Announcements

Instructor

Professor William Loinaz
Office: 223 Merrill Science Center
Phone: (413) 542-7968
email: waloinaz@amherst.edu
Office Hours: M11-12, W5-6, F11-12 or by appointment. You're also welcome to drop by my office. If I'm in and free I'm happy to meet with you, but it's not so often during the day that I'm in and I'm free. I'll post a skeleton of my weekly schedule on my office door.

• Grader: Matt Willis
• Lab TA: Mark Wheeler

Course Information

Course Description:

In the first part of the course we'll consider systems of huge numbers of particles whose microscopic motions are random. The study of such systems is known as statistical mechanics. We'll find that by ignoring the details of the random motions of individual particles and looking at such systems in terms of only macroscopic observables we can come to very general and powerful conclusions about their behaviors. Ultimately we will be able to describe essentially all macroscopic thermal phenomena (thermodynamics), and we will be able to answer the question of why time appears to flow forward.

The latter part of the course is devoted to 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. 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. We'll also see how geometrical (ray) optics can be obtained from wave optics in the short-wavelength limit. If time permits, we'll broach the subject of nonlinear waves and solitons.

In the laboratory portion of the course we will get our hands on some thermal and wave phenomena and geometrical optics. We'll also continue our study of electronics, begun in Physics 33, with an introduction to operational amplifiers.

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

Schedule

• Class: MWF 10-10:50, Th 1-1:50 (Merrill 211)
• Lab: W 2-5 (Merrill 217)
• Problem Session (informal): (tentative) Monday night at 8 pm, physics student lounge (Merrill Science 114/116).
• Additional problem session--Women in Physics study session: last semester it was Tuesdays (in the physics student lounge), after 9 pm open to all. When I know the schedule for this semester I'll post it here.

Prerequisites

Course requirements

• Attendance:
  Come to class. Lots of stuff will happen there and you wouldn't want to miss it. Lectures and in-class discussion will generally NOT duplicate the texts, so don't assume you can just "get it from the book". You'll find this to be more the case in this course more than in other physics courses, in part because there are no textbooks written for a course like this (and in part because I like to do things my own way).

  It's your affair how you allocate your time and I won't explicitly penalize you for being absent, but if you're going to be absent please do me the courtesy of letting me know in advance, if possible. It's a small class--I'll notice if you're missing. If you arrive late, please enter quietly at the back of the classroom. Obviously it will be your responsibility to find out what happened in the class you missed. Also, you must attend all of the labs.

• Homework:
  I'll assign weekly problem sets, due Tuesday @ 11:59 pm. You may leave your homework in my mail slot near the physics department office, or of course you may give it to me personally (please do NOT leave it in the box beside my office or stick it under my door). Homework submitted late without prior arrangement will receive a 50% penalty if submitted within three days of the due date (i.e. by Friday @ 11:59 pm), and will not be accepted after that. For those of you that took Physics 33, take note that more often than last semester I WILL be around to collect homework when it is due.

  Why do the homework?
  I can't emphasize enough the importance of working the problems. In some of your classes homework is primarily evaluative; the point is for you to demonstrate what you've learned from the readings and lectures. In physics the homeworks are primarily instructional; you learn physics primarily by working problems. You must work the problems, think about the results, and understand any mistakes you've made if you wish to attain the type of understanding of the subject required of a working physicist. In at nutshell: If you can't work problems you don't know physics. I (or a grader) will grade the problems, and I'll post solutions to this web page as quickly as I can. I encourage you to read the solutions and understand any mistakes immediately. If it doesn't make sense, ask me about it right away---don't wait until right before an exam. Pragmatically, year after year I observe a strong correlation between performance on homework and overall performance in the courses I teach. While missing a homework or two does not have a profound impact on your grade, remember that the combined weight of the homework is that of a midterm exam, so skipping them all is not advised. A more serious consequence of skipping homework is missed opportunity to sharpen your understanding.

  Homework grading:
  I instruct the grader to give full credit only to a clear, correct and complete solution. I always encourage the grader for the course to be picky in grading the homework. The point is not to frustrate you, but to bring to your attention problems (from sign errors to sloppy reasoning) so that you can clarify your thinking and improve your problem-solving skills. If you lose points, be grateful that someone is paying sufficiently close attention to your work to give you valuable feedback. Of course, the grader is a student like you, and has only a limited amount of time to expend on grading. I've told him/her that if s/he doesn't see your logic or can't read your solution, don't give credit. If s/he makes a mistake in the grading, simply bring it to me and when you explain it I'll correct the grade.

  Extensions
  If you've got a compelling reason why you need an extension, come talk to me in advance. I will not grant a homework extension without penalty if you ask for it on the day the homework is due, so don't ask for one. [If you need such a last-minute or post-facto extension due to extenuating circumstances (e.g. death in the family, sudden illness, travel problem), you'll need to have the Dean of Students or your Class Dean formally make such a request to me and suggest a rescheduled due date. You should also take this route if you need an extension but you don't want to tell me why (say, it's for personal or legal reasons). If you explain your reason to a Dean and the Dean tells me it's OK, that's good enough for me.] In general, though, life will be easier for you and for me if you get into the habit of doing your best to finish the problem set on time and handing in as much as you've been able to complete by the deadline. Even if you finish your homework after the three-day deadline, you can turn it in. I won't award you credit, but I will record that you did the problem set.

• Labs: A weekly lab will be held in (Location: Merill 217), Wednesday 2-5. Attendance at all labs is mandatory; if you must miss a lab for some compelling reason, please see me well in advance so that we can schedule an alternative time for you to work the lab. I'll hand out a lab manual at the beginning of the semester. Please read the relevant portions of the lab manual before coming to lab. Some labs will be graded by exit inteviews, others by formal lab writeups (listed respectively as EI or formal in the last column of the lecture/lab schedule below). Please bring to lab a bound lab notebook that can be used exclusively for Physics 34 (I collect your lab notebooks at some point during the semester). It can be a spiral or sewn notebook, or any other type that has pages which cannot be removed, and it should be quadrille ruled. I also recommend you either bring a floppy disk for saving data, etc., or get into the habit of saving these in your network filespace.

  The formal lab writeups are due one week from the day the lab was performed, unless otherwise noted. Late labs (and rewrites) will be penalized 10% per day late (including weekends). In any case, each lab not performed or lab report not submitted will automatically cost at least a full letter grade in the final course grade.

  Unlike Physics 33, I will grade the lab reports myself. The standard for clarity and completeness will be somewhat higher than in Physics 33, and in particular I'll take care to note that you've done the error analysis. The book by D. C. Baird (listed below) continues to be a good guide to style in lab reports.

• Exams: There will be two mid-term exams and a final, and these will serve as the primary evaluative mechanisms for the course. The exams will be three hours long and will be held during the normally-scheduled lab period, so they shouldn't conflict with your other commitments. They will be closed-book, and all course material (lectures, labs, handouts, text readings and homeworks) will be fair game for the exam. I'll give you relevant formulae, so the exams will be not be memorization exercises. I tend to have some mix of short-paragraph written questions and problems. I tend to like problems that ask that you derive results utilizing key derivations from class, then use the result to do something new.

  Each faculty member has a style of exam they prefer. Exams in this course will be challenging, and you should not be discouraged if you don't receive perfect scores. I try to construct problems so that if you've got an idea what the problem is about and you've got a moderate working knowledge of the physics needed to solve it, you should be able to get at least 2/3 of the points. If you get stuck during an exam, don't panic! You should formulate a question and come ask me. I may not answer your question, but I certainly won't fault you for asking. The purpose of the exams is for to demonstrate your knowledge, and it doesn't serve that purpose for you to turn in blank pages just because you didn't see the mental picture I had when I wrote the problem.

  Unlike in Physics 33, in this course I do have some exams from previous years which you can use as a study aid. Just ask.

  The midterms will be scheduled during lab time, dates listed in the table below. In the unlikely event you have a conflict with these days, let me know immediately.

• Extensions: In the interest of fairness I will hold fast to the deadlines and policies above. In particular, I won't grant extensions to homeworks on the day they're due, and I won't reschedule the exam for an individual to a different day from the rest of the class. Should circumstances render such rescheduling unavoidable, you'll need to have the Dean of Students or your Class Dean contact me with a formal request for an extension and a suggested rescheduled time. Such matters should be taken care of before the exam if at all possible. If the matter is personal or confidential, the Deans need not provide me with any particulars, only their opinion that the rescheduling is reasonable.

  The College requires that all written work for a course except for a final be submitted by 5 pm on the last day of classes. The physics department takes this deadline seriously. After that day/time, no homework or lab reports will be accepted, nor will I conduct exit interviews for labs.

Statement of Intellectual Responsibility:

• I strongly encourage you to discuss the homework problems and learn the labs with your classmates---discussing and debating the concepts and procedures is a very effective way to learn. However, the final write-ups of your assignments or lab reports should be your own. For example, the copying homework solutions in part or in whole from other students (current or prior) or from other sources (commercial or otherwise) is unacceptable. I don't mind if you use other texts to learn from, and if the answer to a homework problem is worked as a example in some other text you may utilize it (although you should first try to solve it on your own as best you can). But in that case you should make an explicit reference to the source in your homework, and of course you still need to explain the solution to the problem in your own words. It goes without saying, but I'll say it anyway: tests are written without help.
• In the lab, lab partners are expected to share equally in the collection of data. However, each student must keep a separate record of the data and do all calculations independently. Lab writeups should be done independently, although you may discuss the data and analysis with other members of the class. Copying or paraphrasing any part of another lab writeup is obviously inappropriate. In addition, we wish to emphasize that intellectual responsibility in lab work extends beyond simply not copying someone else's work to include the notion of "respect for the data". By this we mean that you should not alter, "fudge" or make up data just to have your results agree with some predetermined notions. It is always best to simply state that your results did not turn out as anticipated and try to understand the discrepancy between your expectation and the data. You should never erase data which appear to be wrong. It is perfectly legitimate to state that you are going to ignore some data in your final analysis if you have a justifiable reason to suspect a particular observation or calculation.
• If you have any questions about what is or is not acceptable under this policy, please ask us. In all cases, the spirit of the Statement of Intellectual responsibility will take precedence over legalistic convolutions of the text.

How to get the most from this class:

• Come to class awake and on time.

• Do the relevant reading and read through the problems assigned for the week before the lecture (I'll announce the readings and problems in class and post them on the website). Even if you don't understand the readings fully at the time, try to get the broad outline of the material so you'll have some hooks on which to hang the ideas that we talk about in class.

  The roles of lectures and textbooks
  Lecture will not be a regurgitation of the text, a summary of all you need to know for the course, or a how-to guide for the homework. Rather, I'll try go deeper into selected points. In lecture I'll cover material and do demonstrations related to the readings, 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, 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; it will be difficult to reap the maximum benefit from that format if you're not sufficiently prepared to fully participate.

• Ask questions: in class, after class, during office hours, in problem sessions, the lab, the hallways. Ask the questions you think you're supposed to know the answer to, the questions you're sure everyone else knows the answer to (they don't), questions about the overarching logic or the minute details, questions about the points or conclusions that weren't made that seem like they should follow. If individual arguments, their interconnection, or the entire point of the lecture don't seem clear to you, ASK. The main benefit to taking a class, especially at a small school like Amherst, is that you can ask questions of the experts.

• Work the problems: Start early. Try all of them. Struggle with them awhile yourself---some will be clear, simple exercises meant to familiarize you with a procedure, others will be meant to stretch your understanding (some will be intentionally vague, so that you have to clarify the picture before solving the problem). Be sure you can state what ideas (mathematical and physical) are being utilized in each problem; even if you still can't solve the problem you're most of the way there. The ability to work problems is not sufficient to claim an understanding of the physics, but it is a necessary step.

  For the problems you can't solve, talk to classmates, attend the problem sessions, or ask me. When you ask me, either try to give you just enough of a hint to get you through, or I'll guide you through the problem with a series of leading questions. I'll never just tell you how to do it. If you run out of time and don't finish the set, start earlier next week. When the solutions come out, look over them right away, before you've forgotten all of the points you were confused about. You think you'll just get clear on it before the next exam, but there's never as much time as you think.

• Read the labs in advance!

• If things aren't going as you'd like, take an active role in improving your situation. Use all of the resources at your disposal. Step 1 is almost always to come talk to me. If you don't understand what's going on in lecture, lab, the book, or the problems, if you feel like you can't keep up, come talk to me. I can help you, and I can point you to additional resources. Don't hide.

  On the other hand, if you find the class too slow for your liking, if you have questions that you aren't getting answers to, if you'd like more detail, if you are frustrated that we aren't digging deeply enough, if you crave more applications, come talk to me. I'm very happy to provide you with additional materials or explanations that will will stimulate you and challenge you at whatever level you can handle.

  One word of warning: Amherst College students tend to have lots of extracurriculars of all types. I support this (enthusiastically), and I am occasionally willing to be flexible to facilitate your participation in range of activities, but don't let your extracurriculars overshadow your academics. If you become concerned that your courses are getting in the way of your extracurriculars, you definitely have the wrong mindset. Remember why you're here.

  If circumstances in your life beyond the class are the problem, you can come talk to me, but also talk to your class Dean.

Grading:

• Homework: 20%
• Lab: 15%. (However, all labs, lab reports and exit interview must be completed to instructor's satisfaction or large automatic penalties will apply.)
• First Midterm: 20%
• Second Midterm: 20%
• Final: 25%

Textbooks:

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

• An Introduction to Thermal Physics (ISBN: 0201380277)(hardcover), by Daniel V. Schroeder
  [This book is about the right level, although it contains more material that we'll cover (it's designed for a semester-long course). It was used in this course last year and met with mixed reviews.]
• The Physics of Vibrations and Waves (5th ed.) (ISBN: 0471985430)(softcover), by H.J. Pain
  [This book is at a pretty good level. It too contains more material that we'll cover, and we'll cover a few topics with greater sophistication than the book. Unfortunately, despite the fact that it is in its fifth edition, it is riddled with typesetting errors.]
• In addition, obtain a bound lab notebook dedicated to Physics 34 labs (i.e. one that I can collect and keep for as long as I like). Bring it to lab on Wednesday.

• Lectures in Physics, Chap. 39-46 (vol. 1), R. P. Feynman

• Wave Phenomena (ISBN: 0-486-65818-X)(softcover), by Dudley Towne (a former Amherst College Professor)
  [The level is about right, although the book contains more material than we'll cover, is not very flexible in the ordering of topics, and is a bit old-fashioned. Good value for the price, though.]
• Lectures in Physics, (vol. 2), Richard P. Feynman [Feynman's insights are always unique and worthwhile.]

• Experimentation: An Introduction to Measurement Theory and Experiment Design (3rd. ed.), D.C. Baird [A good overview of general techniques useful in lab work.]

• Six Ideas that Shaped Physics: Some Processes are Irreversible, by Thomas Moore [One of the texts used two years ago in Physics 34. It was unpopular with the class, although I like it.]
• Understanding Thermodynamics, H. C. van Ness
• Thermodynamics, Enrico Fermi [a small book by one of the masters]
• Thermodynamics and Heat Power, Granet & Bluestein [engineering applications]
• Thermal Physics, C. Kittel and H. Kroemer [advanced text occasionally used in Physics 75]
• Thermal Physics, Ralph Baierlein [advanced text occasionally used in Physics 75]

• Optics (4th ed.), Eugene Hecht [Talks about waves, but obviously with a focus on electromagnetic waves.]
• An Introduction to Optics (2nd. ed.), Pedrotti and Pedrotti
• Vibrations and Waves, French
• Electricity and Magnetism, Chap. 9, E. Purcell [The text used in Physics 33 last semester.]
• Waves, F. Crawford [Develops waves from discrete mechanics. Lots of nice at-home experiments. Out of print.]
• The Physics of Waves, Howard Georgi [Similar to Crawford in approach, but with more sophisticated mathematics.]
• Classical Dynamics of particles and systems, Marion and Thorton. Chap 13 covers waves, Chap 3 covers Fourier series. [A succinct treatment of the wave equation. The text has been used in Physics 42.]
• Physics of Waves, William C. Elmore and Mark A. Heald [One of the standards at this level. An excellent book, but more sophisticated than the level of this course.]
• Optics (Schaum's Outline Series), Eugene Hecht [Worked examples are always nice for studying.]
• Fundamentals of Physics (Sixth Edition): Part 4 (contains Chaps. 34-48) (ISBN: 0-471-36039-2)(softcover), by Halliday, Resnick & Walker
  [This book is a bit lower level than I'd like--it's often used in first-year courses-- but it provide a good coverage of geometrical optics if you're seeing the subject for the first time.]
• Building Scientific Apparatus (Third Edition), John H. Moore, et. al. [A compendium of techniques for building useful stuff.]

• An Introduction to Error Analysis, John R. Taylor [A good introduction to error analysis of the sort that is useful in our lab work.]
• The Elements of Style (Fourth Edition), William Strunk Jr. and E. B. White [Just because you're writing lab reports doesn't mean you can ignore grammar, punctuation and usage. This little book is full of tips that will improve your writing in ALL of your courses, including this one. Buy it, read it, use it.]

• QED, R. P. Feynman [an introduction to the quantum theory of light. I have the lectures on which this book was based on videotapes. I'll hold viewings during the semester.]
• Mathematical Methods for Physicists, Arfken [a mathematical physics book that has the details about Fourier series and Fourier transforms that we gloss over in class]
• Mathematical Methods in the Physical Sciences (2nd ed.), Mary L. Boas [another mathematical physics book that has Fourier analysis stuff. at a lower level than Arfken. very popular around here.]
• Mathematical Handbook (Schaum's Outline Series), Murray R. Spiegel [a convenient compendium of useful mathematical formulae, including integrals and special functions at a low, low price. You should buy a copy---you'll use it through your entire physics career.]
• Fourier Analysis (Schaum's Ouline Series), Murray R. Spiegel [lots of worked examples of Fourier series and Fourier transforms, if you want more practice]

Other Comments:

Problems

Lecture/Lab Schedule

Week	Notes	Hmwk	Lab
1. January 27	Thermodynamics: Zeroth and First Laws Jan 27:Introduction to the course Administrative stuff / course overview / the big picture of thermal physics. Why does time flow forward? [Handouts: web page, student info sheet [source], Lab 1, Notes on Uncertainty analysis [source], Thermometers and Thermostats handout] Jan 29: What is temperature? Paradigmatic thermal process. Phenomenological approach to temperature: temperature, thermoscopes, zeroth law of thermodynamics. Temperature standard: constant volume gas thermoscope and T=CP. [Handouts: Romer article on temperature] Jan 30: Thermal Energy and Ideal Gases Thermometers. Temperature related to energy via the specific heat. How is energy stored in matter? Ideal gases: Ideal gas law, kinetic theory model of ideal gas. Jan 31: Kinetic theory model of ideal gas Kinetic energy related to temperature. Internal energy stored as microscopic mechanical energy. How well does the model work? Comparison of prediction of specific heat to experiment. Equipartition theorem.	Read: Schroeder, Chap. 1 Problems: Chap. 1: 1.8, 1.16, 1.20, 1.22, 1.27, 1.31, 1.34, 1.38, 1.39, 1.40 Deadline extended to Wed. 11:59 pm	Lab 1: Ideal gas thermometry [MSWord source]	EI
2. February 3	Thermodynamics: First and Second Laws Feb 3: Ideal Gases / First Law Equipartition redux Quantum mechanics determines how degrees of freedom are counted for equipartition theorem. Typical energy scales for quanta. Einstein solid. First Law Heat, work defined. First law is conservation of energy. Expansion-compression work. [Handouts: Lab 2] Feb 5: PV diagrams and constrained processes Quasistatic processes. PV diagrams. Calculating work and heat transfers for quasistatic isothermal, isobaric, isochoric, and adiabatic processes. Closed cycle processes. [Handouts: Additional notes on specific heats, Notes on formal lab writeups [MSWord source] and uncertainty analysis [MSWord source], more notes on formal lab writeups [MSWord source], article on Liedenfrost effect] Feb 5 Lab: Heat capacity and Latent Heat Cv, Cp, in general and for ideal gases. Latent heat. Feb 6: Approaching the Second Law: Two-state model Microstates, macrostates, multiplicity. Two-state system: model, counting microstates, probabilities, multiplicities of macrostates. Feb 7: Two-state model continued Stirling's approximation. Simplifying the multiplicity function for large N. Sharpness of the multiplicity function and probability distribution. Sharp probability distribution implies well-defined physical properties.	Read: Schroeder, Chap. 2 Problems: Chap. 1: 43, 46, 55; Chap 2: 4, 8, 18, 19, 22, 24	Lab 2: Latent heat of liquid nitrogen [MSWord source]	Formal
3. February 10	Entropy and the Second Law Feb 10: Generalizing lessons of the two-state model Fundamental assumption combined with sharp multiplicity function ensures macroscopic regularity for general systems. Einstein model: model, equipartition theorem results. Quantum mechanics of harmonic oscillators. Microstates, macrostates. [Handouts: Lab 3, notes on multiplicity in Einstein solids using generating functions] Feb 12: Einstein Model / Systems in Thermal Contact Calculating the multiplicity. Multiplicity in the classical limit. Multiplicity for general systems in thermal contact. Multiplicity for a pair of Einstein solids in thermal contact. Feb 13: Irreversibility of Heat Flow / Ideal gases Irreversibility: Multiplicity sharply peaked about a particular macrostate (equal number of quanta per oscillator). How sharp is the peak? Sharp peak in probability implies irreversibility. Ideal Gases: Basic quantum mechanics of an ideal gas: particle-in-a-box. In the classical limit, multiplicity proportional to area of a shell in 3N-dimensional space. Feb 14: Multiplicity of an ideal gas Relation between multiplicity and area of 3N dimensional sphere. Area of d-dimensional sphere. Discussion of "thickness factor". Correction for indistinguishability of identical particles. Observe relation between exponent of U and number of d.o.f. [Handouts: Entropy, Information and computation article]	Read: Schroeder, Chap. 2 Problems: Chap 2: 2.25, 2.26, 2.30, 2.32, 2.34, 2.38, 2.40, 2.42, Appendix B: B.14	Lab 3: Measurement of Cp/Cv [MSWord source]	EI
4. February 17	Entropy and Ideal Gases Feb 17: Ideal gases in thermal and mechanical equilibrium Multiplicity for gases in thermal contact are sharply peaked: thermal equilibrium. Multiplicity for gases in thermal contact when volume can fluctuate sharply peaked: thermal and mechanical equilibrium. Second law: multiplicity tends to increase, given the opportunity. Entropy defined via log of multiplicity. Entropy is extensive. [Handouts: Complex numbers and the meaning of Exp[ix] [source], Complex numbers and AC circuits [source], Input and Output Impedance and Thevenin's Theorem [source], Solutions to problem set 2, Notes on use of the oscilloscope [source], Lab 4: operational amplifiers, Feedback operational amplifiers (Horowitz and Hill), Operational amplifiers (Diefenderfer) ] Feb 19: Ideal gases (with a side of Op Amps) Ideal gases: Sackur-Tetrode equation. Processes with gas in a piston: isothermal expansion, sudden expansion. Mixing ideal gases: Gibbs paradox. Reversibility and irreversibility. Op Amps: What they are, what they're used for. Golden rules of op amps. Inverting amplifier. [Handout: op amp data sheet] Feb 19 lab: Op amps Inverting amplifier. Noninverting amplifier. Thevenin's theorem, input and output impedance. Rule of 1/2. Feb 20: Consequences of the Second Law: Thermodynamics Microscopic understanding of thermal equilibrium. Thermal equilibrium condition: dS/dU same for subsystems. Defining temperature from entropy using the ideal gas. Temperature is a measure of a system's propensity to give up energy (but NOT necessarily a direct measure of energy). Temperature in Einstein solids. Three possible S vs. U curves. Feb 21:Connection between Entropy and Heat / Two-state model Five-step process to go from multiplicity to specific heat. Demonstrate for Einstein solid. Properties of Cv from shape of S vs. U curves. Obtaining entropy from the Cv(T). Cv(T) vanishes as T->0 (third law). Heat is energy that carries entropy. Two-state model: energy of magnetic dipoles in a B field. Macrostates: energy or total magnetic moment.	Read: Schroeder, through sec 3.4. Problems: From Schroeder, Chap. 3: 3.5, 3.7, 3.8, 3.10, 3.14, 3.15, 3.16, 3.23, 3.25, 3.26	Lab 4: Operational amplifiers [MSWord source]	EI
5. February 24	Thermodynamics and Equilibrium Feb 24:Two-state model / Mechanical equilibrium Two-state model: Entropy (exact and Stirling approx.). Shape of S vs. U curve implies positive, negative and infinite temperature. Negative temperature "hotter" than positive temperature: 2-state system in contact with Einstein solid will equilibrate at positive temperature. Calculate T(U), invert to get U(T) and M(T). Mechanical equilibrium and Pressure: Set up system to analyze. [Handout: Solutions to problem set 3] Feb 26: Complex Numbers, AC Circuits, and Op Amps Review of complex number, Euler's formula, and the use of complex numbers in solving AC circuits. Start analysis of frequency-dependent op-amp circuits: high-pass inverting amplifier. Feb 26 lab: Op Amps continued Integrator. Differentiator. High pass inverting amplifier (cont'd). Three decibel point. Feb 27: Generalized equilibrium Generalize ideas from study of thermal equilibrium to mechanical and diffusive. Expression for pressure from condition of diffusive and thermal equilibrium. Verify in ideal gas. Thermodynamic identity. Chemical potential from diffusive equilibrium condition. Demonstrate that systems with larger chemical potential tend to give up particles. Extend thermodynamic identity. Feb 28: Heat engines Second law limits the amount of heat that can be turned into work in cyclic processes. Abstract model of heat engine. Efficiency defined. Second law limits maximum value of efficiency. Carnot cycle as a realization of reversible engine.	Read: Finish Schroeder, Chap 3. Also Schroeder 4.1, 4.2, 4.3; 6.1,6.2. Problems from Schroeder: 3.34, 3.36, 3.39, 4.1, 4.3, 4.14, 4.18, 6.5, 6.6	Lab 4: Operational amplifiers (cont'd)	EI
6. March 3	Wrapup of thermal physics / start waves Mar 3: Carnot engines / Boltzmann factor Carnot engines: Heat and work at each stage of a Carnot engine (with ideal gas working medium). Efficiency of Carnot engine. Boltzmann statistics: Idea: characterize systems at fixed temperature. Derive Boltzmann factor. [Handout: 2002 Midterm 1 and solutions] Mar 5: Boltzmann factor finale [Demos: Compression igniter, Two steam engines] Quick recap of Boltzmann factor derivation. Partition function. Significance of kT as scale of typical energy fluctuations. Example: Two-state paramagnet. Example: simple harmonic oscillator. Mar 6: Op amps and Optics Op amps: Low pass inverting amplifier. Band pass amplifier. Optics: Position of geometrical optics in the "grand scheme". Some facts basic geometrical optics facts: speed of light, index of refraction. [Demos: Laser pointers, refraction in a tank of water] Mar 7:Simple facts about geometrical optics Snell's law, law of reflection, total internal reflection, chromatic dispersion. Applications: rainbows, optical fibers, fake diamonds. Fermat's principle: deriving Snell's law. [Demos:Reflection, refraction, and total internal reflection in fishtank.] [Handout: geometrical optics handout]	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	Exam #1	N/A
7. March 10	Mirrors Mar 10: Mirrors (mostly plane) Real and virtual images. Plane mirrors: Image distance vs. object distance, orientation and magnification, front-back reversal. some thought questions. Spherical mirrors: concave and convex-- summary. focal point and focal distance. [Demos: plane mirror, big and small spherical mirrors] Mar 12: Mirrors (mostly spherical), part I Reflections are not equivalent to rotations. Focal points: single focus for paraxial rays only. Spherical aberrations. qualitative for convex and concave mirrors. f=R/2. sign conventions for f and R. proof that f=R/2 for paraxial rays. Images: state lens formula. ray tracing. example: concave mirror, object inside and outside focal point. [Demos: blackboard optics -- concave spherical mirror] Mar 13:Mirrors (mostly spherical), part II Proof of spherical mirror formula. Proof of magnification formula. Summary of sign conventions for mirrors. Fermat's principle: recap. imaging rays are isochronous. mirrors that are conic sections make perfect images. Mar 14:Fermat's principle in action early version of Fermat's principle: rays are paths of least time. modern version: rays are paths of stationary time. Derive mirror equation and magnification formula using Fermat for general optical delay D(h). Relate D''(h) to focus. Demonstrate that D(h) for spherical mirror gives correct expession for focal length.	Read Halliday, Resnick & Walker, Chap. 35 Halliday Resnick & Walker, Chap 35: 13,15,20,26,29,31,34,35,37	Lab 4: Operational amplifiers (cont'd)	Formal
March 15-23	Spring Break!	---	woo-hoo!
8. March 24	Lenses Mar 24: Spherical refracting surfaces Location and nature of images (real or virtual) via ray tracing. Spherical refracting surface formula. Sign conventions. Focal length. [Demos: blackboard optics -- spherical refracting surface] Mar 26: Spherical refracting surfaces / Thin lenses Derive spherical refracting surface formula. Converging and diverging lenses (qualitative). Thin lens formula and lensmakers formula. Sign conventions. [Demos: blackboard optics -- converging lenses; lasers and lenses] Mar 27: Thin Lenses Derivation of thin lens formula. Finding images with ray tracing. Magnification. Check image distance and magnification for converging and diverging lenses. [Demos: blackboard optics -- diverging lenses; lasers and lenses; a few big old lenses] Mar 28: Thin Lenses from Fermat / Systems of Lenses Deriving thin lens formula and lensmaker's equation from Fermat's principle. Systems of lenses.	Read: Skim Pain, Chaps. 1-3 as a review of harmonic oscillators. You can skip all of the starred sections. Problems: problems	Lab 5: Mirrors [MSWord source]	EI
9. March 31	Waves: 1D transverse waves on a string Mar 31: Deriving the wave equation Assumptions. Use Newton's second law to derive the waves equation in the small-slopes approximation. Verify the travelling wave solution. Apr 2: Solving the wave equation Small-slopes approx. means tranverse speed << wave speed. D'Alembert's solution to the wave equation: left-movers and right-movers. Qualitative kinematics. Apr 3: Sinusoidal waves Importance of linearity of eqn. Basic properties of sinusoidal waves. Aside: Finding travelling waves from initial conditions. Apr 4: Superposition (Interference) of sinusoidal waves Two examples of travelling waves from initial conditions. Causality and finite strings. Interference Interference of two out-of-phase (+) waves. Interference in time: beating. [Demos: Beats with tuning forks. Beats applet 1 , Beats applet 2 . ]	Read: Pain, Chap.5, p. 113-122 and 135-142, and Pain, Chap. 10. Problems: problems	Lab 6: Lenses [MSWord source]	EI
10. April 7	Fourier Synthesis: superposition gone wild Apr 7:Standing waves and Fourier Synthesis Standing waves. Fourier Synthesis: main idea. Fourier's theorem. Trig and exponential expansions. How to find the coefficients? Orthogonality relations. [Demo: standing waves applet ] [Handouts: lab, problem solutions] Apr 9:Fourier analysis: example Finding the Fourier coeffients using orthogonality relations. Derivation of an orthogonality relation. Trig Fourier expansion of square wave. [Demo: one Fourier synthesizer , another Fourier synthesizer , a third Fourier synthesizer , a nice Fourier movie . If you have a microphone on your computer, you may be find this SILS speech analysis software interesting. ] Apr 10:Qualitative features of Fourier series Exponential series Fourier coefficients of square wave. Qualitative significance of large Fourier coefficients. Dirichlet conditions. General observations about coefficients. Vector space interpretation of Fourier analysis. Apr 11:Pulses and Power spectra Power spectrum. Fourier series for a periodic pulse. Bandwidth-pulse duration relation.	Reading: Pain Chap. 10 Problems: problems	Lab 7: Fourier Synthesis [MSWord source] and Speed of Waves [MSWord source]	EI
11. April 14	Acoustic Waves Apr 14:Fourier transforms / Longitudinal waves Fourier transform, coefficient equation, and orthogonality relation. Dirac delta function. Example: square pulse. Bandwidth-pulse duration relation again. Longitudinal waves Qualitative features. Ideal fluid medium. Force on a fluid element is proportional to pressure gradient. [Demos: transverse waves on a spring, longitudinal waves in a slinky] Apr 16: Acoustic waves Simplifying assumptions. Notation in the Lagrangian formulation. Derivation of the wave equation: Conservation of mass, Newton's second law, equation of state. Combine and linearize to obtain 1-D wave equation and expression for speed of sound. [Demos: Longitudinal waves Longitudinal waves (II) Longitudinal waves (III) Longitudinal waves (IV) Longitudinal waves (V) Longitudinal waves (VI) ] Apr 17: Speed of Sound Speed of sound in isothermal approximation gives the wrong value. Adiabatic approximation is much better. Expression for speed of sound in terms of elastic bulk modulus. Keeping the nonlinearities gives amplitude-dependent speed of sound. Apr 18: More on acoustic waves and wave equation More on the propagation of shock waves. Quickie derivation of wave equation by linearizing early. Introduce convenient variables. Useful features of solutions to the wave equation.	Reading: Problems: problems	Exam #2	N/A
12. April 21	Transmission and Reflection of Waves Apr 21:Impedance Impedance: Define acoustic wave impedance as ratio of driving force to particle velocity. Analog for transverse waves on a string. Phase relations between physical quantities in acoustic waves. Qualitative transmission and reflection: Reflected waves inverted upon "hard" reflection, not inverted upon "soft" reflection. Transmitted wave not inverted. [Demos: Reflections from boundaries Reflection of a pulse Reflection of a sine wave ] Apr 23: Reflection and Transmission: Boundary Value Problems Example: Reflection of transverse waves on a string from a rigid surface. Incident sinusoidal waves give standing waves in this case. Example: Reflection of acoustic waves from a rigid surface. Example: Acoustic waves produced by a moving boundary. Set up scenario for transmission and reflection at an interface with impedance mismatch. Apr 24: Transmission and Reflection at an Interface Procedure: Write general form of wave equation in each region. Choose boundary conditions at infinity (e.g. sending in a wave from the left but not the right). Determine and apply boundary conditions at interface. Example: Longitudinal waves in fluids Boundary conditions for longitudinal waves at interface: displacement/velocity continuous, pressure continuous. Apply boundary conditions to obtain solution transmitted and reflected velocity waves in fluid. Transmission and reflection coefficients for velocity defined and obtained. Observations about qualitative features of velocity transmission and reflection coefficients. Apr 25: Transmission, reflection and a plate Finish qualitative observations of transmission and reflection at a massless interface. Example: Transmission and reflection of acoustic waves through a thin massive plate. Deduce boundary conditions. Note that arbitrary wave packets will be deformed, so we use exponential (sinusoidal) incident waves. Apply boundary conditions, obtain (complex) velocity transmission and reflection coefficients. Observe that plate acts as a low-pass filter.	Reading: Problems: problems	Lab 8: Measuring the wavelength of light with a ruler [MSWord source]	Formal
13. April 28	Interference of spherical waves Apr 28: Finish transmission/reflection / Start interference Finish transmission/reflection: Define pressure transmission/reflection coefficients, make general observations about them. Consider limits of extreme impedance mismatch and impedance matching. Interference from point sources in 2D and 3D: General form of wave from point sources in 2D and 3D. Discussion of r-dependence of amplitude. Sinusoidal waves. Scenario: interference from two point sources of equal frequency, viewed at a distance large in comparison to their separation (far-field approximation). Find expression for total wavefunction at observation point, note that it has nodes and antinodes reminiscent of standing waves in one dimension. Claim: nodes and antinodes lie on hyperbola. [Demo: Ealing film loop: Interference of waves] Apr 30: Two-source inteference Curves of constant phase are hyperbola, since phase difference is proportional to difference in distance from observation point to source. Simple approximation for difference in distance in far-field limit (assume rays parallel); curves of constant phase become lines. Two-source interference from phasor perspective. [Demo: ripple tank: 2D interference , Ealing film loop: Interference of waves] May 1: Two-source interference in various limits Time-averaged intensity. Small source spacing: single source of double amplitude. Large source spacing: closely-spaced fringes. Determining intensity maxima and minima by comparing difference distances in source- observation point distances to wavelength. Intermediate spacing: antenna patter. Consider each case in using (1) phasors, (2) exact expression, (3) distance difference vs. wavelength. [Demo: antenna/interference ] May 2: N-source inteference Formulation of the problem and the far-field approximation. Maximal constructive interference occurs when path-length differences are integer numbers of wavelengths. Simple expression for phase difference in far-field approx. Exact expression for total wave at observation point: summing the series. Total time-averaged intensity. Examine resulting expression in large-spacing limit: rapidly oscillating numerator, denominator that blows up. Denominator gives the maxima corresponding to path-difference reasoning.	Reading: Pain, Chap 12 (especially the latter part, starting at Division of the Wavefront on p. 355 (5th edition)) Problems: Pain, Chap 12: 3,4,5,6,8,10,13,14,15,16	Lab 9: Two-source interference [MSWord source]	EI
14. May 5	Diffraction and Polarization May 5: N-source inteference leads into diffraction N-source interference in the large-source-spacing, small-spacing, and intermediate-spacing regimes. The latter was the case for the CD in the lab. Phasor perspective. N-source inteference in the limit N goes to infinity leads conceptually to diffraction: interference from extended, continuous sources. Archetypical problem: diffraction of waves from a slit. [Demos: N-source phasor applet diffraction applet (I) diffraction applet (II) diffraction applet (III) diffraction applet (III) diffraction applet (IV) Diffraction patterns] May 7: Diffraction through a slit Huygens principle. Expression for total wave as sum of point sources along the slit: N-source sum goes into an integral over the aperture. Fraunhofer (far-field) approximation. Expression for total wave at observation point in this limit. Evaluate integral, find locations of minima. Time-averaged intensity. Connection between diffraction through a slit and Fourier transform of a finite pulse. May 8: Diffraction Short-wavelength (geometrical optics) and long wavelength (point source) limits of diffraction through a slit. Obtaining diffraction time-averaged intensity from N-source interference time-averaged intensity. Finding the nodes of diffraction pattern by cancelling waves pairwise. Diffraction formalism can be extended to more complicated geometries (e.g. rectangle). [Demos: Ealing film loops: diffraction around obstacles, single slit diffraction. ripple tank: diffraction 3D wave box: diffraction diffraction ] May 9: Diffraction from arrays of slits / Polarization Diffraction: Diffraction through a pair of slitshas an intensity pattern that is a product of that of a single slit times that of two point sources. This generalizes to N slits. Polarization: Rederive the wave equation from Maxwell's equations. General solution for a plane wave now has a left-mover and a right-mover associated with each component of the electric field vector, all of which are potentially different. Polarization is the direction of the E-field. Linear polarization. Circular polarization. Elliptical polarization. Natural light as randomly polarized. Linear polarizer sheets absorb one component of the incident E-field, allow the other to pass. Series of polarizers. Course evaluations. [Demos: Sets of crossed polarizers on overhead projector. Glare reflected from the wax on the floor is polarized.]	No problem set.	Finish interference	EI
May 12-16	Final exam period	Final: TBA

Website

Useful Links

Interesting talks in the Five-College area:

Area Seminars and colloquia

Interesting and useful papers:

Interesting and useful websites:

Six Ideas website

Statmech program referred to in the Six Ideas text (if that doesn't work try this .zip version).

Stirling Engine Society website

Mark Wheeler's fascination with Liquid Nitrogen
• Swallowing LN2 in the Darwin Awards
  
• LN2 ice cream
  
• LN2 and Guiness (see italics at the bottom of that page. Thanks to Mark Wheeler)
  

Perpetual motion machines
• Professor Hibbert's Perpetual Motion Page
• Eric's History of Perpetual Motion and Free Energy Machines
• The Museum of Unworkable Devices
• Perpetual Motion Machines
• sci.skeptic FAQ Strange Machines

Assorted waves and optics links

• Physics applets from MSU
  
• Norimari
  
• More physics applets from MSU
  
• Physlets
  
• drussell
  
• 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 (www.phy.ntnu.edu.tw)
  
• 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
  Some more links and physics applets (or "physlets"):
  General physics
  Some physics applets from MSU
  More physics applets from MSU
  Physlets from Davidson College. An organized collection of physics applets ("physlets") from a textbook with CD. It includes questions based on the applets. Look under Part II: Curricular Material.
  More physlets, this time scripted by Peter Sheldon `89, a professor at Randolph-Macon Woman's College.
  A lot of math and physics applets. The ripple tank applet has an ENORMOUS number of options: try adding in your own walls to the plane wave simulator.
  The Virtual Physics Laboratory at National Taiwan Normal University You can find the applets through a link to each subject area at the top of the page.
  Nori's Personal Computer Physics page. Contains applets and QuickTime movies. I suggest adding your own homemade sound effects to the "Billiards of Molecules" applet.
  Physics 2000 at UC-Boulder. Each of the three "units" - Einstein's legacy (modern physics and technology), The Atomic Lab (quantum physics), and Science Trek (how things work) - contains a large collection of applets. Beware of old male prof answering young female's silly questions.
  From ExploreScience.com. A collection of Shockwave programs illustrating various physics concepts, including waves and optics.
  This one is in French. Some of the applets, such as the Fourier synthesizer, are more self- explanatory than others.
  The HyperPhysics website at Georgia State University. This site has helped me with many a lab writeup. No applets, just some java calculators and a very well-organized summary of physics information.
  King's University College in Canada. Another collection of applets on general physics topics.
  Stat Mech:
  Four applets on Fresnel diffraction, the Cornu spiral, and Brownian motion and diffusion into a liquid. Whatever you do, don't click on the pop-up ads!
  Waves and Optics:
  The Science Joy Wagon. Contains various interactive applets and Shockwave demonstrations.
  Only two applets towards the bottom, but a bunch of Mathematica animations from some guy at Kettering University. Kind of unwieldy, but pretty thorough text explanations.
  Traveling and standing pressure waves in tubes. (Unfortunately, I was not able to find one single website that contains links to both applets.)
  Very introductory material on the physics of sound from the electrical engineering department of San Jose State University. There is a succinct explanation of logarithmic scales.
  Links to two applets on Fraunhofer diffraction and the Huygens-Fresnel principle. The link itself is in German, but the applet info is in English.
  Several applets on optics from York University in Canada. Look under "Web-tutorials on:"
  Music stuff:
  A Shockwave piano. Has links to applet pipes, a drum, and more things with which you can waste your time.
  A "virtual guitar" applet. Pretty neat.
  The "Little Shop of Music" at Colorado State University. Has Shockwave programs used in a Physics of Sound and Music course. "Auditory Illusion" and "The Beat Goes On" are the most educational.
  A large collection of links on the physics of music.
  A 1999 Scientific American article on the throat singers of Tuva, Siberia.
  Interactive notes from a Music and Computers course at Dartmouth. You can access the various applets on each topic by clicking on the pulsating apples.
  Miscellaneous:
  A speech analyzer. That is, a speech viewing and analysis software thingy.
  A Physics Today article on how humans map sounds.
  Lecture notes from a course on hearing and sound perception at the University of Sussex.
  Several applets on sound and modern physics from a Professor Dan Boye, again at Davidson College.
  The department of Mathematics and Statistics at Langara College. A really large collection of links to various internet resources in mathematics.
  An instructive site from Rice University: how to build an inexpensive Galilean-type telescope.