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

Kelistrikan dan Kemagnetan

**Topics covered:**

Doppler Effect

The Big Bang

Cosmology

**Instructor/speaker:**Prof. Walter Lewin

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### Video

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Today I want to talk with you about Doppler effect, and I will start with the Doppler effect of sound which many of you perhaps remember from your high school physics.

If a source of sound moves towards you or if you move towards a source of sound, you hear an increase in the pitch.

And if you move away from each other you hear a decrease of a pitch.

Let this be the transmitter of sounds and this is the receiver of sound, it could be you, your ears.

And suppose this is the velocity of the transmitter and this is the velocity of the receiver.

And V should be larger than 0 if the velocity is in the direction.

And in the equations what follow, smaller than zero it is in this direction.

The frequency that the receiver will experience, will hear if you like that word, that frequency I call F prime.

And F is the frequency as it is transmitted by the transmitter.

And that F prime is F times the speed of sound minus V receiver divided by the speed of sound minus V of the transmitter.

So this is known as the Doppler shift equation.

If you have volume one of Giancoli you can look it up there as well.

Suppose you are not moving at all.

You are sitting still.

So V receiver is 0.

But I move towards you with 1 meter per second.

If I move towards you then F prime will be larger than F.

If I move away from you with 1 meter per second then F prime will be smaller than F.

The speed of sound is 340 meters per second.

So if F, which is the frequency that I will produce, is 4000 hertz, then if I move to you with 1 meter per second, which I'm going to try to do, then the frequency that you will experience is about 4012 hertz.

It's up by 0.3 percent.

Which is that ratio one divided by 340.

And if I move away from you with 1 meter per second, then the frequency that you will hear is about 12 hertz lower.

So you hear a lower pitch.

About 0.3 percent lower.

I have here a tuning fork.

Tuning fork is 4000 hertz.

I will bang it and I will try to move my hand towards you one meter per second roughly.

That's what I calculated it roughly is.

Move it away from you, towards you, away from you, as long as the sound lasts.

You will hear the pitch change from 4012 to 3988.

Very noticeable.

Have you heard it?

Who has heard clearly the Doppler shift, raise your hands, please?

OK.

Chee chee chee chee it's very clear.

Increased fre- frequency and then when I move my hands, away a lower pitch.

Now you may think that it makes no difference whether I move towards you or whether you move towards me.

And that is indeed true if the speeds are very small compared to the speed of sound.

But it is not true anymore when we approach the speed of sound.

As an example, if you move away from me with the speed of sound, you will never hear me.

Because the sound will never catch up with you, and so F prime is 0.

And you can indeed confirm that with this equation.

But if I moved away from you with the speed of sound, for sure the sound will reach with you.

And the frequency that you will hear is only half of the one that I produce.

So there's a huge asymmetry.

Big difference whether I move or whether you move.

So I now want to turn towards electromagnetic radiation.

There is also a Doppler shift in electromagnetic radiation.

If you see a traffic light red and you approach it with high enough speed you will experience a higher frequency and then you will see the wavelengths shorter than red and you may even think it's green.

You may even go through that traffic light.

To calculate the proper relation between F prime and F requires special relativity.

And so I will give you the final result.

F prime is the one that you receive.

F is the one that is emitted by the transmitter.

And we get here then 1 - beta divided by 1 + beta to the power one-half.

And beta is V over C, C being the speed of light, and V being the s- speed, the relative speed between the transmitter and you.

If beta is larger than 0, you are receding from each other in this equation.

If beta is smaller than 0, you are approaching each other.

You may wonder why we don't make a distinction now between the transmitter on the one hand, the velocity, and the receiver on the other hand.

There's only one beta.

Well, that is typical for special relativity.

What counts is only relative motion.

There is no such thing as absolute motion.

The question are you moving relative to me or I relative to you is an illegal question in special relativity.

What counts is only relative motion.

If we are in vacuum, then lambda = C / F and so lambda prime = C / F prime.

Lambda prime is now the wavelength that you receive and lambda is the wavelength that was emitted by the -- by the source.

So I can substitute in here, in this F, C / lambda which is more commonly done.

So this Doppler shift equation for electromagnetic radiation is more common given in terms of lambda.

But of course the two are identical.

And then you get now 1+ beta upstairs divided by 1- beta to the power one-half.

The velocity, there if I'm completely honest with you, is the radial velocity.

If you are here and here is the source of emission and if the relative velocity between the two of you were this, then it is this component, this angle is theta, this component which is V cosine theta, which we call the radial velocity, that is really the velocity which is in that equation.

Police cars measure your speed with radar.

They reflect the radar off your car and they measure the change in frequency as the radar is reflected.

That gives a Doppler shift because of your speed and that's the way they determine the speed of your car to a very high degree of accuracy.

You can imagine that in astronomy Doppler shift plays a key role.

Because we can measure the radial velocities of stars relative to us.

Most stellar spectra show discrete frequencies, discrete wavelength, which result from atoms and molecules in the atmosphere of the stars.

Last lecture I showed you with your own gratings a neon light source and I convinced you that there were discrete frequencies and discrete wavelengths emitted by the neon.

If a particular discrete wavelength, for instance in our own laboratory, would be 5000 Angstrom, I look at the star, and I see that that wavelength is longer, lambda prime is larger than lambda, then I conclude -- lambda prime is larger than lambda, that means the wavelength the way I observe it is shifted towards longer wavelength, is shifted in the direction of the red, and we call that redshift.

It means that we are receding from each other.

If however I measure lambda prime to be smaller than lambda, so lambda prime smaller than lambda, we call that blueshift in astronomy, and it means that we are approaching each other.

And so we make reference to the direction in the spectrum where the lines are moving.

I can give you a simple example.

I looked up for the star Delta Leporis what the redshift is.

There is a line that most stars show in their spectrum which is due to calcium, it even has a particular name, I think it's called the calcium K line, but that's not so important, the name.

In our own laboratory, lambda is known to a high degree of accuracy, is 3933.664 Angstroms.

We look at the star and we recognize without a doubt that that's due to calcium in the atmosphere of the star and we find that lambda prime is 1.298 Angstroms higher than lambda.

So lambda prime is larger than lambda.

So there is redshift and so we are receding from each other.

I go to that equation.

I substitute lambda prime and lambda in there and I find that beta equals +3.3 times 10 to the -4.

The + for beta indeed confirms that we are receding, that our relative velocity is away from each other, and I find therefore that the radial velocity -- I stress it is the radial component of our velocity is then beta times C and that turns out to be approximately 99 kilometers per second.

So I have measured now the relative velocity, radial velocity, between the star and me, and the question whether the star is moving away from me or I move away from the star is an irrelevant question, it is always the relative velocity that matters.

How can I measure the wavelength shifts so accurately that we can see the difference of 1.3 angstroms out of 4000?

The way that it's done is that you observe the starlight and you make a spectrum and at the same time you make a spectrum of light sources in the laboratory with well-known and well-calibrated wavelength.

Suppose there were some neon in the atmosphere of a star.

Then you could compare the neon light the way we looked at it last lecture.

You could compare it with the wavelength that you see from the star and you can see very, very small shifts.

You make a relative measurement.

So you need spectrometers with very high spectral resolution.

So there was a big industry in the early twentieth century to measure these relative velocities of stars.

And their speeds were typically 100, 200 kilometers per second.

Not unlike the star that I just calculated for you.

Some of those stars relative to us are approaching.

Other stars are receding in our galaxy.

But it was Slipher in the 1920s who observed the redshift of some nebulae which were believed at the time to be in our own galaxy and he found that they were -- had a very high velocity of up to 1500 kilometers per second, and they were always moving away from us.

And it was found shortly after that that these nebulae were not in our own galaxy but that they were galaxies in their own right.

So they were collections of about 10 billion stars just like our own galaxy.

And so when you take a spectrum of those galaxies, then of course you get the average of millions and millions of stars, but that still would allow you then to calculate the redshift, the average red shift, of the galaxy, and therefore its velocity.

And Hubble, the famous astronomer after which the Hubble space telescope is named, and Humason made a very courageous attempt to measure also the distance to these galaxies.

They knew the velocities.

That was easy because they knew the redshifts.

The distance determinations in astronomy is a can of worms.

And I will spare you the details about the distance determinations.

But Hubble made a spectacular discovery.

He found a linear relation between the velocity and the distances.

And we know this as Hubble's law.

And Hubble's law is that the velocity is a constant which is now named after Hubble, capital H, times D.

And the modern value for H, the modern value for H is 72 kilometers per second per megaparsec.

What is a megaparsec?

A megaparsec is a distance.

In astronomy we don't deal with inches, we don't deal with kilometers, that is just not big enough, we deal with parsecs and megaparsecs.

And one megaparsec is 3.26 times 10 to the 6 light-years.

And if you want that in kilometers, it's not unreasonable question, it's about 3.1 times 10 to the 19 kilometers.

So I could calculate for a specific galaxy that I have in mind, I can calculate the distance if I know the red shift.

I have a particular galaxy in mind for which lambda prime -- for which lambda prime is 1.0033 times lambda.

So notice again that the wavelength that I receive is indeed longer than lambda, so there is a redshift.

I go to my Doppler shift equation which is this one.

I calculate beta.

One equation with one unknown, can solve for beta.

And I find now that V is 5000 kilometers per second.

Very straightforward, nothing special, very easy calculation.

But now with Hubble's law I can calculate what D is.

Because D now is the velocity which is 5000 kilometers per second divided by that 72 and that then is approximately 69 megaparsec.

Again we have the distance if we do it in these units in megaparsecs.

That's about 225 million light-years.

And so the object is about 225 million light-years away from us.

So it took the light 225 million years to reach us.

So when you see light from this object you're looking back in time.

And if you have a galaxy which is twice as far away as this one, then the velocity would be twice as high.

And they're always receding relative to us.

I'd like to show you now some spectra of three galaxies.

Can I have the first slide, John?

All right, you see here a galaxy and here you see the spectrum of that galaxy.

That may not be very impressive to you.

The lines that are being recognized to be due to calcium K and calcium H are these two dark lines.

Some of you may not even be able to see them.

And this is the comparison spectra taken in the laboratory.

These lines are seen as dark lines, not as bright lines.

We call them absorption lines.

They are formed in the atmosphere of the star.

Why they show up as dark lines and not as bright lines is not important now.

I don't want to go into that.

That's too much astronomy.

But they are lines and that's what counts.

And these lines are shifted towards the red part of the spectrum by a teeny weeny little bit.

You see here this little arrow.

And the conclusion then is that in this case the velocity of that galaxy is t- 720 miles per second which translates into 1150 kilometers per second, and so that brings this object if you believe the modern value for Hubble constant at about 16 megaparsec.

This galaxy is substantially farther away.

No surprise that it therefore also looks smaller in size, and notice that here the lines have shifted.

These lines have shifted substantially further.

And if I did my homework, using the velocity that they claim, which they can do with high degree of accuracy because you can calculate lambda prime divided by lambda, those measurements can be made with enorm- accuracy, I find that this object is about 305 megaparsecs away from us, so that's about 20 times further away than this object.

So the speed is also about 20 times higher of course because there's a linear relationship.

And if you look at this one which is even further away, then notice that these lines have shifted even more.

The next slide shows you what I would call Hubble diagram.

It was kindly sent to me by Wendy Freedman and her coworkers.

Wendy is the leader of a large team of scientists who are making observations with the Hubble space telescope.

You see here distance and you see here velocity in the units that we used in class, kilometers per second.

Forget this part.

That's not so important.

But you see the incredible linear relationship.

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Ucapan Terima Kasih Kepada:

1. Para Dosen MIT di Departemen Fisika

a. Prof. Walter Lewin, Ph.D.

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

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

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.

Terima Kasih Semoga Bermanfaat dan mohon Maaf apabila ada kesalahan.

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