Waves and Quantum Physics
Physics 214
Lecture 1, p 1
Lectures C:
Labs:
Active Learning (Learn from Participation)
Do it on the web !!
Presentations, demos, & ACTs.
Bring your calculator.
Group problem solving.
Starts this week
Up close with the phenomena.
Starts next week
Prelabs are due at the beginning of lab.
Young and Freedman. Assignments on Syllabus page
James Scholar Students: See link on course website for information.
Textbook:
he Chec P
This Friday only: Bonus point for doing the survey.
Ask the Prof. See the website under SmartPhysics
feature for each lecture.
Lecture 1, p 2
Prelectures:
10 for the semester see SmartPhysics calendar, worth 1 pt each
(note you must actually do them to get credit, not just click the slides)
Format:
Homework:
Lecture:
Discussion:
Lab:
http://online.physics.uiuc.edu/courses/phys214
All course information is on the web site. Read it !!
Faculty: Lectures A&B:
Discussion:
Welcome to Physics 214
ed ab e ce
>2 ab
e =a
a cF
ea e h
.
Letter grade ranges are listed on the web.
Excused absence forms must be turned in within one week of your return to class.
If you miss too many classes, whether excused or not, you will not get course credit!!
U e c
The lowest quiz score will be dropped. No other scores will be dropped.
The official grading policy (See the course description for details)
Your grade is determined by exams, homework, quizzes, labs, and lecture.
Lecture 1, p 3
Here you will find:
http://online.physics.uiuc.edu/courses/phys214
announcements
course description & policies
syllabus
( ha e e d g e e
ee )
Look at it !!
lecture
slides
Need to send us email?
lab
information
Send it to the right person.
discussion
solutions (at the end of the week)
See c ac I f
homework
assignments
on the web page.
sample exams
gradebook
Almost all course information is on the web site
WWW and Grading Policy
Lecture 1, p 4
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e ha c ed
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properly registered (wait ~2 weeks to see).
Once again: NO iClicker EXCUSES.
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Everyone will get iClicker credit for lecture 1, so:
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I d e
a e h ch ec e
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Batteries: If the batteryd ca f a he ,
worth of energy, i.e., NO iClicker EXCUSES.
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Lectures Use iClickers
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Lecture 1, p 5
e.
A. Engineering (not physics)
B. Physics
C. Chemistry
D. Other science
E. Something else
Act 0:
What is your major?
iClicker
Practice
Lecture 1, p 6
Lecture 1, p 7
If you are confused by something in a MW lecture (and didn’t ask during
that lecture), ask about it on Friday.
Or better still, submit your question to the SmartPhysics AskTheProfessor
Checkpoint for the next lecture.
Friday lectures will focus more on problem solving and question/answer.
MW lectures will mostly focus on concepts, ACTS, and demos.
Unlike P211 and P212, we have three lectures per week (MWF):
Three Lectures per Week
Lecture 1, p 8
Optical Resolution - diffraction-limited e
Optical Spectroscopy - diffraction gratings
Diffraction:
f e
Precise measurements, e.g., Michelson Interferometer
Interferometers
Constructive and destructive interference
Amplitudes and intensities
Colors of a soap bubble, . . . (butterfly wings!)
Interference and the principle of superposition
Sound, electromagnetic waves, waves on a string, etc.
Traveling waves, standing waves
Classical waves (brief review)
Wave phenomena (the first two weeks)
e ,
Lecture 1, p 9
Interference!
Many physical phenomena of great practical interest to engineers,
chemists, biologists, physicists, etc. were not in Physics 211 or 212.
What is 214 all about? (1)
Probability and uncertainty are part of nature!
When you observe a wave (e.g., light),
f d
a a ( a c e-like behavior).
Instead of a continuous intensity, the result is
a probability of finding quanta!
Waves act like particles!
QM explains the nature of chemical bonds,
molecular structure, solids, metals,
semiconductors, lasers, superconductors, . . .
microscope (STM)
image of atoms and
electron waves
Lecture 1, p 10
Particles (electrons, protons, nuclei, atoms, . . . )
interfere like classical waves, i.e., wave-like behavior
Pa c e ha e
ce a a
ed e e g e
e a e
a a
The Schrodinger equation for quantum waves describes it all.
Quantum tunneling
Pa c e ca
e h gh a !
Scanning tunneling
Particles act like waves!
Quantum Physics
What is 214 all about? (2)
We
e d he f
Superposition
ee
Wave equations (briefly)
Amplitude and intensity
The harmonic waveform
Wave forms
a e he
Today
e aa da
ca
Lecture 1, p 11
.
Lecture 1, p 12
We usually focus on harmonic waves
that extend forever. They are useful
because they have simple math, and
accurately describe a lot of wave
behavior.
Wavepackets: like harmonic waves, but
with finite extent.
Pulses caused by brief disturbances of
the medium
We can have all sorts of waveforms:
A
Wave Forms
ca ed
e a e
v
v
Lecture 1, p 13
A cos
2
x vt
A cos kx
2 ft
k
wavelength
frequency
A
speed
A cos kx
2 f
2
angular frequency
wavenumber
A
t
This is review from Physics 211/212.
For more detail see Lectures 26 and 27 on the 211 website.
defined
to be
positive A
Amplitude
Wavelength
amplitude (defined to be positive)
A snapshot of y(x) at a fixed time, t:
f
v
y is the displacement from equilibrium.
y x, t
v
Lecture 1, p 14
x
A function of
two variables:
x and t.
The Harmonic Waveform (in 1-D)
Period T
t
T
= 2 f = radians/second
f = 1/T = cycles/second.
f
Be careful: Remember the factor of 2
Angular frequency:
Frequency:
v
Speed: The wave moves one wavelength, , in one period, T.
So, its speed is:
A
Amplitude A
For a fixed position x :
Period: The time T for a point on the wave to undergo one
complete oscillation.
Wave Properties
Lecture 1, p 15
Movie (tspeed)
Lecture 1, p 16
-0.8
-0.4
0
0
Time, t, in seconds
.02 .04 .06 .08 .1 .12
If this wave moves with a velocity v = 18 m/s,
what is the wavelength, , of the wave?
What is the period, T, of this wave?
.14 .16
Displacement vs. time at x = 0.4 m
What is the amplitude, A, of this wave?
y(t)
0.4
0.8
Wave Properties Example
Displacement in mm
Lecture 1, p 17
y
v
t)
c) y(x,t) = A cos( kx + t)
b) y(x,t) = A cos(kx + t)
a) y(x,t) = A sin(kx
Which of the following equations describes a harmonic wave
moving in the negative x direction?
A harmonic wave moving in the
positive x direction can be
described by the equation
y(x,t) = A cos(kx - t).
Act 1
Lecture 1, p 18
x
1
v2
f
t2
2
See P212, lecture 22, slide 17
Electromagnetic waves:
Sound waves:
1 d 2p
v 2 dt 2
1 d 2E x
c 2 dt 2
d 2E x
dz 2
Also Ey Bx and By
p is pressure
Lecture 1, p 19
You will do some
problems in discussion.
The appendix has a
discussion of
traveling wave math.
t), satisfies the wave equation.
d 2p
dx 2
Examples of wave equations:
(You can verify this.)
The harmonic wave, f = cos(kx
f
x2
2
What is the origin of these functional forms?
They are solutions to a wave equation:
For any function, f that satisfies the wave equation:
f(x vt) describes a wave moving in the positive x direction.
f(x + vt) describes a wave moving in the negative x direction.
The Wave Equation
Lecture 1, p 20
peak differential pressure, po
peak electric field, Eo
power transmitted/area (loudness)
power transmitted/area (brightness)
Intensity, I
I
1
c
2
o
1
E02
I = A2
or
A=
In this course, we will ignore them and simply write:
I
Lecture 1, p 21
For a harmonic wave, the time average,
denoted by the <>, gives a factor of 1/2.
We will usually calculate ratios of intensities. The constants cancel.
Example, EM wave:
E2
oc
For harmonic waves, the intensity is always proportional to the time-average
of the power. The wave oscillates, but the intensity does not.
Sound wave:
EM wave:
Amplitude, A
Intensity: How bright is the light? How loud is the sound?
Intensity tells us the energy carried by the wave.
Intensity is proportional to the square of the amplitude.
Amplitude and Intensity
A cos kx
t
y
2
k
; the speed is v
f
k
A2
A
Note: In general for spherical waves the intensity
will fall off as 1/r2, i.e., the amplitude falls off as 1/r.
However, for simplicity, we will neglect this fact in
Phys. 214.
x
Lecture 1, p 22
Sound waves or EM waves that are created from a point source are spherical
waves, i.e., they move radially from the source in all directions.
These waves can be represented by circular arcs:
These arcs are surfaces of constant phase (e.g., crests)
The intensity is proportional to the square of the amplitude: I
The wavelength is
For a wave on a string, each point on the wave oscillates in the y
direction with simple harmonic motion of angular frequency .
The formula
describes a harmonic plane wave
of amplitude A moving in the +x direction.
y x ,t
Wave Summary
dx
d y +z
dy dz
+
dx dx
The derivative is a
ea
ea
.
x2
2
1
v2
h1 + h2
t2
h1 + h2
h2
x2
2
1
v2
h2
t2
2
This is superposition. It is a very useful analysis tool.
In general, if h1 and h2 are solutions then so is ah1 + bh2.
h1 + h2 is also a solution !!
Add them:
2
h1
and
t2
2
1
v2
h1
x2
2
Consider two wave equation solutions, h1 and h2:
Use the fact that
A key point for this course!
Superposition
Lecture 1, p 23
Lecture 1, p 24
v
Lecture 1, p 25
We focus on harmonic waves, because we are already familiar with the math
(trigonometry) needed to manipulate them.
It is a mathematical fact that any reasonable waveform can be represented
as a superposition of harmonic waves. This is Fourier analysis, which many
of you will learn for other applications.
v
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 write the more
complicated solutions as superpositions of the simple ones.
Wave Forms and Superposition
Many (but not all) other waves obey the principle
of superposition to a high degree, e.g., sound,
guitar string, etc.
This has been established by experiment.
Matter waves in quantum mechanics.
Electromagnetic waves in vacuum.
Superposition is an exact property for:
A: Because of superposition, the two waves
pass through each other unchanged!
The wave at the end is just the sum of
whatever would have become of the two
parts separately.
Q: What happens when two waves collide?
Superposition Example
Lecture 1, p 26
c) 3 I1
b) I1
a) 0
This happens when one of the pulses is upside down.
2. What is the minimum possible intensity, Imin?
c) 9 I1
b) 5 I1
a) 4 I1
1. What is the maximum possible total combined intensity, Imax?
Lecture 1, p 27
NOTE: These are not harmonic waves, so
he
e a e age
ef .
B
ea
e
, e ea he
ae f
the peak amplitude.
Pulses 1 and 2 pass through each other.
Pulse 2 has four times the peak intensity of pulse 1, i.e., I2 = 4 I1.
Act 2
Lecture 1, p 28
Ne
e e
ee h
h
.
The sum of two sines having the same frequency is another sine
with the same frequency.
Its amplitude depends on their relative phases.
If you added the two sinusoidal waves shown,
what would the result look like?
Superposing sine waves
Lecture 1, p 29
y
2A1 cos
Amplitude
/2
2
+
2
t + / 2)
kx
cos
Oscillation
2A1 cos( / 2) cos(kx
y1 + y 2
A1 cos + cos
y = y1 +y2
Use this trig identity:
Resultant wave:
Spatial dependence
of 2 waves at t = 0:
t + /2
Suppose we have two sinusoidal waves with the same A1, ,
and k: y1 = A1 cos(kx - t) and y2 = A1 cos(kx - t + )
One starts at phase after the other:
Lecture 1, p 30
Adding Sine Waves with Different Phases
he e
de
a d g
e
Remember Ask-The-Prof bonus survey
Chec
Read Young and Freeman Sections 35.1, 35.2, and 35.3
A Consequence of superposition
Next time:
Interference of waves
Lecture 1, p 31
f(x + vt) will describe the same shape
moving to the left with speed v.
f(x - vt) will describe the same shape
moving to the right with speed v.
Suppose d = vt. Then:
y= f(x - d) is just the same shape
shifted a distance d to the right:
Why is f(x vt) a a e g a e ?
Suppose we have some function y = f(x):
y
y
y
x = vt
y(x) Ae
v
x=d
Ae
2
Ae x / 2
y(x )
y( x )
x
2
x
( x vt ) 2 / 2
x
( x d )2 / 2
2
Appendix: Traveling Wave Math
Lecture 1, p 32
2