Physics 34 (Waves, Optics and Thermal Physics) Home Page, Spring 2002

Physics 34: Waves, Optics and Thermal Physics


5/20/02 All materials for the course have been graded and your grades have been turned in to the registrar. Lab reports, problem sets and final exams are sitting beside my office door for you to pick up. If you'd like me to send you your materials, please email me your postal address and I'll oblige. I haven't made the usual mass copies of the solutions to the final, to save a bit of paper. If you'd like a copy of the solutions, I'm happy to run one off for you--- ask me. I've enjoyed having you in the class. Have a good summer!

5/13/02 All problem sets have now been graded. They're all sitting outside my office for you to pick up. Lab reports will be done soon as well.

4/29/02 I've posted the next problem set below. This will be the last graded problem set.

4/29/02 Remember: Class will be held 4-5 on Tuesday April 30, so that we can see thesis defense talks 5-6.

4/24/02 The final exam will be: Tuesday May 14, 2-5 pm, Merrill 220.

4/23/02 I've posted the problem set for Week 12 below.

4/20/02 I've posted the next problem set below. It'll be due Wednesday.

4/15/02 The second midterm exam date has been changed to Friday of this week, 7-9 pm, to accomodate John Bahcall's talk at UMass on Wednesday evening.

4/12/02 I've added an assortment of links to applets and other sites germane to this course at the bottom of the page (many of these were collected by Professor Moreau for her Physics of Sound and Music course). If you have any others that are useful, please pass them along. I'd also be pleased to have any feedback on which (if any) you find helpful or interesting.

4/11/02 As requested, I've added some references on error analysis to the list of texts (under lab texts heading). The library has an old version of Baird's book and a new version of Taylor's.

4/9/02 I've posted problem set 10 below.

4/3/02 I handed problem set 9 out in lab today. Also, the deadline on the writeup on the op-amps lab has been extended until Friday at 5 pm.

3/27/02 I've posted problem set 8 below.

3/13/02 I've posted problem set 7 below.

3/9/02 I've posted problem set 6 below.

2/27/02 I've posted problem set 5 below.

2/20/02 I've posted problem set 4 below.

2/11/02 I've posted problem set 3 below.

2/6/02 I've added some links to sites related to liquid nitrogen, courtesy of Mark Wheeler.

1/28/02 As decided in class today, the fourth hour will henceforth be on Tuesdays 4:30-5:20 in Merrill 211. The possibility of a different time is begin contemplated but seems remote.

I've corrected the mid-term exam dates in the text below. The dates that were in the table were correct. Please let me know if you have any conflicts.

The bookstore doesn't have the textbooks yet, and no one was able to tell me when they'd arrive when I called today. I'll let you know more when I know. In the meantime, I've photocopied the first chapter of Schoeder and left it outside my office. It's in two parts, so make sure to pick up both parts.

I'll tentatively schedule my office hours for: Monday 11-12 am, Tuesday 10-11:30 am, and Wednesday 1-2 pm, or by appointment. You're also welcome to drop in to my office. If I'm in and I'll talk to you if I'm free, but that's not so often during the day.

1/26/02 Welcome back! On the first day of class I'd like to try to resolve the question of the fourth hour in Physics 34. It's currently scheduled for Tuesday 2-3 pm. I'm open to the possibility of rescheduling, if we can find a time that's acceptable to all. If not, we'll stick with the Tuesday 2-3 pm slot. With that in mind, please come to the first class ready to discuss and commit to a time for the fourth hour. Due to prior obligations, I must exclude from consideration: Tuesday 11:30-1:30, Thursday after 4 (that's colloquium time), Friday 1-3. Consider as candidates Tuesday or Thursday 10-11 or Tuesday afternoon (say 4-5), which are especially convenient times for me.

1/09/02 On the first day of class I'll consider rescheduling the fourth hour, so try to have your schedule in mind. One possibility: if the Physics 42 fourth hour changes times, we may be able to move into the Thursday 1-2 slot.


Course Information

Course Description:

This is almost a course about the physics of systems with many degrees of freedom and/or particles. I say almost because there are a few extra topics tossed in which don't comfortably fit that characterization. The course, first instituted many years ago, was not conceived with this theme in mind. It was, rather, a course in which you learn stuff you'll need, important stuff, but stuff that isn't taught in any of the other intro-sequence courses with more well-defined themes. Nonetheless, given the material which is to be covered it almost works out to be a "complicated systems" course, and that's the way we'll approach it.

The first part of the course deals with simple thermal phenomena and an introduction to statistical mechanics and thermodynamics. This is the study of systems with huge numbers of particles, each of which moves randomly. We'll find that by ignoring the detailed random motions of particles and looking at such systems in terms of only macroscopic observables we can come to very general and powerful conclusions about their behaviors. The latter part of the course is the study of linear waves, a class of coherent motions commonly present in systems of large numbers of particles (e.g. a big metal rod). Our approach to this problem will be to neglect the discreteness of the system and instead approximate the many particles by a continuous field, analogous to the electromagnetic field from Physics 33. As a result, we will be able to study both many sorts of waves in various media and waves, including electromagnetic waves. The same principles will apply in quantum mechanics as well, where matter itself is treated as a wave (although you'll have to wait until you take Physics 35 to see this).

The general characteristics of wave motion will be approached through the wave equation and the solution to the boundary value problem. Subsequent discussion cover energy relationships in waves, diffraction, interference, reflection, refraction and polarization.

There are a pair of "outsider" topics as well. One is geometrical (ray) optics, which is really a consequence of the behavior of electromagnetic waves but which not be treated in the same fashion. Another is operational amplifiers, which will be useful in Physics 35 but which have nothing to do with anything else in the course.

Throughout the course, new mathematical techniques including probability and combinatorics, Fourier analysis and matrix algebra will be introduced as needed. Mathematica and/or Calculation Center may be introduced to broaden the range of problems you'll be able to tackle.


Times and places:


Math 13 and Physics 33 or the equivalent, or instructor's permission.

Course requirements

Statement of Intellectual Responsibility:



There is no single textbook designed for a course covering this material at this level. The comprehensive intro books would not adquately challenge you. Plenty of specialty texts are written on waves, optics, thermal physics and electronics individually, but they are designed to be used in semester- or year-long courses devoted to these subjects (and often cost of order $100 apiece). Perhaps at some point this semester I'll have lecture notes in typed form that would constitute a text of sorts, but that will be a Herculean task and not guaranteed to be completed. I've tried to find a few good, not-too-expensive books that roughly cover the material of this course, and I will supplement these with suggested and required readings from other texts, journal articles, web pages and my own written supplements in places where their coverage of the course material is sparse. Be forewarned: this is not like other physics courses where you might hope to read the text chapter-by-chapter in lieu of the lectures. It will be more like some humanities courses in which there are required readings, and the lectures tie them together, provide a look at overarching themes, and explore subtleties and extensions.

Required (should be available at the Jeffrey Amherst bookstore):

I've asked the library to order copies of these books. They'll be placed on reserve when they arrive.

Additional useful references (if the library doesn't have them, I'll try to get them):

On thermodynamics and statistical mechanics: General texts on waves and optics: Lab Work: Specialty books:

Other Comments:

Class preparation: I strongly recommend that you try to read the relevant sections of the text before the corresponding lecture and that you try and exercises embedded in that text. Lecture will not be a regurgitation of the text. I will cover related material in lecture, but I won't feel obliged to be comprehensive in those places where I feel the text is adequate, and I may focus only on a few points that I feel are particularly interesting or subtle. You shouldn't expect to understand what's going on without close study of the readings I suggest, and you should come to class with questions you have on the readings. Further, after we settle into the semester a bit, I expect the classes will become less lecture-oriented and more participatory, and it will be difficult to reap the maximum benefit from that format if you're not sufficiently prepared to fully participate.

Lecture/Lab Schedule
Week Notes Hmwk Lab
1. January 28 Intro thermo: zeroth and first laws
Jan 28: Administrative stuff / Course overview / Big picture of thermal physics. Why does time flow forward?
[Handouts: Intro pages, info sheet, first lab]
Jan 29: What is temperature? Paradigmatic thermal process. Thermoscopes, temperature, thermal equilibrium and the zeroth law of thermo. Constant volume gas thermoscope.
Jan 30: Thermometers. How is energy stored in matter? Connection between energy and temperature. Ideal gases: ideal gas law, kinetic theory model of ideal gas.
[Handout: Romer AJP article on temperature scales]
Feb 1: How well does our ideal gas model work? Specific heat prediction and comparison to experiment. Equipartition theorem. Role of quantum mechanics in turning off degrees of freedom.
Read Schroeder, Chap. 1 (you may omit section 1.7)
Problems from Schroeder, Chap. 1: 8, 16, 20, 22, 27, 31, 34, 38, 39, 40.
Lab 1: Ideal Gas Thermometry EI
2. February 4 Finish First Law, start Second
Feb 4: More on quantum mechanics and mechanical degrees of freedom. Heat and Work. Definitions. Types of work. Calculating work. PV diagrams and constrained processes. Quasistatic processes.
[Handout: second lab; "Hot", by Nan Kim-Paik]
Feb 5: Calculating heat and work for some interesting processes. Heat capacities. Latent heat.
Feb 6: Second law: microscopics. Microstates, macrostates, and multiplicity. Two state system: model, counting states, probabilities, calculating multiplicities for macrostates.
Feb 8: Stirling's approximation. Simplifying the multiplicity function. Large and very large numbers. Sharpness of the multiplicity function and the probability distribution. Sharp probability distribution implies well-defined average physical properties.
[Handout: Walker's "Amateur Scientist" article on the Leidenfrost effect.]
Read Schroeder, Chap. 2
Problems from Schroeder: Chap 1: 43, 46, 55; Chap 2: 4, 8, 18, 19, 22, 24.
Lab 2: Latent heat of liquid nitrogen Formal
3. February 11 Entropy and the Second Law
Feb 11: Fundamental assumption combined with sharp multiplicity functions implies macroscopic regularity. Einstein Model: model, equipartition theorem results, and basic quantum mechanics of harmonic oscillators. Calculating multiplicity function.
[Handout: Calculating the multiplicity of an Einstein solid using generating functions]
Feb 12: Irreversibility of heat flow using the Einstein model: multiplicity for systems in thermal contact. How sharp is the peak? Sharp peak (with most of the weight) implies irreversibility. Ideal Gases: multiplicity.
[Handouts: (1) Lab 3--Measuring ratio of specific heats, (2) Complex Numbers and AC Circuits]
Feb 13: Finish the multiplicity of ideal gas. Mulitiplicity for gases in thermal and mechanical contact. Sharp peak means macroscopic regularity, which means well-defined equilibrium temperature and pressure. Define entropy. Second law of thermodynamics: entropy tends to increase.
[Handouts: (1) Complex Numbers and the meaning of exp[ix], (2) Complex Numbers and AC circuits.]
Feb 15: Finish up the Second Law. Complex Numbers.
[Handouts: (1) Input and output impedance and Thevenin's theorem, (2) and (3) Exerpts on op-amps from Horowitz and Hill, (4) Exerpt on op-amps from Diefenderfer.]
From Schroeder, Chapter 2: 2.25, 2.26, 2.30, 2.32, 2.34, 2.38, 2.40, 2.42. Lab 3: Measurement of Cp/Cv EI
4. February 18 Thermal Physics
Feb 18: Connections between entropy, temperature, and heat.
[Handout: Lab 4--Op Amps]
Feb 19: Complex numbers and AC circuits.
[Handouts: Corrected versions of Lab 4 and Complex Number and AC Circuits.]
Feb 20: AC circuits and op amps.
Feb 22: Heat and specific heat. Paramagetism and negative temperatures.
Read Schroeder, Chapter 3 (we'll cover up through 3.4 this week). From Schroeder, Chapter 3: 3.5, 3.7, 3.8, 3.14, 3.15, 3.16, 3.23, 3.25, 3.26. Lab 4: Operational amplifiers EI
5. February 25 Thermal physics
Feb 25: Third law of thermodynamics.
Feb 26: Mechanical equilibrium and pressure. Diffusive equilibrium and chemical potential. Start refrigerators and engines.
Feb 27: Op amps
Mar 1: Heat engines: efficiency. Carnot cycle: step-by-step analysis, efficiency. Refrigerators.
Finish Schroeder, Chap 3. Also Schroeder 4.1, 4.2, and the first part of 4.2; 6.1,6.2.
Problems from Schroeder: 3.34, 3.36, 4.1, 4.3, 4.14, 4.18, 6.5, 6.6
Operational amplifiers EI
6. March 4 Thermal Physics / Geometrical optics
Mar 4: Boltzmann statistics: General idea; derive the Boltzmann factor; probabilities; partition function; (probability-weighted) average values.
Mar 5: Op Amps
March 6: Exam #1, 7 pm
Mar 6: Optics: general intro--connection between wave and geometrical optics mirrors that of stat mech to thermodynamics and quantum mechanics to classical mechanics. Basics of ray optics: index of refraction, law of refraction, law of reflection, total internal reflection, start chromatic dispersion.
Mar 8: Chromatic dispersion. Deriving Snell's law using Fermat's principle.
Read Halliday, Resnick & Walker, Chap. 34.7, 34.8, start Chap. 35
Halliday Resnick & Walker, Chap 34: 49,51,56,57; Chap 35: 3,8,11
Operational amplifiers EI
7. March 11 Geometrical optics
Mar 11: Flat mirrors: real and virtual images; ray tracing; front-back reversal. Spherical mirrors: summary of behavior; paraxial rays, focal point.
Mar 12: Connecting focal point to radius of curvature. Ray tracing with spherical mirrors. Spherical mirror formula. Magnification formula derived. Sign conventions for spherical mirrors.
Mar 13: Derivation of spherical mirror formula. Spherical refracting surfaces: work out all of the cases using ray tracing, summarize with a single formula.
Mar 15: Derive spherical refracting surface formula.
Read Halliday, Resnick & Walker, Chap. 35
Halliday Resnick & Walker, Chap 35: 13,15,20,26,29,31,34,35,37
Lab 5: Operational amplifiers Formal
March 16-24 Spring Break! nada woo-hoo!
8. March 25 Geometrical optics / Transverse waves on a string
Mar 25: Thin lenses: general discussion; sign conventions; derive thin lens formula and lensmaker's equation from two spherical refracting surfaces. Ray tracing.
Mar 26: Thin lenses: magnification formula. Characteristic features of concave and convex lenses. Systems of thin lenses: general treatment; two lenses in the limit that they're close together; two lenses more generally. Start treatment of simple magnifying lens: angular magnification.
Mar 27:
Finish discussion of simple magnifier. Waves: General discussion of waves on a string. Begin derivation of wave equation using Newton's Second Law.

Mar 29:
Finish Newton's Second Law derivation of linear 1D wave equation. Progressive wave solution. Transverse velocity << propagation speed. Start D'Alembert solution to wave equation.
Read Towne, Chap. 1
Towne, 1.1, 1.3, 1.8, 1.11, 1.12, 1.13
Lab 6: Mirrors EI
9. April 1 Transverse waves on a string: General solution, superposition and sinusoidal waves

Apr 1:
Finish D'Alembert's solution to the wave equation. Interpret results as left- and right-moving waves. Qualitative kinematics of wave. Superposition and sinusoidal waves: importance of sinusoidal waves.

Apr 2:
Explicit example: nonlinear equations generally lack a linear superposition principle. Sinusoidal waves (both trigonometric and exponential forms): basic features. Aside on small slopes approximation. Relation between simple harmonic motion and waves on a string.

Apr 3:
Determining waves on a string from initial conditions: two examples. Sinusoidal waves revisited: superposition of two out-of-phase travelling waves.

Apr 5:
Interference in time: beat phenomena. Interference in space: standing waves. Start Fourier analysis: state Fourier's theorem, in both trigonometric and exponential form.
Demo: Beats using two tuning forks.
Reading: There's no single source for this material from the required course texts, so your primary source should be your class notes. However, you might find Chapters 17 and 18 from Halliday, Resnick and Walker helpful. It's on reserve at the Science Library.

Problem set distributed in lab on 4/3/02.
Lab 7: Lenses EI
10. April 8 Fourier analysis

Apr 8:
More Fourier analysis: relating trig Fourier series coefficients to exponential Fourier series coefficients. Given a periodic function, obtain the coefficients of the trig Fourier series. Recall orthogonality relations for trig functions.
Handout: Boas, Chap. 7 (Fourier series)

Apr 9:
Vector space interpretation of Fourier series. More overlap means large coefficients. Obtaining coefficients for the exponential Fourier series. Start Fourier analysis of square wave.
Demo: Fourier Synthesizer applet
Handouts: Lab 8; pp. 647-654 from Boas (Fourier transforms)

Apr 10:
Finish exponential Fourier expansion of square wave. Convert to sine wave expansion. General observations about coefficients. Start discussion of power spectrum.
Handouts: Fourier analysis part of lab; solutions to most recent three problem sets; a graded homework.

Apr 12:
Power spectrum of the square wave: qualitative feature and significance, spectral envelope. Power spectrum of a periodic pulse: calculation, qualitative features, spectral envelope. Bandwidth-pulse duration relation (anticipates uncertainty principle in QM). Fourier transforms: write down the analogs for the Fourier series for nonperiodic functions. Introduce Dirac delta-function in the analog of the orthogonality relation.
Reading: Handouts from Boas. You may find Towne, Chap. 15 helpful also.
Problems from Boas handouts: p. 312, #5; p. 321, #18, 20; p. 327, # 23, 24; p. 330, # 4, 10; p. 653, # 9, 12
Lab 8: Fourier Synthesis/Speed of waves EI
11. April 15 Fourier Analysis / Plane Acoustic Waves
Apr 15: Dirac delta function and its use. Example: cosine wave of finite length: Fourier transform to obtain power spectrum.
Apr 16: Cosine wave example: obtain spectral width and pulse-bandwidth duration relation. Acoustic plane waves: define variables (including Lagrangian formalism), state assumptions. Derivation of wave equation: start conservation of mass equation.
Apr 17: Derivation of wave equation for acoustic waves: finish conservation of mass equation. Newton's second law. Equation of state. Combine these to obtain nonlinear wave equation, then linearize. Obtain expression for speed of sound. Compare prediction for speed of sound to experiment: note discrepancy, attribute it to implicit isothermal assumption.
Apr 19: Exam #2, 7 pm
Apr 19: Derive correct expression for speed of sound using adiabatic assumption. Re-express in terms of adiabatic bulk modulus. Simplified form of linear equations for acoustic waves in terms of acoustic variables. Impedance: re-express equations in terms of impedance. Write solutions to wave equation (left- and right-movers) in terms of impedances.
Reading: Towne, Chap. 2
Problems: Towne, Chap. 2: 2-8, 2-9, 2-14, 2-16, 2-17, 2-19, 2-20
(due Wednesday, rather than Monday)
Finish speed of waves Formal
12. April 22 Transmission-Reflection/Energetics of Waves/Interference
Apr 22: Analogs between acoustic waves and waves on a string. Sinusoidal acoustic waves and their propagation. Qualitative treatment of transmission-reflection phenomena for waves on a string: reflection from fixed end and free end, transmission and reflection between light and heavy strings. Boundary value problem treatment of transmission-reflection phenomena: "hard" reflections in general and with sinusoidal waves for waves on a string. Acoustic waves reflected from hard surfaces.
Apr 23: Boundary value problems: acoustic waves produced by moving boundaries. Transmission and reflection at interfaces with impedance mismatch: general formulation, boundary conditions for fluids (continuity of displacement and of pressure), apply boundary conditions to obtain transmitted and reflected waves. Define velocity transmission and reflection coefficients.
Apr 24: Qualitative comments on velocity transmission and reflection coefficients and transmitted and reflected velocity waves. Transmitted and reflected pressure waves, and corresponding coefficients. Examine cases of extreme impedance mismatch. Example: two fluids separated by a massive plate--formulate problem and obtain new boundary conditions.
Apr 26: Solve problem in case of incident sinusoidal waves, obtain transmission and reflection coefficients. Note that the plate acts as a low pass acoustic filter.
Reading: Towne, Chap. 3 (you can omit 3.8), and Chap. 4 sections 4.1-4.3, 4.6, 4.8, 4.10-4.12.
[If you want more background on this week's lab than is contained in the lab handout, you may wish to read Halliday & Resnick, Chap. 36.]
Problems: 3-3, 3-5, 3-6, 3-9, 3-10, 3-17, 4-6, 4-14, 4-15
Lab 9: Measuring light wavelengths with a ruler Formal
13. April 29 Energetics of Waves / N-source interference and diffraction
Apr 29: Instantaneous and average kinetic energy, potential energy, and power for waves on a string. Special case: sinusoidal waves.
Apr 30: Energetics of sinusoidal waves. Connection with power spectrum. 2D and 3D waves. Intro to two-source interference for sinusoidal waves.
May 1: Average intensity pattern for two-source interference: obtaining convenient forms for the expression in the far-field limit.
May 3: Shortcut to the far-field limit approximation. Start N-source interference.
Reading: HRW Chap. 36 and 37 give the fundamentals. Towne, Chap. 11 (sec. 1-8) and 12 give more details.
Problems: HRW Chap 36, # 29, 43, 60; Chap 37, # 12, 18, 24, 25, 30, 38, 64; Towne Chap 11, #6
Lab 10: Two-source interference EI
14. May 6 N-source interference and diffraction
May 6:Interference notebook
Finish N-source interference. Phasor approach to N-source interference. May 7:Diffraction patterns
Diffraction: generalities, formulate as N-source problem. May 8: Diffraction: Derive expression for totat wavefunction in Fraunhofer approximation.
May 10: Diffraction: finish the single-slit problem, understand the qualitative behavior from exact solution.
No required problem set. Finish interference; Course evaluation EI
May 13-17 Final exam period Final: TBA


I'll keep scheduling information on this site primarily. I'm not yet used to Blackboard, but as I get used to it I may post more stuff on there.

Useful Links

I'll post interesting or useful links pertinent to the course here as they I come across them. If you come across any others, please let me know.

Interesting talks in the Five-College area:

You should start attending the departmental colloquia early and often. They are intended primarily for you, to broaden your exposure to current physics in ways that the department faculty alone cannot. They'll give you an overview of what exciting work is going on in physics and who's doing it. In the begining you won't always understand all of the talks, but you'll be surprised by how much you can understand even now. In addition, the colloquium food here is better than anywhere else I've ever been. Plus, I organize the colloquia, and it warms my heart to see you there.

Area Seminars and colloquia

Interesting and useful papers:

Interesting and useful websites:

Physics applets from MSU
More physics applets from MSU
SIL Speech Analyzer
Shockwave Virtual Piano
Virtual Guitar
Tacoma Narrows Bridge Collapse
Reflection of a pulse
Production of a standing wave
Vibrating Drum Head
Traveling Pressure Wave in a Tube
Standing Pressure Wave in a Tube
Spherical Waves From a Sound Source
Interference from Multiple Sound Sources
Sound Generator
Fourier Synthesizer
Shepard Scale (Auditory Illusion)
Human Ear Hearing
Eardrum, Ossicles and Oval Window moving model
Cross Section of Coiled Cochlea
3D Cochlear Cross Section
Cochlear Cross Section
A Clear Schematic of the Inner Ear Anatomy
Stiffness vs. d along Basilar Membrane
f vs. d along Basilar Membrane
Traveling Waves Along Basilar Membrane
The Organ of Corti
Organ of Corti Mechanics
Lifesize Hammer Anvil and Stirrup
Size of the Cochlea
Fourier Synthesizer
Movie of Vibrating Vocal Cords
Sound and Hearing Page
Acoustics and Vibration Animations
Fourier synthesizer (
Fourier synthesis
Dartmouth: music and computers course
Physics of music and sound links at Harvard
Boye's site at Davidson
MAP_North Deliverable List
Internet Resources for the Mathematics Student ( Langara College - Department of Mathematics and Statistics)
Galileo telescopes (courtesy of Mark Wheeler)
loaded string
a bunch of math/physics applets by paul falstad
Fraunhofer diffraction applet
N-source phasor applet