Fisika untuk Universitas

Fisika untuk Universitas

Ditujukan untuk meningkatkan kualitas proses dan hasil perkuliahan Fisika di tingkat Universitas

Kelistrikan dan Kemagnetan

Topics covered:

Resonance
Destructive Resonance
Electromagnetic Waves
Speed of Light
Radio - TV
Distance Determinations using Radar and Lasers

Instructor/speaker: Prof. Walter Lewin

Information about the Tacoma Narrows Bridge Collapse:
http://www.pbs.org/wgbh/nova/bridge/tacoma3.html
http://www.ketchum.org/bridgecollapse.html

Free Downloads

Video

• iTunes U (MP4 - 105MB)
• Internet Archive (MP4 - 208MB)

  » Download this transcript (PDF)

  Before we're going to dive into electromagnetic waves, I would like to discuss a few more mechanical resonances with you.

  Last Friday, we discussed the resonances of string instruments and wind instruments.

  But there are several that you see around you quite often -- without realizing it, perhaps -- that you're looking at a resonance frequency.

  You may have noticed that traffic signs have the tendency, sometimes, to do this, and at certain wind speeds, they go like this.

  Enormously strong amplitude, that's a form of resonance.

  Undoubtedly, you have been motels or at homes where you open a faucet, and then all of a sudden, when the water's running in a certain way, you hear an incredible noise, a terrible noise.

  You close the faucet a little, or you open it a little further, and that noise goes away.

  That's clearly an example of resonance.

  You drive your car, or you're in someone else's car, and at a certain speed, something begins to rattle.

  Very annoying.

  You go a little faster, it stops.

  You go a little slower, it stops.

  Or, if you go a little faster, something else begins to rattle, there's some other resonance of something else in the car.

  And of course, there are cars whereby something rattles at any speed.

  But in any case, there's this idea, then, of resonance, which is all around us.

  I remember when I was in a student, and when we had an after-dinner speaker which we didn't like, we would very quickly empty our wine glasses -- in those days, we were still allowed to drink, by the way -- and what we would do is the following, something extremely annoying.

  We would generate the fundamental of our wine glasses.

  You take your finger, you make it wet, and you rub it like this.

  Listen.

  [Rubs glass]

  Believe me, if 100 students do that, it's very annoying.

  But it's also extremely effective.

  Speaker -- speaker gets the message very quickly.

  [Rubs glass].

  What the glass is doing, it's the fundamental of the glass, it's the lowest frequency, the glass is actually doing this.

  And there are rumors that people can break glasses by singing.

  And we'll talk about that in a minute.

  Um, I remember a, um, commercial, Memorex.

  Memorex is an audio tape.

  And they bragged about breaking glasses -- some of you may actually have seen that commercial.

  There was a, uh, a picture that I can show you that goes with the commercial, and then a very dramatic story.

  The story is that someone goes to a concert.

  And there is a woman singer, puts a glass on the table, raises her voice, hits the resonance frequency of the glass, [pshew!], and there goes the glass.

  And this gentleman was recording it, of course, on his Memorex tape.

  So let's, um, see this, uh, this slide.

  So if we get the slide -- yes! You see this, um, this glass, maybe you can focus a little better John, thank you.

  Memorex.

  So the story then goes that the guy goes home and tells his wife about this.

  Well, she is smart enough not to believe this story.

  But he plays back his tape.

  And at the moment that this glass breaks at the concert, he has some wineglasses himself at home, and lo and behold, they also break.

  And so then the idea is, that is the commercial -- that's the great pitch of Memorex -- that the reason why they break at home is because of the enormous quality of this tape which is made of very special material.

  And the material, as you could have read on the box, is a very special chemical compound, it is MRX2.

  Two atoms of X, one of R, and one of M, and then you make it oxide, and then you have the best tape that you can imagine in the world.

  Well, they overlook a small detail, and that is that, um, for one thing, a tape recorder would never generate enough volume to break a glass in the first place.

  But in the second place, the glasses that this guy had at home, obviously didn't have exactly the same resonance frequency as the glass at the concert.

  So this could never have happened.

  But like with all commercials, you know that you're being swindled, and this, of course, no exception.

  I've always questioned whether it is actually possible that a person, without the aid of strong amplification, and without the aid of huge sound volumes which you can generate with loudspeakers, whether you can actually break a glass.

  I've always wondered about that.

  People say it can be done.

  Caruso, famous singer, was known for being able to do that.

  He put the glass there, he would rub it with his finger so that he knew the resonance frequency [kllk], and there he would go, and [poit] bingo.

  Frankly speaking, I don't believe it.

  I don't believe it can be done by a human being without the aid of amplifiers and speakers.

  And when I lectured 8.01 several years ago, together with Professor Feld here at MIT, we discussed the -- the possibility of designing something that actually would be able to break a glass.

  And -- and he actually deserved a lot of credit for that, he worked with a graduate student, and he managed to design a setup that works most of the time.

  But don't put your hopes too high, it doesn't work all the time.

  So here is a wineglass, the same series as that one.

  By the time -- when -- when he got it to work, we bought 500 of those glasses -- we got a good discount, by the way, because we wanted to be sure that we can do it for years to come.

  So here's the wine glass, and here is the loudspeaker, and we are going to generate sound very close to the resonance frequency of this glass, which we have already determined before you came in, 488 Hertz.

  You're going to see the glass there, and to make you see, actually, this wonderful motion of the glass, we will strobe it with light at a frequency slightly different from the frequency of the sound so you see the glass move very slowly.

  And then we will increase the volume of the speaker, and then with some luck, if we are right on resonance, [poit], the glass may actually break.

  I think this is the sound that you're going to hear at low volume.

  [tone].

  And I think I turned on the, um, the strobe light now.

  [tone] So I'm going to go make it dark.

  [tone] And I want to warn you that the sound level is going to be quite high.

  [tone] I will have to protect my ears, [tone] and you actually may have to do the same.

  [tone] I will first increase the volume of the sound to see whether I'm close enough to resonance.

  [tone] So this slow motion that you see [tone] is the result [tone] of the strobe, [tone] which is not exactly at the same frequency as the glass.

  I can change that a little.

  [tone] All right.

  So we are very close to resonance.

  [tone] The glass is clearly responding to the sound, [tone] and now I will [tone] cover my ears [tone] and slowly increase the [tone] sound volume.

  [tone] I can't go any louder.

  [tone].

  It's tough glass.

  [tone] [glass breaking] [tone] It was a tough glass.

  [applause].

  I think you will probably agree with me now that for a person to do that without electronic help is just not so believable.

  The most dramatic example of destructive resonance is the collapse of the bridge in Tacoma in 1940.

  Many of you may have seen that dramatic movie, but some of you may not have seen it.

  And even if you have seen it, it's worth seeing it again.

  There's a little bit of wind, there's a little bit more wind, and just like with these wind instruments, you're dumping a whole spectrum of frequencies onto a wind instrument, and it picks out the resonance frequency.

  And this bridge, as you're going to see, picks out its own resonance frequencies.

  And the consequences are quite dramatic.

  So if you can start, Marcos, with this movie.

  [sniffles].

  It was 1940, and at this, uh, in Washington State.

  Movie: On the First of July, 1940, a delegation of citizens met in Washington State.

  Movie: The weather was beautiful, the occasion historic, and the speech-making and fanfare altogether appropriate.

  Movie: This was the grand opening of the Tacoma Narrows Bridge.

  Movie: From the beginning, the bridge, which spanned Puget Sound between Seattle and Tacoma, was traveled in style.

  Movie: As well it should have been.

  The Tacoma Narrows Bridge was one of the longer suspension bridges on Earth.

  Movie: And, if somebody hadn't overlooked something, it probably would have remained one of the longer suspension bridges on Earth.

  Movie: The problem wasn't that, right from the beginning, a lot of people didn't pay a lot of attention to details.

  They did.

  Movie: But somewhere along the line -- and this was obvious in the end -- it looks as if someone forgot -- Look at those cables over -- the significance Movie: of resonance.

  Movie: Among other things, the Tacoma Narrows Bridge was the most spectacular Aeolian harp in history.

  Movie: Unfortunately, its first performance was destined to run only about four months.

  Movie: In the meantime, she was a beautiful bridge.

  Movie: Beautiful, but a little strange.

  Movie: Even before construction was completed, people observed its peculiar behavior.

  Movie: That was because, even in a light breeze, ripples ran along the bridge.

  After a while, one of the local humorists called her Galloping Gertie.

  Movie: And for fairly obvious reasons, the name stuck, at least until the seventh of November, 1940.

  Movie: Then as now, Seattle and Tacoma were sports-minded cities.

  For four months, a regional sport was to drive across the bridge on a windy day.

  Movie: While some claimed it was like riding a roller coaster, others found it a little disconcerting to see the car in front disappear.

  [laughter] Movie: How popular this bridge sport was, or to what extent it might have spread across the country, is anybody's guess.

  Movie: On November seventh, 1940, the winds were relatively moderate, about 40 miles per hour.

  Movie: A mew mode appeared.

  Rather than ripple, the bridge began to twist.

  Movie: A wind of 40 miles per hour is not too strong, but it was strong enough to start the bridge twisting violently.

  I contacted the physics teacher of the local high school, and we'll see him very shortly.

  Thought he might be able to fix it.

  There he comes.

  I've known his son, who told me that it was his father.

  No other example of re- destructive resonance is more impressive than this one.

  All right.

Pengembangan Perkuliahan

1. Buatlah sebuah Esai mengenai materi perkuliahan ini

2. Buatlah sebuah kelompok berjumlah 5 orang untuk menganalisis materi perkuliahan ini

3. Lakukan Penelitian Sederhana dengan kelompok tersebut

4. Hasilkan sebuah produk yang dapat digunakan oleh masyarakat

5. Kembangkan produk tersebut dengan senantiasa meningkatkan kualitasnya

Ucapan Terima Kasih Kepada:

1. Para Dosen MIT di Departemen Fisika

a. Prof. Walter Lewin, Ph.D.

(http://web.mit.edu/physics/people/faculty/lewin_walter.html)

b. Prof. Bernd Surrow, Ph.D.

(http://web.mit.edu/physics/people/faculty/surrow_bernd.html)

Staff

Visualizations:
Prof. John Belcher

Instructors:
Dr. Peter Dourmashkin
Prof. Bruce Knuteson
Prof. Gunther Roland
Prof. Bolek Wyslouch
Dr. Brian Wecht
Prof. Eric Katsavounidis
Prof. Robert Simcoe
Prof. Joseph Formaggio

Course Co-Administrators:
Dr. Peter Dourmashkin
Prof. Robert Redwine

Technical Instructors:
Andy Neely
Matthew Strafuss

Course Material:
Dr. Peter Dourmashkin
Prof. Eric Hudson
Dr. Sen-Ben Liao

Acknowledgements

The TEAL project is supported by The Alex and Brit d'Arbeloff Fund for Excellence in MIT Education, MIT iCampus, the Davis Educational Foundation, the National Science Foundation, the Class of 1960 Endowment for Innovation in Education, the Class of 1951 Fund for Excellence in Education, the Class of 1955 Fund for Excellence in Teaching, and the Helena Foundation. Many people have contributed to the development of the course materials. (PDF)

2. Para Dosen Pendidikan Fisika, FPMIPA, Universitas Pendidikan Indonesia.

Terima Kasih Semoga Bermanfaat dan mohon Maaf apabila ada kesalahan.

Mengenal Alat Pendeteksi Dini Tsunami dengan Sensor LASER

Oleh: Dr. Bambang Widyatmoko, M. Sc.

(Pusat Penelitian Fisika LIPI, Alumni The University of Tokyo)

Jepang yang juga merupakan negara rawan gempa telah memasang alat pendeteksi gempa, baik di darat maupun di laut. Alat yang dipasang di laut juga dilengkapi dengan pendeteksi tsunami. Alat inipun dilengkapi dengan komputer super cepat beserta sarana komunikasinya. Dengan demikian, ketika tsunami terjadi, hanya dalam hitungan 2-5 menit, seluruh data komplet tentang ancaman tsunami itu tersiar ke publik melalui jaringan televisi. Mekanisme peringatan dini inilah yang dikembangkan di Jepang kini.

Sebenarnya ada beberapa metode yang bisa digunakan untuk mendeteksi adanya tsunami yang dikembangkan. Salah satunya adalah seperti yang dikembangkan Dr. Sakata, peneliti ahli tsunami dari The National Research Institute for Earth Science and Disaster Prevention (NIED). Jepang, telah menciptakan metode baru dengan memakai laser. Metode ini sangat sederhana dan sangat sensitif sebagai sensor tsunami ataupun sensor pergeseran / tekanan. Disamping itu, alat ini terbebas dari suara bising karena yang dikirim ke sensor yang berada jauh dari pantai adalah cahaya laser melalui fiber optik sedang seluruh perangkat elektronik diletakkan di darat.

Gambar menunjukkan sistem pendeteksi tsunami dengan laser. Ada dua bagian yang terpisah, yaitu bagian sensor utama yang diletakkan di dasar laut beberapa kilometer dari pantai dan bagian monitoring atau kontrol yang berada di darat (ruang kontrol / monitor). Dua laser diode digunakan sebagai sumber cahaya sekaligus sebagai slave oscillator. Dari masing-masing laser dibagi menjadi dua bagian dengan perbandingan 9:1. Bagian yang 90 persen dikirim ke bagian sensor melalui fiber optik, demikian pula cahaya balik dikirim melalui fiber optik ke tempat penerima (ruang kontrol).

Cahaya balik dari sensor akan dideteksi oleh photo detector dan kemudian sinyal dipakai untuk mengunci frekuensi laser terhadap transmisi puncak dari resonator. Bagian lain disatukan memakai fiber coupler untuk membangkitkan beat signal dan diukur frekuensinya.

Sensor utama yang diletakkan di dasar laut berupa dua buah Fabry-Perot resonator dengan free spectral range (FSR) yang sama. Masing-masing cavity ini terbentuk dari dua buah cermin yang terpisahkan dengan jarak Lc dan dipasang bersilang (sumbu x dan y). FSR didefinisikan sebagai FSR = C/(2 n Lc), dengan C adalah kecepatan cahaya (m/detik), n adalah indeks bias medium (= 1) dan Lc adalah jarak antara dua cermin. Cavity ini hanya akan memberikan transmisi puncak bila frekuensi laser bersesuaian (beresonansi) dengan FSR dari cavity. Kemudian cavity dimasukkan ke dalam tabung silinder yang terbuat dari bahan antikarat yang masing-masing cermin dikunci dengan dinding tabung. Bentuk bagian dalam dibuat sedemikian rupa sehingga ada beda tebal dari dinding silinder pada arah x dan y (lihat gambar).

Apabila dinding tabung terkena tekanan akibat gelombang tsunami, Lc akan berubah yang mengakibatkan FSR dari cavity berubah. Perbedaan tebal dinding juga mengakibatkan perbedaan perubahan panjang dari cavity 1 dan cavity 2. Gambar A menunjukkan grafik transmisi puncak dari resonator sebagai fungsi sweepfrekuensi laser. Seperti digambarkan dalam grafik bahwa dengan tekanan yang sama ada perbedaan perubahan FSR dari resonator 1 dan 2. Perubahan ini yang dideteksi lebih lanjut dengan beat frekuensi dari dua laser yang masing-masing frekuensinya terkunci pada dua cavity tersebut. Locking laser terhadap peaktransmisi dari sensor dilakukan dengan rangkaian sederhana berupa auto-lock circuit. Gambar B menggambarkan transmisi puncak dari sensor dilihat menggunakanoscilloscope, sedangkan gambar C menunjukkan sinyal setelah laser dikunci. Terlihat bahwa daya transmisinya sama dengan puncak dari sensor, yang berarti laser terkunci dengan baik terhadap sensor. Kecepatan sistem kontrol adalah 10 KHz, kecepatan ini cukup untuk mengantisipasi kecepatan perubahan sensor.

Sensor bekerja bila kedua laser terkunci dengan baik ke masing-masing pasangan resonator. Kemudian dari sebagian cahaya laser yang digabungkan dideteksi beatsinyalnya memakai photo detector.

Sumber cahaya beserta kelengkapannya yang diletakkan di darat. Dari alat ini dapat dimonitor perubahan frekuensi laser yang bersesuaian dengan dengan tinggi tsunami dan seterusnya disalurkan ke pusat pengamatan gempa memakai saluran telepon. Perubahan beda frekuensi 12 MHz dideteksi untuk setiap perubahan tsunami 1 cm. Untuk jarak antara dua cermin 10 cm, FSR dari resonator kira-kira 6 GHz, sehingga akan bisa mendeteksi tsunami yang tingginya mencapai 5 meter. Besarnya tsunami yang dapat dideteksi bisa diperbesar dengan memperbesar jarak dua cermin atau mempertebal dinding tabung. Jarak sensor ke darat dapat mencapai 50-100 km tergantung pada daya laser yang dipakai. Dengan jarak sensor 100 km dari pantai juga memungkinkan untuk memberi peringatan dini lebih dari puluhan menit ke darat bila di bagian sensor terjadi tsunami.

Sejauh ini sensor tsunami bukan merupakan produk yang banyak terjual di pasar karena biasanya pemakai adalah pemerintahan (badan penelitian), sehingga harganya cukup mahal. Namun, dari segi teknologi sensor ini bukanlah hal yang susah didapat sehingga 100 persen bisa dibuat (dirakit) di Indonesia. Tentu hal ini membutuhkan dukungan dari pemerintah untuk semaksimal mungkin memanfatkan potensi SDM dalam negeri dan menjalin kerjasama dengan pakar penemunya di Jepang. Masalahnya kini, maukah kita melakukannya ?

The Tsunami® mode-locked Ti:Sapphire laser provides the widest pulse width range, the broadest wavelength coverage and the highest power levels of any ultrafast oscillator on the market. It also offers the best long-term stability and reliability in both femtosecond and picosecond domains.

Key Features

• Broadest pulse width coverage (>
• Output power >3 W for high-power harmonic generation and OPO pumping
• Proprietary broadband optics cover 700–1080 nm
• Uses Millennia® series all-solid state pump lasers (5–15 W)
• Regenerative mode-locking for long-term stability, prevention of pulse dropouts, broadest wavelength coverage, and long picosecond pulse width capability
• Low thermal expansion, Invar based resonator design
• Gimbaled mirror mounts with three-point ball-bearing registry of all optics
• Small footprint
• Accessories include Lok-to-Clock® synchronization, harmonic generators, OPOs, kHz regenerative amplifiers, OPAs, and more

Applications

• Multiphoton microscopy
• Time-resolved fluorescence
• Pump-probe experiments
• Nonlinear spectroscopies
• Optical-computed tomography (OCT)
• Surface second harmonic generation (SHG)
• Amplifier seeding
• Terahertz imaging
• Materials processing
• Ultrafast ultrasonics

Fisika untuk Universitas

Fisika untuk Universitas

Ditujukan untuk meningkatkan kualitas proses dan hasil perkuliahan Fisika di tingkat Universitas

Kelistrikan dan Kemagnetan

Topics covered:

Traveling Waves
Standing Waves
Musical Instruments

Instructor/speaker: Prof. Walter Lewin

Free Downloads

Video

• iTunes U (MP4 - 107MB)
• Internet Archive (MP4 - 210MB)

  » Download this transcript (PDF)

  So today, I will start with a general discussion on waves, as an introduction to electromagnetic waves, which we will discuss next week.

  We'll start with a very down-to-earth equation, Y equals one-third X.

  And I'm going to plot that for you, so here is Y and here is X, and that's a straight line through the origin, Y equals one-third X.

  Suppose, now, I want this line to move.

  I want this line to move with a speed of 6 meters per second in the plus X direction.

  All I will have to do now is to replace X in that equation by X - 6T.

  Notice the minus sign.

  I will go, then, in the plus X direction.

  The equation then becomes Y equals one-third times X - 6T.

  So look at it at T equals 1.

  At T equals 0, you already have the line.

  At T equals 1, you now have Y equals 1/3 X - 2.

  That means, here it will intersect at - 2, and there it will intersect at + 6, and the line parallel to the first one, this line is now T = 1, and this is T = 0.

  And it has moved in this direction, with a speed of 6 meters per second.

  And so what this is telling us, that if we ever want something to move with a speed V in the plus X direction, then all we have to do in our equations to replace X by X - VT, and if we want it to move in the minus X direction, then we replace X by X + VT.

  That's all we have to do.

  So now, I'm going to change to something that is a real wave.

  I now have Y = 2, times the sin 3X.

  That's a wave.

  It's not moving, not yet.

  So I can make a plot of Y as a function of X, and that plot will be like this.

  This is zero, so when the sine is zero, this is pi divided by 3, and this is 180 degrees, and it's again zero, this is 2 pi divided by 3, it's again zero.

  And lambda, which we call the wavelength, lambda, in this case, is from here to here, that is 2 pi divided by 3, this goes also from here to there.

  I will introduce a symbol K that you will often see, we call that the wave number, and K is simply defined as 2 pi divided by lambda.

  So in our specific case, K is 3.

  This here is K.

  If you know this number, you can immediately tell what the wavelength is.

  Now, I want to have this wave move.

  I want to have a traveling wave.

  And I want to have it move with 6 meters per second in the plus X direction.

  So the recipe is now very simple, all I have to do replace this X by X - 6T.

  So now I get Y equals 2 sin [3(X-6T)].

  And if you now look at this curve, this equation, and you plot it a little bit later in time than T0 -- this is already T0 -- a little later in time, you will see that, indeed, it has moved in the plus X direction.

  And it's moving with a speed of 6 meters per second.

  So this equation, when you look at it, holds all the characteristics of the oscillation.

  It holds the amplitude.

  This 2 is the amplitude.

  This is - 2, that's the amplitude.

  This information, K, holds the information on the wavelength, and this information tells you what the speed is.

  And the minus sign, which is important, tells you that it's going in the plus X direction, and not in the minus X direction.

  Can we make such a traveling wave?

  Yes, we can do that, actually, quite easily.

  Suppose I have here a rotating wheel -- rotate with angular frequency omega, and let this has a radius R, and I give it 2 units, so that I get the same amplitude that I have here.

  And I attach to this a string, and I put some tension on the string, so that I create a wave as I rotate it, and the string is attached here, and as it rotates, the wave is going to propagate into the string with a velocity, let's say, V.

  So I can generate a traveling wave.

  The period of one oscillation -- if you were here on the string, you're going up, you're going down, you're going up, you're going down, that's all you're doing, when the wave passes by -- the period of one whole oscillation is obviously 2 pi divided by this omega.

  The wavelength lambda that you are creating -- from here to here is lambda -- well, if you know the speed with which it is traveling, and you know it has been traveling capital T seconds, one oscillation, that's a distance lambda.

  So this is V times T.

  But this is also V divided by F, if F is the frequency in Hertz.

  And so the frequency F is then also given by the speed divided by lambda.

  And so I can write down this equation now in a somewhat different form, Y equals 2 times the sine, and now I bring the 3 inside, so I get 3X-18T.

  This 18 is now that omega.

  This is omega T.

  In here is all the timing information.

  Omega, the period T, everything is in here.

  Here is all the spatial information.

  This is K.

  In here is the information about lambda.

  And so if I know omega, and I know K, then I can also find the velocity, which is omega divided by K.

  So everything is in here, omega divided by 3 gives me back my 6 meters per second.

  So once you have the equation, I can ask you any question about that wave, and you should be able, then, to answer.

  Wavelength, frequency, in hertz, in radians per second, speed, everything.

  You may ask me now, "Why do you discuss this with us?" Well, we are coming up to electromagnetic waves next week, and electromagnetic waves, you're going to see lambdas, you're going to see omegas, you're going to see capital Ts, you're going to see frequency, you're going to see Ks, everything you see there you're going to see next week.

  One exception, that Y, the displacement Y, will not be in centimeters or meters, but it will be an electric field, a traveling electric field, volts per meter.

  Or a traveling magnetic field, tesla.

  But other than that, all these quantities will return in exactly the same way.

  Now I want to discuss with you a standing wave first, because standing waves are going to be important.

  This is a traveling wave.

  And now comes something even more intriguing, which is a standing wave.

  Suppose I have a wave traveling in this direction, and I call that Y1, and Y0 is the amplitude, sine (K X - omega T).

  And notice now, I have all the symbols that we are familiar with.

  We have the K here, we have the omega here, and we have the amplitude here.

  And the minus sign tells me, [wssshhht], it's going in the plus direction.

  But I have another wave.

  And the wave is exactly identical, in terms of amplitude, in terms of wavelength, in terms of frequency, identical, but it's traveling in this direction.

  And so this is Y2, which is Y0 sine (KX + omega T).

  This plus sign tells me it's going in this direction.

  And so if this is a string, the net result is the sum of the two.

  So I have to add them up.

  So Y = Y1 + Y2.

  So I have to do some trigono- trigonometric manipulation, and this is what I leave -- I'll leave you with that, that's high school stuff -- you add the two up and you'll find 2 Y0-- notice that the amplitude has doubled -- times the sine (K X) times cosine (omega T).

  That's the sum of those two.

  And this is very, very different from a traveling wave.

  Nowhere will you see K X - omega T any more.

  K X is here, separate under the sine, and omega T is separate under the cosine.

  All the timing information is now separate from the spatial information.

  And so what does a standing wave like this look like?

  Well, let's -- a bracket here.

  Let's make a drawing of such a standing wave.

  So here we have Y, and here we have X.

  Let's only look at the sine K X for now.

  If X is 0, the sine is always 0, so this point will never move.

  But if K X is 180 degrees, it's also 0, always.

  So lambda over two will never move.

  X is lambda, when this is 360 degrees, it will never move.

  - lambda / 2, will never move.

  So what will it look like?

  Well, you're going to see something like this, let's take the moment when T equals 0, so when cosine omega T is plus 1.

  So we're going to have a curve like this, so this goes up to 2Y0 like this -- and this here is then my 2Y0.

  These points will never move, they will always stand still.

  There's nothing like a traveling wave.

  If it's a traveling wave, these points will see the wave go by, they will go up and down, they never do that.

  They sit still.

  They have a name.

  We call them nodes.

  Let's now look at little later.

  Let's look at T equals one quarter of a period.

  Now, the cosine is 0.

  So there's not a single point on the string that is not 0.

  So the string looks like this.

  If you took a picture of the string, you wouldn't even know it's oscillating.

  It would be just a straight line.

  And now, if we do -- look a little later, and we look at T equals one-half the period, then the cosine is -1.

  So now the curve will look like this.

  And so what does it mean?

  If we just look what's here happening, this is what's going to happen.

  The string is just doing this, and there are points that stand still.

  Nothing is going like this, nothing is going like this.

  You see this point going up and down, up and down, up and down, and this will do the same, and these nodes will do nothing.

  So that is what a standing wave will look like, and I think the name standing wave is a very appropriate name, very descriptive, because it's really standing, it's not -- it's not moving.

  At least, not traveling along the X direction.

  Can we make a standing wave?

  Yes, we can, and I will do that today.

  A standing wave can be made by shaking -- or rotating, in that fashion -- a string.

  So here I have a string, I -- say I attach the string to the wall there, and I move it up and down here.

  So a wave goes in -- I do just this, like the rotating disc -- the wave travels, but the wave is reflected, and so I have a wave going in and I have a wave coming back, so I have now two waves going through each other.

  And if the conditions are just right, then these reflective waves -- this one will reflect, when it arrives here, it will reflect again, it goes back again, and it will continue to reflect -- so if the conditions are just right, then these reflective waves will support each other, and they will generate a large amplitude -- as I will demonstrate to you -- but that's only the case for very specific frequencies, and we call those resonance frequencies.

  The lowest possible frequency for which this happens -- which we call the fundamental -- will make the string vibrate like this.

  So the whole thing goes.

  [wssshhht], [wssshhht], [wssshhht], and we call that the fundamental.

  We call that also the first harmonic.

  If now I increase the frequencies, then I get a second resonant frequency, and a node jumps in the middle -- there is already a node here, and there is a node here, because this motion of my hand here is very small, as I will demonstrate to you, for all practical purpose you can think of this being a node -- and so now the string in the second harmonic will oscillate like this.

  [Wssshhht], [wssshhht], [wssshhht], [wssshhht], so this is the second harmonic.

  And if we go up in frequencies, then -- this should be right in the middle, by the way -- and if I go up in frequency one step more, then I get another resonance whereby we get an extra node, and so we get the third harmonic, and you just can go on like that.

  You get a whole series of resonance frequencies.

  And so, for the fundamental, lambda 1 -- the 1 refers to the first harmonic -- is 2L, if L is the length of my string.

  This is L.

  You only have half a wavelength here, so L is 2L.

  But we know that the frequency is the velocity divided by the wavelength -- we see that there, frequency is velocity divided by the wavelength -- so the frequency F1 is the velocity divided by lambda 1, so that's divided by 2L.

  So that's the frequency in the fundamental for which this resonance phenomenon occurs.

  For the second harmonic, lambda 2 equals L.

  You can tell, you see a complete wavelength here.

  And F2, that frequency, is going to be twice F1.

  And F3 is going to be 3 F1.

  And if you want to know, for the Nth harmonic, N being Nancy, then lambda of N equals N -- 2L/N.

  Substitute in N1, and you find the wavelength for the first harmonic.

  Substitute for N2, and you find the wavelength for the second harmonic.

  And so on.

  And the frequency for the Nth harmonic -- N stands for Nancy -- is N times V divided by 2L.

  So here you see the entire series of frequencies and wavelengths for which we have resonance.

  Unlike in our LRC system that we discussed last time, where you had one resonance frequency, now you have an infinite number of resonance frequencies, and they are at very discrete values, equally spaced.

  I want to demonstrate this to you with a violin string, it's a very special violin string, it's here on the floor, it's a biggie, and I need some help from someone.

  You helped me before, would you mind helping me again?

  So here is, uh, one end of the string, which you're going to hold, you're going to be a node, believe it or not.

  Hold it better, two hands -- no, much better.

  You will see shortly, why -- no, no, no, much better.

  That's it.

  And walk back a little, walk further.

  Yes, that's good, hold it.

  I will put on a white glove, and there is a reason for that, because I want you to be able to see my hand when we're going to make it dark, so that you will convince yourself that my hand, which is generating the wave, is hardly moving at all.

  For practical purposes, it's a node, and yet we get these wonderful resonance phenomenon.

  So I'm going to make it very dark so that the UV will do its job, and you can see the string better, that's the only way we can make you see the string well.

  All right.

  Don't let go, er- under any circumstances, you will hurt me if you do that.

  Of course, if I let go first, then [pfft], I will hurt you, but that's not my plan.

  OK, so let's try to go a little bit further back.

  Let's try to, uh, find, first the -- the fundamental.

  And I'll try to find it by exciting just the right frequency with my hand.

  There it is.

  I think I got it.

  That's the fundamental.

  And look how little my hand is moving here.

  And you will see a very large amplitude in the middle.

  And so these reflected waves, one runs to him, it runs back at me, it runs back at him, keeps reflecting many times, they support each other in a constructive way, that's what resonance is all about.

  And now I'll try to find the second harmonic -- so you'll see another node coming in at the middle.

  It's easier for you to see than for me, actually.

  And it's not always easy to find the -- no, no, no, I'm too low frequency, I have to go up.

  I think I got it now.

  Is this it?

  Yes, one extra node in the middle?

  Speak out up, please.

  [chorus of agreement] Ah, that's better.

  Now I can hear you, thank you.

  Um, there are three nodes now.

  My friend there is a node, I'm a node, and then there is one in the middle.

  If you subtract 1, the 3-1 is 2, then it's the second harmonic.

  And so now I will try to generate a very high frequency, in resonance, and then you count the number of nodes, subtract one, and then you know which harmonic I was able to generate.

  But I will try to -- not so easy to get a resonance in there.

  No, I'm off resonance.

  No.

Pengembangan Perkuliahan

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4. Hasilkan sebuah produk yang dapat digunakan oleh masyarakat

5. Kembangkan produk tersebut dengan senantiasa meningkatkan kualitasnya

Ucapan Terima Kasih Kepada:

1. Para Dosen MIT di Departemen Fisika

a. Prof. Walter Lewin, Ph.D.

(http://web.mit.edu/physics/people/faculty/lewin_walter.html)

b. Prof. Bernd Surrow, Ph.D.

(http://web.mit.edu/physics/people/faculty/surrow_bernd.html)

Staff

Visualizations:
Prof. John Belcher

Instructors:
Dr. Peter Dourmashkin
Prof. Bruce Knuteson
Prof. Gunther Roland
Prof. Bolek Wyslouch
Dr. Brian Wecht
Prof. Eric Katsavounidis
Prof. Robert Simcoe
Prof. Joseph Formaggio

Course Co-Administrators:
Dr. Peter Dourmashkin
Prof. Robert Redwine

Technical Instructors:
Andy Neely
Matthew Strafuss

Course Material:
Dr. Peter Dourmashkin
Prof. Eric Hudson
Dr. Sen-Ben Liao

Acknowledgements

The TEAL project is supported by The Alex and Brit d'Arbeloff Fund for Excellence in MIT Education, MIT iCampus, the Davis Educational Foundation, the National Science Foundation, the Class of 1960 Endowment for Innovation in Education, the Class of 1951 Fund for Excellence in Education, the Class of 1955 Fund for Excellence in Teaching, and the Helena Foundation. Many people have contributed to the development of the course materials. (PDF)

2. Para Dosen Pendidikan Fisika, FPMIPA, Universitas Pendidikan Indonesia.

Terima Kasih Semoga Bermanfaat dan mohon Maaf apabila ada kesalahan.

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Kelistrikan dan Kemagnetan

Topics covered:

Driven LRC Circuits
Resonance
Metal Detectors (Beach/Airport)

Instructor/speaker: Prof. Walter Lewin

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  » Download this transcript (PDF)

  So we have covered RC circuits and RL circuits, and today, we will spend the entire lecture on LRC circuits.

  We will only discuss them in series so that you get the basic idea.

  I have here a driving power supply, alternating, and here I have a capacitor C, self-inductor L, and a resistance R, this is AC, and let the driving voltage be V0 cosine omega T.

  We have to set up the differential equation for this, and I want to remind you that Kirchhoff's Loop Rule does not hold.

  So the closed loop integral of E dot dL, in spite of what the author of your book wants you to believe, that is not 0.

  So how do we set it up?

  There are various ways that you can do that, I have my own discipline.

  I, in my mind, I think of this first being a, a battery -- by this is the plus side, and this is the minus side -- a current is going to flow, capacitor is going to charge up, electric field inside the capacitor is in this direction, the electric field in the self-inductor is always 0, because the self-inductor has no resistance.

  There's no electric field inside the self-inductor, no matter what some of your books want you to believe.

  Then, the electric field in the resistor is in this direction, and the electric field inside the power supply goes from plus to minus, would be in this direction.

  So if I set up the differential equation, I start here, I always go in the same direction as I, because only then is the closed loop integral -L dI/dt.

  So I go over this capacitor, that is V of C, then I go through the wire of the self-inductor.

  There is no electric field, so the integral E dot dL there is 0.

  Then I go through the resistor, so I get IR, and then I have here my power supply, so I get -V0 cosine omega T, and that, now, according to Faraday's Law, equals L, minus L dI/dt.

  The current equals dQ/dt.

  If the current is positive -- this is my positive direction -- then the charge of the capacitor will increase.

  And I also know that V of C, the potential difference over the capacitor is the charge on each one of the capacitor plates, divided by C.

  And so I substitute that in this equation, and I bring the L dI/dt to the left side.

  That is conventionally done.

  You don't have to do that, but that's often done.

  So I get a plus L, dI/dt now becomes d2Q/dt squared -- my goal is to get everything in terms of Q -- then my IR become R dQ/dt, and my V of C becomes Q / C -- notice that I ranked them in order, D2Q/dt squared, dQ/dt, and then Q, you don't have to do that, but there is nothing wrong with doing that -- and then we get here, equals V0 cosine omega T.

  And this is the form in which most books would present this differential equation.

  And they arrive that in various ways, most books arrive at this equation in a completely wrong way, but they get -- anyhow, they end up with this equation.

  And so, you have to solve this equation, which is really beyond your present abilities, it's second-order differential equation, it's really part of 18.03, so I will give you the solution.

  The basic idea being that you find a solution for Q as a function of time, and once you know Q as a function of time, you have, of course, the current, because then you take the derivative of your solution, and you get the current.

  I will give you the current as a function of time.

  So I, that satisfies that differential equation, is the V0 divided by [whistles] R squared + omega L - one over omega C squared, and the whole thing times cosine omega T minus phi.

  And the tangent of phi equals omega L minus one over omega C divided by R.

  We give this upstairs here a name, we call that the reactance.

  The reactance, and that X, or sometimes it's called chi, is omega L minus one over omega C.

  And the units are also ohms.

  We call the entire square root that you see here, we call that capital Z, which is called the impedance, so the square root of R squared plus that X squared equals Z, that also has units of ohm, and that is called the impedance.

  And so Z is an effective resistance, because this whole thing behaves like a resistance.

  But the resistance depends not only on R, L and C, but also on the values of omega.

  This solution is what we call a steady-state solution, it is the solution that you get if you wait a certain amount of time.

  If you turn the instrument on, so you all of a sudden start this experiment, then in the beginning, you get a different solution, which is more complicated, you get transient phenomenon, but these transient phenomenon die out, and you end up with this solution.

  Now, there are several interesting things that you can see in this solution.

  We have to start digesting, this whole hour, this solution.

  It has very interesting aspects.

  For one thing, you can see that the current can be delayed over the driving voltage when phi is positive.

  Then the current comes later than the voltage.

  And that's the result of the inductor, we've discussed that before.

  But now, that's also possible that the current is leading the voltage, which is very hard to understand intuitively.

  That is the case when this term dominates over this one, then phi becomes negative, and so minus phi becomes positive.

  If minus phi is positive, the current is leading the voltage.

  Now you may say, "How can it possibly be?

  Does that meant that before I switch the instrument on, that I already have a current?" Of course it doesn't mean that.

  But that's the transient solution, remember?

  When you turn something on, when you switch it on, this solution doesn't hold yet.

  This is the steady-state solution.

  So the value for I Max, we have always called what is front of the cosine term, we've always called that I Max, that value for I Max is a function of omega itself -- as we will analyze in detail today -- and of course, also, of R, L and C.

  And there is one particular value for Z, and therefore for omega, whereby this value reaches a maximum, and that's what we call resonance.

  There is no value for omega for which the current is any higher.

  And so I will call here, the situation, at resonance.

  It is at resonance when X equals 0, so when omega L is one over omega C, so when omega is one over the square root of L C.

  And we call that the resonance frequency, and we often give a little subscript 0 there to remind you that you're dealing with the resonance frequency.

  And Z is then just R, because when X is 0, the omega L and the one over omega C eat each other up.

  They are not there any more, it's gone.

  And so the system behaves as if there were only a resistor.

  And so you also see that the maximum current that you get is then, simply, V0 divided by that value for R, because Z, the impedance, is now R.

  And in addition, if you're interested in phi, phi then becomes 0, so the driving voltage is then in phase with the current that follows.

  And so the signal that you will see is a cosinusoidal variation in the current, so if I have here the current as a function of time, and you get a signal like so, and this here, this period T equals your 2 pi / omega.

  So that is the -- directly connected to your driving frequency.

  And if the impedance Z is very low, then this maximum value of the current, this is what we call the maximum value -- and, of course, the maximum value is also here, except that the cosine is -1 here, and the cosine is +1 here -- so if Z is very low, then this will be high.

  If Z is very high, this will be low.

  And there is only one and one value of Z for which the system is at resonance, and that is when the self-inductance and the capacitor eat each other up, and then you get the maximum possible value for the current at maximum, which is V0 over R.

  And that's the highest value that you could ever get them.

  Imagine that we have an LRC circuit, and we have L and R and C fixed, but we change the driving frequency.

  So we move over various values of Z by changing omega from a very low value to a very high value.

  If you start at a very low value for omega, let's say it approaches 0, then notice that Z goes to infinity, and so the maximum current becomes 0.

  And the person responsible for that is the capacitor, because if omega goes to 0, this goes to infinity.

  And that's intuitively pleasing, because omega 0 really means you have no AC any more, you have DC.

  And with DC, what you're doing is, you charge up the capacitor when it's fully charged, no current can flow any more.

  So that's intuitively pleasing.

  When omega becomes very high, let's call it infinity, then Z, again, goes to infinity.

  So again, the maximum current, again goes to 0.

  And the person responsible for that is the self-inductor, because when omega goes to infinity, again, Z goes to infinity.

  So again, you get 0 here.

  And that's also intuitively pleasing, because if you have an infinitely high frequency, that means the self-inductance puts up an enormous fight.

  It's ideal for a self-inductor to fight currents if the time over which the changes occur go to 0.

  And so, then, again, it says, "Sorry, you can't have any current." So that's also intuitively pleasing, that the self-inductance, then, becomes the dominant factor.

  And so what I can do now, I can plot the I Max as a function of omega.

  So here is omega, and here is I Max, and we already agreed that when omega is 0, then I Max is 0.

  But when omega is very high, it's also 0.

  But when omega is at resonance, omega 0, which is one over the square root of L C -- notice that R has nothing to do with the resonant frequency, it's really determined by L and C, because it's the chi, it's the X that you want to make 0, and X is only a function of L and C -- at this frequency, we have a value here which is V0 divided by R.

  And so the curve that you're going to see, which we call the resonance curve, is something like this.

  You start out with an extremely small current, you go through resonance, we have a high current, and then at high frequencies, again, you go down to 0.

  And so the left part, when you are below resonance, it's really the capacitance which is the dominant guy in the whole game -- and phi, by the way, is here, less than 0 -- here it is the inductor that plays the key role, and here phi equals larger than 0, and right here, phi, and only there, phi is 0, only when you're exactly at resonance.

  I'd like to show you some numerical results, and for that I have a transparency -- it's also on the web, so you don't have to copy the numbers, uh, you can download them -- these are just some numerical numbers which I want to digest with you, so that you get a feeling for the effect, that you see it in front of your own eyes, what is happening, how this curve evolves.

  We have here a given R, L, and C: ten, 5 times 10 to the -2 henry, and 3 times 10 to the -7 farads.

  The resonant frequency is a little over 8000 radians per second, you see it here in kilohertz, and you see here the impedance -- and what I do here, I have a driving frequency which is 10% below the resonance frequency.

  And I calculate for you, the omega L, which is 367 ohms, and one over omega C, which is 453 ohms.

  You are a little bit below resonance, and so C dominates.

  And you can see, indeed, that this ohm value is larger than this one.

  And so out of that pops a value for X, out of that pops a value for Z.

  Notice that X is 86, and Z is only a hair larger than 86, because this R almost doesn't add to Z, because you get here the square root of 10 squared plus 86 squared, that is almost 86.

  It becomes 87.

  And then you see that the current, the maximum current, which is this value for V0 divided by, uh, the Z, by 87, becomes 0.11 amperes.

  And now, the system is driven at resonance, and notice that it's exactly characteristic for resonance that omega L and one over omega C have the same value.

  They are not there any more, they're gone.

  And so X becomes 0, so the impedance becomes ohm -- 10 ohms, which is the resistance, and so the maximum current is now V0 divided by R, which is 1 amperes.

  And when you're 10% over resonance, then the self-inductor becomes to be more powerful than the capacitor, and again, your current is substantially down, in this, case, 8 times lower than at resonance.

  We define, at a height of 0.7 times the value at resonance, we define a width of this curve.

  And this width is given in terms of delta omega.

  And that width -- and I will give you the answer without mathematical proof, it's not so difficult, but it's a little bit of a headache -- that value is R divided by L.

  So the larger R is, the broader it becomes.

  So if we look at delta omega, for the numbers that we have there, the numbers of the transparency -- so this is for, for the numbers that we have there, we have delta omega, would be R, which is 10 ohms, divided by 5 times 10 to the -2, and that is about 200 radians per second.

  We define Q not as charge -- don't never confuse that with charge -- we call that the quality of the resonance, and the quality is defined as omega 0 divided by delta omega.

  Now, omega 0 itself is one over the square root of L C, and delta omega is R divided by L.

  And so that makes the quality 1/R times the square root of L/C.

  And the quality is the measure for omega 0, which is this, what I'm pointing at now, divided by delta omega, which is this.

  So if the quality is high, this peak is relatively narrow, and if the quality is low, it's relatively wide.

  You may ask yourself the question, why do we define delta omega at 70% of the maximum current at resonance?

  Why not at half?

  There's a good reason for that, because, in practice, we are more interested in power than that we are in currents.

  And power is proportional with I squared.

  And so when you square this, you get 0.5.

  And 0.5 means, then, that this is really the width at half-power.

  And so that's the reason why we chose the 0.7 times the maximum current at resonance.

  It's really the half-power width.

  Resonance can be destructive.

  Uh, imagine, if you have a very high-Q system, if you're slightly off-resonance, there's almost no current, no power dissipated in your resistor, and now, you come, all of a sudden, on the resonance, you can an enormous current, and that means there's an enormous power dissipation in your resistor, and you can burn out your resistor.

  You can destroy your circuits, if you're not careful.

  And next lecture and Monday, I will also discuss with you some med- mechanical resonances.

  Mechanical systems can also go into [unintelligible] can also be destructive.

  At certain frequencies, the systems behave -- call it k- violently, they respond extremely strongly to their input frequency, and things can break.

  Humans also have resonance frequencies, you can call them, if you want, emotional resonances.

  All have sensitive nerves.

  Someone makes a particular remark, go through the roof.

  Also, falling in love, when you think about it, is a resonance phenomenon, and that, too, can be rather destructive.

  As many of us know.

  But now I would like to demonstrate to you the resonance curves -- I'm going to choose particular values of, um, R, L, and C, which I can change, and then I will show you the current as a function of frequency.

  And these are the values that I have chosen.

  Again, this is on the Web, you can download it, so you don't have to copy it now.

  And I will change the -- the light setting so that we can also enjoy the demonstration.

  The idea being that, for these values that I have there, in the first line you see R, 60 ohms, and the self-inductance is 50 millihenry, and the capacitance is 0.3 microfarads.

  So that's a given there.

  And I give you here the resonance frequency, 8000, in terms of omega radians per second, this is the resonance frequency in Hertz -- and just in case you're interested, I gave you the Q value there as well.

  And what I'm going to do now for you, is I'm going to sweep the input frequency from 0 to 16000 radians per second.

  So my omega can go from 0 to 16000.

  And I leave the values as they are, here.

  So I'm going to sweep, sweep over this 8000.

  And so you're going to see that curve.

  Except that I'm show -- I'm going to show you I as a function of frequency, not I Max.

  And I is oscillating, because there's a cosine term.

  And so, for instance, if I were here, with this value for omega, you would see then that it goes up, it goes down, it goes up, it goes down, it goes up, and it goes down.

  And when I'm here, you will see this.

  And keep that in mind when you look at the curve that you're going to see there -- and so it's only the envelope, then, that is the I Max.

  But you actually see the entire current as a function of frequency.

  And I am going to do that, then, for all these four values that you see there.

  So, let's first change the light so that we get an optimum situation for you.

  And now, I will show you.

  Already, the results of the first line -- so these are the values that you see there.

  And I go -- I sl- I go very slowly.

Pengembangan Perkuliahan

1. Buatlah sebuah Esai mengenai materi perkuliahan ini

2. Buatlah sebuah kelompok berjumlah 5 orang untuk menganalisis materi perkuliahan ini

3. Lakukan Penelitian Sederhana dengan kelompok tersebut

4. Hasilkan sebuah produk yang dapat digunakan oleh masyarakat

5. Kembangkan produk tersebut dengan senantiasa meningkatkan kualitasnya

Ucapan Terima Kasih Kepada:

1. Para Dosen MIT di Departemen Fisika

a. Prof. Walter Lewin, Ph.D.

(http://web.mit.edu/physics/people/faculty/lewin_walter.html)

b. Prof. Bernd Surrow, Ph.D.

(http://web.mit.edu/physics/people/faculty/surrow_bernd.html)

Staff

Visualizations:
Prof. John Belcher

Instructors:
Dr. Peter Dourmashkin
Prof. Bruce Knuteson
Prof. Gunther Roland
Prof. Bolek Wyslouch
Dr. Brian Wecht
Prof. Eric Katsavounidis
Prof. Robert Simcoe
Prof. Joseph Formaggio

Course Co-Administrators:
Dr. Peter Dourmashkin
Prof. Robert Redwine

Technical Instructors:
Andy Neely
Matthew Strafuss

Course Material:
Dr. Peter Dourmashkin
Prof. Eric Hudson
Dr. Sen-Ben Liao

Acknowledgements

The TEAL project is supported by The Alex and Brit d'Arbeloff Fund for Excellence in MIT Education, MIT iCampus, the Davis Educational Foundation, the National Science Foundation, the Class of 1960 Endowment for Innovation in Education, the Class of 1951 Fund for Excellence in Education, the Class of 1955 Fund for Excellence in Teaching, and the Helena Foundation. Many people have contributed to the development of the course materials. (PDF)

2. Para Dosen Pendidikan Fisika, FPMIPA, Universitas Pendidikan Indonesia.

Terima Kasih Semoga Bermanfaat dan mohon Maaf apabila ada kesalahan.