12-7-11 Web page .. PDF .. Word
Reflection and transmission of waves at interfaces
Physics 213a 2011
Waves and Optics

Instructor: Walter F. Smith (X1332, KINSC Link 110)
Office hours: Tu 11-12, Th 10-11, F 9:30-10:30 or by appointment

Meets: MWF 11:30-12:30, KINSC H108

 Syllabus (also available in PDF or Word Format)

Companion website for our textbook, "Waves and Oscillations: A Prelude to Quantum Mechanics", by Walter Fox Smith

Mathematica keyboard shortcuts & physical constants

Course evaluation form

Assignments
Exams

#1 (due 9-9-11): Web Page .. PDF .. Word
# 2 (due 9-16-11) Web Page .. PDF .. Word
# 3 (due 9-23-11) Web Page .. PDF .. Word
# 4 (due 10-7-11) Web Page .. PDF .. Word
# 5 (due 10-21-11) Web Page .. PDF .. Word
# 6 (due 10-28-11) Web Page .. PDF .. Word
# 7 (due 11-4-11) Web Page .. PDF .. Word
#8 (due 11-18-11): Web Page .. PDF .. Word
#9 (due 12-2-11): Web Page .. PDF .. Word
#10 (due 12-9-11) PDF .. Word


Exam 1: coverage .. practice problems
Exam 2: coverage .. practice problems
Final exam: coverage .

Lecture Summaries
Lecture Summaries (choose a format; PDF files are smaller, Word or PDF files have the nicest formatting):

Monday
Wednesday
Friday
8-29-11 Web page .. PDF .. Word
Harmonic approximation for stable equilibrium, equipartition theorem
8-31-11 Web page .. PDF .. Word
Solving the DEQ for simple harmonic oscillation, dot notation for derivatives, inductors
9-2-11 Web page .. PDF .. Word
LC Oscillators, complex representation for simple harmonic motion, Euler's theorem, commutation relations for Re, complex version of the DEQ, review of complex numbers
Labor Day
9-7-11 Web page .. PDF .. Word
Complex representation for AC circuits, impedance of a capacitor
9-9-11 Web page .. PDF .. Word
high pass filter, impedance of an inductor
Mathematica notebook on high-pass filter
9-12-11 Web page .. PDF .. Word
The wave function, probability density, Schrodinger's equation, principle of superposition, wavenumber, quantum dispersion relation
9-14-11 Web page .. PDF .. Word
Position-wavenumber uncertainty relation, energy-time uncertainty relation, pendula, viscous damping
9-16-11 Web page .. PDF .. Word
Damped oscillators, the quality factor Q
9-19-11 Web page .. PDF .. Word
Decay of energy, damped electrical oscillator, begin driven oscillator
9-21-11 Web page .. PDF .. Word
Amplitude and phase for driven oscillator
9-23-11 Web page .. PDF .. Word
Power resonance, superposing drive forces
9-26-11 Web page .. PDF .. Word
Review for exam 1, transients

9-28-11 Web page .. PDF .. Word
Response to a triangle wave drive
annotated Mathematica notebook

9-30-11 Web page .. PDF .. Word
Driven electrical oscillator, beats, DEQs for symmetric coupled pendula
10-3-11 Web page .. PDF .. Word
Pendulum mode, breathing mode, definition of normal mode
10-5-11 Web page .. PDF .. Word
Superposing normal modes yields beats!, Hilbert space, column matrix notation for Hilbert space vectors, kets
10-7-11 Web page .. PDF .. Word
Inner products, general case of superposed normal modes
  Fall Break  
10-17-11 Web page .. PDF .. Word
Non-zero inital velocities, analogy with molecular orbitals
10-19-11 Web page .. PDF .. Word
Damped, driven coupled oscillators
10-21-11 Web page .. PDF .. Word
Matrix multiplication, determinants, the eigenvalue equation for multiple coupled oscillators
10-24-11 Web page .. PDF .. Word
Procedure for solving the eigenvalue equation
10-26-11 Web page .. PDF .. Word
Finding eigenvectors and eigenvalues with Mathematica, orthonormality, normal mode analysis for multi-object systems
10-28-11 Web page .. PDF .. Word
The beaded string, standing wave guess
10-31-11 Web page .. PDF .. Word
Boundary conditions quantize the frequencies, Number of normal modes and minimum meaningful wavelength for the beaded string, begin example of normal mode analysis for the beaded string
11-2-11 Web page .. PDF .. Word
Example of normal mode analysis for the beaded string, including animation in Mathematica
Mathematica notebook
11-4-11 Web page .. PDF .. Word
Longitudinal oscillations, begin continuous string
11-7-11
Review session for exam 2
11-9-11 Web page .. PDF .. Word
Inner products for continuous systems, normalized eigenvectors for the continuous string, example of normal mode analysis for the continuous string, including animation in Mathematica
Mathematica notebook
11-11-11 Web page .. PDF .. Word
k-space, basis functions, generic orthogonal function analysis, Fourier analysis
11-14-11 Web page .. PDF .. Word
Example of Fourier analysis: the sawtooth, Fourier analysis for functions of time, begin complex version of Fourier analysis
Mathematica notebook
11-16-11 Web page .. PDF .. Word
Complex version of Fourier analysis, cosine with phase version of Fourier analysis, begin experimental Fourier analysis
11-18-11 Web page .. PDF .. Word
Experimental Fourier analysis: frequency resolution, Nyquist limit, aliasing, order of frequencies in the Discrete Fourier Transform
11-21-11 Web page .. PDF .. Word
Windowing, Fourier transforms
11-23-11 Web page .. PDF .. Word
Fourier transform of a Gaussian, The Wave Equation
Thanksgiving break
11-28-11 Web page .. PDF .. Word
E = cB, Poynting vector, superposition principle for traveling waves, non-linear waves, traveling sinusoidal waves
11-30-11 Web page .. PDF .. Word
Waves on transmission lines
12-2-11 Web page .. PDF .. Word
RMS amplitudes, begin group velocity
12-5-11 Web page .. PDF .. Word
Finish group velocity, superposing traveling waves to make standing waves
12-7-11 Web page .. PDF .. Word
Reflection and transmission of waves at interfaces
12-9-11 Web page .. PDF .. Word
Meaning of characteristic impedance of a transmission line, suppressing reflections, Snell's Law




Links, songs, etc.
 
Chapter 1 Links:  

Most of the links for Chapter 1 are on the companion website for our text. Three additional links are given to the right and below.

 

Short movie giving an overview of atomic force microscopy. Watch the opening segment (which is a couple of minutes long). When the voice-over ends, click the link for "tapping mode". (The movie was made by the Imaging Technology Group at the University of Illinois.)
"Complex Z" Lyrics by Walter F. Smith, tune: "Let It Be", by the Beatles. Lyrics & chords.. mp3 (guitar by Matt McCutchan)
Animation showing that the position of a mass on a spring is the same as the horizontal position of a point moving in a circle. [This animation was developed specifically for the text, "Waves and Oscillations: A Prelude to Quantum Mechanics", by Walter Fox Smith.]

Chapter 2 Link:

Applet about the simple pendulum, created by Prof. Wolfgang Bauer.

 
 
Chapter 3 Links:
The links for Chapter 3 are on the companion website for our text.
 
Chapter 4 Links:
The links for Chapter 4 are on the companion website for our text.
 
Chapter 5 Links:
The links for Chapter 5 are on the companion website for our text.
 

Chapter 6 Links:
The links for Chapter 6 are on the companion website for our text.

 
Chapter 7 Links:
The links for Chapter 7 are on the companion website for our text.
 
Chapter 8 Links:
The links for Chapter 8 are on the companion website for our text.
 
Chapter 9 Links:
"Coaxial Waves", Lyrics by Walter F. Smith, Tune: Jingle Bell Rock
This applet by Prof. Fu-Kwun Hwang shows you how sinusoids traveling in opposite directions superpose to make a standing wave.
Try out this applet from Interactive Simulations at the University of Colorado at Boulder that shows the connection between the way the end of a rope is moved and the shape of the resulting wave pulse. For now, you should choose "No End", and set the damping to zero. Although individual beads are shown, the simulation is based on the behavior of a continuous rope.
Try out this keen group velocity applet by Paul Falstad. This emphasizes the addition of two sinusoids to produce the pattern of a carrier wave times an envelope function. Start by slowing the simulation speed to about half the initial value, setting frequency 1 a little less than frequency 2, and setting speed 1 significantly less than speed 2. You should be able to see that the wiggles inside the envelope move at about the average of the speeds of the two component waves.
 
Chapter 10 Links:
Check out this brilliant web page and applet about Snell's Law, put together by Rick Reed.
 

 

 

Researchers at the IBM Almaden Laboratory used a scanning tunneling microsope to position 48 individual Fe atoms in a circular corral on a Cu surface. The waves seen eminating from the center are due to quantum mechanical wavefunctions of the surface electrons forced into circular states by the arrangement of the Fe atoms.

(Thanks to Rob Scarrow for this caption.)