/m2
Now shift phase of one speaker by 90o.What is the
intensity I at the listener?
I
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Act 5 Solution

• Each speaker alone produces an intensity of I1
  1 W/m2 at the listener

I A12 I1 1 W/m2
Drive the speakers in phase. What is the
intensity I at the listener?
I (2A1)2 4I1 4 W/m2
Now shift phase of one speaker by 90o.What is the
intensity I at the listener?
I 4 I1cos2(450) 2.0 I1 2.0 W/m2
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Next time Interference of wavesConsequence of
superposition

• Read Young and Freeman Sections 35.1, 35.2, and
  35.3
• Check the test your understanding questions
• Work problems on the two slides to prepare for
  Lecture 2.

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Problem for next time path length-dependent phase

• Each speaker alone produces intensity I1 1W/m2
  at the listener, and f 900 Hz.

Sound velocity v 330 m/s
d 3 m
I I1 1 W/m2
r1 4 m
Drive speakers in phase. Compute the intensity I
at the listener in this case
Hint f 2p(d/l) with d ? r2 - r1 Do you
see why?
Procedure 1) Compute path-length difference
d 2) Compute wavelength l 3) Compute phase
difference f 4) Write formula for resultant
amplitude A 5) Compute the resultant intensity,
I A2
Check your solution next lecture.
Answer I ?? W/m2
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Home Exercise 1

• Assume two waves with the same amplitude A1 1
  cm and angular frequency ?. They differ only in
  phase ?
• The resultant wave is

y1 A1cos(k x - ? t) and y2
A1cos(k x - ? t ?)

• Determine the amplitude A of the resultant wave
  in the following cases (you complete the table)

f (degrees) f (radians) A (cm) Rough
Drawing 450 p/4 1.85 900
1800 3600 300