Amar G. Bose: 6.312 Lecture 01

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DR. BOSE: Today, I would like to just tell you a little bit about the course, about the motivation behind it, about the somewhat different experience that you're likely to have here, and give you some of the reasons for that. First, just the mechanics, which are already announced: two lectures, one recitation, one tutorial, and three quizzes. The quizzes will be evening quizzes designed to be an hour. There are some Institute regulations that I've heard about, but I have also learned that our TAs generally have had some problems finding the light switch at the end. So I would much rather have you, if you run out of anything, run out of ideas rather than time.

My memories of going through this mill here years ago when we had to take five subjects every term, I have a number of memories in which I just got the idea at the last five minutes and working furiously, knowing that you have the right approach and the instructor pulling on one end of the paper and you tugging on the other end and still writing. So I'm not interested in determining what you can do under those conditions. I'm much more interested in determining what level you can rise to.

As far as staff goes, we are definitely, and I'll get to this a little bit later, understaffed for this number of students. We have a total of five, two of whom are part-time, and myself. And so if it turns out that we're going to have this many, we have to do something about it. And I will try to give you some reasons at the end why some of you might want to take the subject and reasons why some of you might not want to take it. And if we can save these registration cards until the end, I would ask that none of you hand in that registration card if you really don't intend to take the subject or to follow it all the way through.

And with respect to the latter, I would strongly recommend that if you have any question that you might drop the subject, please don't register for it. Now that isn't just for our good. Yes, we would like a smaller number so we can give you all more attention. But it's for your good. Namely, every time you give up on anything, you literally go backwards. Your confidence to attack the next thing you approach, the next subject, or the next problem, is lower having given up somewhere.

Now, it won't be obvious to you why-- maybe it will by the end of the subject-- but I happen to believe with absolute faith that every one of you in this room can not only do the material, but if you applied yourself can get an A. I don't grade on curves. The only time anything gets adjusted is if a quiz average comes out low. Because I'm a strong believer of one, you have an excellent background or you wouldn't be sitting here. Two, if the teaching is done correctly, and three, if you do your homework and you talk with your teaching assistants, if there's a low average on the quiz, it's our fault, not yours. We hope that doesn't happen, but if it does, that gets adjusted. But it doesn't matter to me if everybody in this class gets A. I simply do not believe in this business of grading on any kind of a curve.

Now, I really want you to think carefully about taking up the challenge of the subject. You all can do it. But don't give up once you start. So don't start if you're likely in any way to give up. Last year, we had 100 students registered and only one dropped. And that makes me very happy.

A little bit more about the teaching assistants, and for that matter, myself. I had a student on time, a graduate student from Italy. He was a mature person. He'd graduated in Italy, worked in the industry, had a family, and came here when he was 30 to get his Master's. And just the day before he was going back, I asked him, what was your experience at MIT, and how did it relate to what you experienced in the past in Italy? And his immediate response was, I was absolutely shocked to go into classrooms at MIT and find that someone asked the professor a question and received an answer, I don't know.

He said in Italy, that was impossible. He said the professor had to at least pretend that he knew everything. And he would respond to the student in such a way that the student felt so small that he would never ask another question that was embarrassing.

Well, teaching assistants, I have one criterion for picking them. Namely, that they really care about whether you learn. And they're not expected to have all the answers. I don't know is a perfectly good answer, except that I expect them to try to find out.

In staff meetings, they'll come to me. Much of the time, we'll be able to get an answer. Some of the time we won't. What you have to realize is that teachers, all of us included, we are no different than you. We sat in your seats. Well, I guess it was a very long time ago.


But we remember. And I can remember in 10250 lectures that I thought, my God. How could anybody be so smart to put all this math on the board and whatnot? And gosh, I'll never be at that level.

Turns out we're all the same. If you ask me questions about material that I'll be talking about tomorrow, if you ask me questions six or seven weeks later, I'll really have to stumble around. Because I've been doing a lot of thinking about the material before I walk into the classroom. So when you deal with the teaching assistants, don't think that they're God. They're only people that are trying to help you. That's all that matters.

Now, a little bit about the philosophy of the course. A number things have influenced me over the years as to what I teach and why I teach it, and I'll try to go through just a couple of those so that you'll understand this seemingly different experience that you're going to have. Namely, when I was first on the faculty, I was, as most junior faculty experience, you have to go around and talk to industry about the research that you're doing as part of the industrial liaison program.

So one day, I was visiting General Dynamics in San Diego. And at lunch, there were about 12 VPs sitting around the table, and everybody having a general conversation. And one of them asked me, and this was one sitting very close to me, and he said do you know Professor Lan Chu? And I said yes, he's in the next office to me. And the whole table suddenly got quiet. There used to be an old E. F. Hutton ad on television that would describe that. And I wondered what I'd said. I said, yes, I know him. Why did everybody get quiet?

And another VP said, I believe at General Dynamics, and that's a huge corporation, we could cancel all of our consulting contracts and extend Professor Chu's contract from one week to two weeks and we'd be ahead. Yeah, wow. That's exactly what I thought. And so I asked them, well, tell me about it. What happens?

And they said well, that's it. We really don't know what happens inside this room. But for months in advance, engineers queue up, and they only get a 10 minute appointment. And this is solid 10 minutes, eight hours a day for one week that he's here. And they go in there, and we don't know what goes on inside, but they come out and they can just sail for a few months. They get over the problems they were on and they're just sailing.

So I was in awe of this, and I came back, and you can imagine the first room I was in after I got back. And I asked him, I said what do you do in that room? And he said, well, in order to tell you what I do, I have to tell you how I came to do it. He said when I was a student here-- he also graduated from MIT-- I decided I was going to make electromagnetics my field. He had come over, I guess, from Taiwan and was a student.

And he made that decision, and he said after I made the decision, every problem that came to me in electromagnetics, either was assigned to me or was something that I looked at, I followed a strict discipline. I looked at the problem. I then divided the problem into the smaller problem. Looked at that problem and divided it into a smaller one yet, until I got to the smallest problem, the most elementary problem that I could make out of this seemingly complex problem. And then I decided I would understand that thoroughly, and that involved usually simple mathematics.

And when I understood that simplest problem I could make very thoroughly, I went to the next level back. Went to the next level, to the next level, and finally to the original problem. And he said I did that with iron discipline. He said, now, when I go into the room in General Dynamics and somebody comes in at that time with a slot antenna and an aircraft, he said literally as I look at that problem, it falls apart, and I can immediately tell them what they need to do to solve it. He said it just falls apart into these elements of simple problems, and all of which I have prepared myself very well.

And now he was a master of mathematics also. But he was actually able to direct these people without much of the mathematics to tell them what to do to solve the problem, and then they could go ahead and do it. Well, that influenced me very much, and you're going to see in the subject that we're going to deal always with the simplest problems we can. One-dimensional problems in waves, for example.

You can develop an insight so that you feel for these things. But that insight is developed from the very simple mathematics. And when you go to more dimensions, OK, there are mathematical tools that take you there. And if you can build that insight at an elementary level on simple problems, you'll not only find it'll solve complex problems for you, but it will solve problems in other disciplines as well.

One of the reasons I like to teach acoustics is that, although I'm not sure I wouldn't do it in any subject, but I shove as many different things in as I can from different disciplines. And acoustics lends itself to that. We're going to talk about mechanical systems, electrical systems, acoustical, magnetic, and you're going to see an amazing commonality in these different disciplines. Central to all of is modeling. And modeling is something that I think is one of the most important things you can learn in all your time here.

I've been blessed by being able to work with students after they leave here. Students who graduated a year ago, and students that graduated 30 years ago. And in doing that, I've learned a lot.

First thing I've learned is that I don't know, none of your teachers, and amazingly enough, you don't know what you're going to be doing five years after graduation. You may know what you want to do, but very seldom will life come out that way. You'll have all sorts of surprises. And that-- well in fact, I'll back up and use a couple of examples. I'll use some personal examples.

I think I didn't even get to know what I was going to do while I was here. I had a doctorate thesis for the best professor that I had had at MIT, Professor [? Gilliman ?]. Had a thesis all agreed upon, conformal mapping and network theory. I went over to Europe on an exchange program, came back. I had had a research assistantship, so I thought I was pretty secure. I came back. On the desk, there was a little note: Please see Dr. Wiesner, who you know as the former president of MIT, but he was head of Research Laboratory of Electronics at the time.

So I went in there, and the associate director, Professor Zimmerman, started telling me about Norbert Wiener, who many of you perhaps have heard about. And they told me that he had-- he was in the math department, of course-- and he had some math which they thought really one day would have applications to electrical engineering. And that they had tried three doctorate students on it, but they think that somehow that didn't come out. That there is still more there, and so they want me to work on that.

And I said, wait a minute. I have a thesis. I'm very happy. I know the field. I have a professor. I have the research.

Yes, we know that, but we want you to work on this. And I was a kid of 23, and I was getting a little bit hot under the collar. I didn't like this idea. And I finally said, look, are you drafting me? And they said, well, yes.


They said but, if you don't like it, you come back in the office a year later and we'll change you back. And by this time, I was fuming. I hope I didn't show it, but I said, look, I'm not coming back in this office a year later and starting all over. If you're not going to give me a choice, I'll do it.

Well, I was angry, upset. It changed my field. I had a minor in math, but I didn't have enough mathematics to even say boo to Professor Wiener.


So I was really annoyed. And little did I recognize that all of the money I've ever earned in my lifetime could never have paid for the experience that I got, which started a 10 year very close association in which we met almost every day. Not on the doctorate thesis. It didn't last that long. But in any case, you don't have the slightest idea of field change. When I finally did graduate, the only thing that I was certain of is that I never, under any circumstances, wanted to be a teacher, and look what happened. So you just never know.

I also had no interest in corporate things at all. I couldn't imagine myself getting involved in that. The arithmetic of accounting, and the management things, and the only thing that I knew I wanted to do is research. That today is the thing that I'm happiest doing, and if I go any period of time without that, I get very frustrated. But you have to do all these other things, and you will have to do other things as well.

With any job comes a lot of things that you would not like to do. If I could get out of all the management stuff today, I'd be happy as could be. But you can't. So what you have to be able to do is go into all of those things and get to the top. So your years here are really years that are spent preparing for an unknown future. That's what it really boils down to.

And when I look at these students that graduated 20, 30 years ago, or even more recent ones, what always goes through my mind is what could we have done in the university to make them better in whatever they're doing today? Even though many of the ones are stars, the ones that came from here. Well, one of the things that you realize right away is it can't be the facts that we teach that are important.

You're not using them in many cases. If we teach them field theory or network theory, they may never work a problem in that discipline in their whole life. So what is important? It's how clearly you can solve problems. How clearly you can think. And then you can go into any direction.

You also, in these surprises that you'll get in your life, I can remember when we first formed the company. About a year later, bankers came along and said, oh, you're going to have to go back to the till certainly within three years. Well, we could figure out what the till meant-- it was the capital market-- but we couldn't figure out why do we have to go back to it? And so we asked the question, why?

They looked at us as, boy, are you guys naive. If you double your business in five years, you're going to need double the working capital. Where are you going to get it? And that was it. That was the explanation. That was the limit of the banker's ability to explain.

And so that wasn't satisfactory, so we went back now-- I have to put the time frame here clearly, this is BC. Not the BC you're thinking of, but before computers. And basically, we went back and sort of asked, is this really like the first law of thermal? You're stuck with it? Do you actually have to go back to the till, in which case your company couldn't be private, and you have to worry about all this stuff that people worry about in public companies? Or is there a solution?

So we started making mathematical models, and I emphasize the word model. That's what we're going to dwell on. A mathematical model, which we wouldn't have ever done if we hadn't graduated from here I don't think.

But, a model for the growth of a corporation without external financing to see if there was a solution. And the answer could have been no solution also. Well, it turned out after all the smoke cleared and the equations and whatnot boiled down, it boiled down to a relationship between working capital, profit after tax, and growth rate. Not quite working capital, but something very close.

Looked at this thing. And if you pick two, of course you have a mathematical relationship between three, you pick two and you've got the other one. So scrambled around and said, well, maybe 20% growth rate can happen, et cetera, and picked two of the variables and then that nailed the third. And we believed in the model. And what happened at that point was we couldn't understand the bankers. The bankers couldn't understand calculus, and so at an early path, we went aside.


And to this day literally, they think some miracle happened. Because we followed what we understood, and it worked. And it shouldn't have according to them. And it's an anomaly, but it did.

Well, it told you a lot of things in the model. It said, boy, you better have assembly lines that you can change in 15 to 20 minutes. You can't have more than three days of finished goods inventory, because that's working capital needs. It told us about what we had to do with things like accounts receivable, squash them down. We could figure out all the different parameters, and since that's the only thing we understood, we followed it religiously.

Well, this is what modeling can do for you. It can be applied to problems that you will meet that you'd never think about today. That you have no idea up and I have no idea of. So if you can get into that mode of thinking.

Also, your learning should be, in my view, learning like a child learns language. You should learn the subject. A child after dinner doesn't sit down with a vocabulary list and memorize it. He wants to communicate. And in the process of communicating, he picks up not only the vocabulary, but the grammar.

It's the same way you should do with subjects. Never try to memorize anything. In the quizzes here, you can bring anything with you but a friend.


Basically, they won't help. But at least you know you don't have to memorize everything because you can have it all there. You can have books or whatever you wish. The real thing that we want to test, and it's not really testing, is the quiz as far as the faculty is concerned is not test you. It's to cause you to study and develop. If I had gone through MIT with no quizzes, I'm sure I would've gotten very little out of it, because you had to do well on the quiz, and that's what caused you to work. So from the faculty point of view, when you enter the quiz room, it's all over before you even start the quiz, because now you have worked and you have risen.

Now in this subject, like it should be in any subject, don't expect to learn anything. Well, that's an extreme case, but don't expect to learn anything significant if you don't do the homework. The homework is designed such that you will get that experience of problem solving.

If you went to a gym and you had an instructor who told you how to do a certain exercise, and you daily walk out and say, well, I know how to do that, and you don't actually do it. You don't get any of the benefit from it. So the benefit is not from what I'm telling you in class. The benefit is from doing the homework. If you are inclined to be a person that would like to copy homework, please don't hand in your registration.

I don't mind if you talk to people about it, but watch out that the talk doesn't get in the position in which one person is giving me ideas, the other person's receiving them and writing down the solution. if you work together, if you discuss the material, I don't care about that. But the benefit that you will get only comes from your thinking about the problem. Because the problems that you're going to face when you get out, with certainty, you're not going to have people around that are such that you can copy from.

You're not going to have a book. Even the engineering problems, when you first get out, you'll find out that the tendency is, we've all gone through it, that you look at a problem that you're given in an industry, and, well, that's 6001. Whip out the bible, and that talks to about 5% of the problem. You find out that it's always broader than the collection of your courses. So that experience you have to do, just like the person has to do the exercise to develop.

So, homework is the most important aspect of the subject. If you take the subject as a listener, you might find it here and there amusing, but you won't get much out. You get the benefit that I know you need, that we all need, that comes from doing the work. Very, very, very, very important.

Now, a nice thing in acoustics to me is that it covers three decades in frequency. The acoustics that we're going to deal with, which is mainly that part which pertains to what people can hear, covers three decades. When you go to ultrasonics and whatnot, its of course much larger. But it's an interesting three decades, and this is what gives the excuse to give problems that are covering a very important spectrum.

Namely, it's three decades in which at the lower end, the wavelength of sound is very large compared to the objects that are generating this sound, and at the high end, the wavelength is very small compared to the objects that radiate it. Now, it turns out that this consideration is a very, very significant one in any discipline in which you're dealing with waves, whether it's mechanical engineering and waves in a rod, whether it's electromagnetics, whether it's acoustics.

There's a thing called lump parameters when the wavelength is very large compared to the objects, and you use them. How many of you are EEs, by the way? Oh. How many of you are not? Let me get a sampling here. MEs? OK, physics? Math? Geez, what else? Any others? Computer grid? OK.

Now, what you'll find is if you have built an intuition or an insight in any one of the dimensions based on lump parameters, for example. It doesn't matter whether you're a mechanical engineer, you might think in terms of mechanical; electrical engineer, in terms of electrical. You'll be able to transfer that to acoustics, to magnetics, to circuits, to all sorts of things.

And why do lump parameters exist? I mean, those of you that are EEs all have heard of Kirchhoff's Laws. Where did they come from? Did they descend one Sunday from somewhere and land on somebody's desk, or do they come from something? If asked to derive where they came from, would you be in good shape to do it, even if you've had electromagnetics? I hope you'll be in good shape to do that kind of thing, even in electromagnetics, at the end of the subject.

It all comes from one body of knowledge. In electromagnetics, it's Maxwell's Equations. Lumped parameters, where the wavelength is large compared to the circuits, come from Maxwell's Equations.

Then when you get to the other end where the wavelength is very small compared to the circuits, then you can't deal with lump parameters. A resistor is no longer a resistor. The best you can do in lump parameters is model that resistor. Depending on the frequency, there's a number of other parameters. Simple model, a capacitor across the resistor just because there are electrostatic fields in the wires. And then an inductor and series because there is inductance in the wires, et cetera.

Well, it used to be, for example, that if you were asked to do a receiver design of three decades from just say 1 MHz to 1 GHz. That would be a heck of a problem. Because at 1 MHz, you have your AM broadcast band. Lump parameters are fine. You can build a radio. It used to be 20 years ago that when you got to 200-300 MHz, resistors weren't resistors, capacitors weren't capacitors, and it was only art in that region. Twenty years ago, 200 MHz to 1 GHz, electromagnetics was pure art. In fact, I don't think it was taught in most universities, because you had to sort of feel for what those things were really doing, and you never knew. It wasn't something that you could just make a simple model of.

And then when you got above 1 GHz, of course it's all waves. And you talk about waveguides and chambers and whatnot. That has moved up, and why has it moved up? Because components have gotten smaller. Now you can make 1 MHz to 1 GHz in lump parameters, only because the components got very small.

And small compared to what? As it turns out, it's going to be small compared to about 1/6 of the wavelength. When the whole circuit get small compared to that, lump parameters work in any discipline. When the circuit is smaller compared to that. When the circuit is large compared to that, waves. When it's comparable to it, art. That's all. So acoustics offers this really nice opportunity. It also offers the opportunity, as I mentioned before, of modeling in electrical circuits, in mechanical circuits, in acoustics, in magnetics, and seeing the commonality that is behind all of this.

Now, another thing that has motivated some of the things we're going to do in this subject, is what I observed in the years working with Wiener. Just to give you a little, how many of you have ever heard of Norbert Wiener. Geez. That is amazing. I didn't realize that he was still known.

He was sort of an unusual person you might say. He got his bachelor's degree from Tufts at 14, his first of two doctorates at 18. He knew nine languages. At five and six years old, he was reciting things like Iliad and Odyssey in Greek. And everybody thought he was a genius obviously. At 25, he was a world-renowned mathematician. At 29, he was perhaps thought to be one of the top three in the world.

You'll see an exhibit of his out in the corridor, building 10 sometime. Read it. There's a letter that he wrote to his sister when he met-- I think it was about 1925-- when he just by chance met Einstein on a train I think traveling from Geneva to Lausanne. And he writes to his sister about what happened in this meeting. It's fascinating. You ought to just read the letter. It's pretty short.

But the thing that I learned from him, and he drilled it into me for 10 years to the point where I really did believe it, and that was that he didn't enter this world any different than you and I. It turned out that his father and another Harvard professor-- his father was a professor of languages-- decided to see what you could do if you took somebody at the cradle and really worked on them-- what level you could bring the person to. And both parents started this competition. And Norbert Wiener resented this through his entire life. Didn't do it to his own daughters, but said again and again that everything I am is due to what my father did.

At six years old, his eyes went bad, and the doctor ordered no reading for a year. He then of course was faced with aborting this experiment, the father. His father said, nothing doing. He was already in hot competition with the other faculty member, and so he made him do everything in his head. And as Wiener said, when I was seven, I realized that my mental capabilities had just opened enormously because my father forced me to do all the math and everything in my head. And he said as a seven-year-old, I realized I was a totally different person than when I was six.


And it was amazing, too, because I can tell you that the last book he wrote was written over years on my blackboard. He'd visit me for half an hour to an hour a day, and he'd put all these equations on the board. He didn't need a board like this it turned out. He was right-handed, and he would go along like this, and he had the eraser here.


So he never had to stoop over or anything. And so it turned out in the end, he got a bunch of us to go through all of this. And there were errors galore in it. But throughout the whole book, there was never a result that was wrong. And these are huge-- this was in non-linear coupling. I won't go into details, but there were huge mathematical integrals, and there was never an error in any result in the entire book. All the steps that got to it were questionable.


After he got to the next to the last step, he'd make a giant error and write down the right answer.


Because he had never seen this stuff on the blackboard before. It all was done in this head, and he could jump the steps, and he knew exactly what things were going to come out like.

You, believe it or not, all have that same ability. It's all a question of what you decide to develop. Absolutely a question of what you decide to develop. And I want to see how much of it you can do, or at least make a step in that direction.

His father got him at the cradle. I don't have that opportunity. Not that I could do the same thing.

OK. Another aspect of acoustics that interests me is the fact that it brings in, as many other disciplines also do, both the discipline of physics, and the discipline of the psychophysics. If you imagine three sets here in which every point in this set represents some sort of a physical device, and every point in this set represents a measurement on that physical device, and every point in this set is a point of perception. In other words, a human being over here perceives whatever this thing is differently than that.

Here's a physical device. I'll give you an example. Let's say, for something you might hear. Let's suppose this is and amplifier, A1, and this is an amplifier A2. And let's suppose that this one has a distortion, D1, and this one has a distortion, D2. Now, you could as an engineer be given a problem, ah, you want this distortion to get lower and lower as the so-called hi-fi industry has done. And you can pay a lot of money now for 0.001% distortion. Well, let's suppose that that was D2, and let's say this was D1.

Now imagine that both these points map into the same perception. All your labor, all your engineering work is for naught, except for some marketing guy who might be able to advertise that he has 0.001% instead of 0.1. Well, nobody alive on speech and music can hear the difference in turns out. That's why they map into the same point.

So this dimension from here to here is called physics, or in the case of acoustics, physical acoustics. And this dimension from here to here is called psychophysics, or in this case, psychoacoustics. So the relationship between the device and the measurement is physical acoustics. The relationship between the measurement and the perception is in fact psychoacoustics.

In the so-called audio field, this has been done terribly. Care hasn't been taken here. Everything ends here.

In the video field, a very good job has been done in this whole picture since the late '40s. Example: In the early '40s, if you asked anybody what it would take for the bandwidth of color television, which didn't exist, they would tell you, well, it takes 4 MHz for black and white. Three primary colors. 12 MHz. Then in the late '40s, they started making experiments in this area, the psychovisual. They found out that if you hold up a thread in front of people and it subtends a sufficiently narrow angle to the eye, that you don't see the color. You can't distinguish the color. You only can distinguish its luminance, its brightness.

And of course, to produce a TV picture, you scan across the screen. So something that was a thread requires a very high bandwidth. It's just the signal, it's like an impulse at one point. So realizing that the eye couldn't distinguish color when in fact it subtends a sufficiently small angle led to all of the signal of color being only 600 KHz instead of an additional 8 MHz, and they squashed the whole thing into the same bandwidth as black and white.

Audio on the other hand did nothing like that. They still have all sorts of superstition about coherent sources and loudspeakers so that the wave arrives at you at the same time from a tweeter and a woofer. Distortion characteristics. Oh boy, the more zeroes after the decimal place, the better. Transient distortion, all of this. Most of it is total folklore. In fact, if you pick up-- this is the part I'm going to give you to try to reduce the class. Namely, if you've come here to learn about hi-fi, I can almost guarantee that when you leave the subject, if you stay through it, and if you register I want you to, if you stay through it, you will leave the room at the end of the year saying, God, I know a lot less than I knew when I entered. Because most of what you know is pure, unadulterated folklore that's in these hi-fi magazines.

You can go out to the library and get a copy of Hans Christian Andersen's Emperor's New Suit, and every time you come to new suit, read hi-fi, and you will have a pretty accurate picture of the field as practiced today. So if you've come to learn about that, that's not what we're going to do here.

The attitude of the whole course will be fundamentals and problem solving and modeling. That's basically it. If that's of interest to you, it's OK. What you've got to do some time when you graduate, you'll find out that if you can generate an interest in problem solving, you will be at the top of your fields wherever you go.

Problems when presented to you have got to be like puzzles. This person I talked to you about Professor Chu. Other faculty used to bring him problems all the time like a machine, just to see what he would do with them. And it was amazing what would happen. I mean, all of the faculty were in awe of this person. And he just loved them. He just ate them up. Like oh boy, this is a puzzle I have to find the answer to it. And his mind went.

If you can look at all of your problems that way, you'll be OK. The things that you don't want to do in life, if you look at them that way. If you enter any of those things that are going to fall on you for sure, and you say, God bless it, now I have to do this now. This is miserable. You're going to do a lousy job.

You may not want to start. I have a heck of a time with that. I mean, if I have to get involved in some of these other things, marketing or sales, my thought is oh God. But once I'm in there, you would never know that this wasn't the most interesting thing in my life. And when I finished, phew, now I go back to what I really like. But while you're solving anything, you have to be excited about it. And if you can get excited about solving problems, that is all you need with the background that you will have at MIT to go on to an incredible success.

One other dimension, again for trying to reduce the class. If you like to talk, that's fine to me. If you like to talk to your neighbor, don't sign up, because I regard that as an enormous discourtesy to everybody else who wants to hear and wants to learn.

So I think I've given you the dos and don'ts. By the way, at any time you can ask questions. Don't be afraid. MIT is recording all of this series for the whole class. Just try to ignore it. And if you can't, if it is in any way troublesome, let your teaching assistants know or let me know, and we'll try to make adjustments for it. But I think you're big enough that you could just ignore the stuff as I do.

Well, we'll take a minute. I just want to give you a-- oh. After all of this emphasis on problem solving and whatnot, you're going to hit the first problem set and you're going to say, oh my God, is this doggie stuff. Is this what the subject is going to be like?

The first problem set is supposed to be review. There is what appears to be doggie things, but they're there because they are mistakes. In many problems later on, there may not be much calculation, but there are simple mistakes in complex algebra that tie people up. It's amazing how you can get so mixed up if you don't understand some simple mathematics. So this is a review of that, and don't mind asking the simplest questions. There is no such thing.

Some years ago, I was asked to give a talk to all the new teaching assistants in 10250 for that year, and somebody very sincerely asked me, what do you do when you're asked a stupid question.

And I answered, I don't know, because I've never been asked one. There is no such thing as a stupid question. And I've always found that when somebody has the courage to ask that what you might call simple question, about 20 or 30 other people are like, phew, thank God. Now I can know it, but they wouldn't have the courage to ask. So please, please, please do that.

Now, just a little word so that you have some background, because the first set will look like that. Then we'll go on to a little bit more sophisticated but simple math. The first third will look like it's sort of abstract. It'll look like you're emphasizing mathematics as supposed to insight building. Once that mathematics is out of the way, then we will be clear to think in terms of our insight building, and we'll build a tremendous insight on that. So hang in there for the first maybe third of the subject, and then you will see what that first floor that is built really is enabling you to do.

And now for your thinking in the meantime on how a sound wave might be propagated, just think if you had here a bunch of, on a frictionless table, springs and masses. Now what would happen, in fact, if you took this end of this spring-- this is on a frictionless surface-- and you just went like that real quick? This spring would compress. If you went fast enough back and forth, this fellow doesn't even have time to get going. But when the spring was compressed, you put a force in there, and so he would later accelerate. You've already brought your hand back, but he accelerates.

When he accelerates, he compresses this spring. And of course, now that this has come back, when this fellow moves forward, there's a force that pulls him back again. But in the meantime, he's imparted, just like your hand did over here, a force to this spring. That force gets this mass accelerated. And so what you would see, if you have a whole long string of this, if you went like that here, you would find the same motion being repeated all the way down the line and it would travel.

Now nothing traveled down here in terms of mass. No particles traveled down. Just energy travels, and that's the characteristic of a wave. Matter doesn't move from the radio station to your radio receiver, but energy does. And this is a very simple model. Now it turns out in air, as we'll see tomorrow, these things are really all together.

If you imagine a surface. Just take an imaginary surface here. As I speak, what happens is the sound wave comes along and it squeezes. The pressure goes up first on this side of it. It squeezes that little mass of air. Think of encompassing a constant mass. It squeezes it and it pushes it. So in air, you think of these two things as being in the same element.

You know what air acts like a spring. I mean, put it in a balloon and squeeze it. You also know it acts like a mass. It's almost a kilogram per cubic meter. So it has both the mass and the spring, and what happens is it goes like this. These little particles that you would imagine following. By particles, I don't mean molecules. I mean just imagine a small, small volume of air, which we'll call a particle. It gets squeezed and it moves, squeezed and it moves. And that's all it does. It never goes from here to there.

So that's a model, and based on just that simple model, we'll be able to get the equations that govern all this. So please now, those of you who decide you want to take it for sure, sign up. Those who don't, please don't. Because I'm very much afraid that we're going to have a very hard time getting the teaching assistants, and I don't want to have to go for it if I don't need to. Thanks.