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
out, 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 hundred 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, this 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 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 M R X two. 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 had
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 eight oh
one, 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 five hundred 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, four hundred and eighty eight
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 like,
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 nineteen forty. 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. With 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 nineteen forty, and at this,
uh, in Washington State. Movie: On the First of July,
nineteen forty, 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 travel 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, alot of
people didn't pay alot 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 [unintelligible]
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, nineteen forty.
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, nineteen forty,
the winds were relatively moderate, about forty miles per
hour. Movie: A mew mode appeared.
Rather than ripple, the bridge began to twist.
Movie: A wind of forty 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 him some, he told me that it was his
father. No other example of re-
destructive resonance is more impressive than
this one. All right.
So now, we've had so much fun, and we have to really get into
electromagnetic waves. So we turn back to Maxwell's
equations as you see them here. And Maxwell -- who was credited
for this extra term that he added to Ampere's Law,
the displacement current term, was able to predict that
electromagnetic waves should exist, he predicted the
existence of radio waves, which were later discovered by
Hertz, and that was a great victory for the theory.
But, as I will show you today, there was another enormous
victory around the corner. Electric and magnetic fields
can move through space and satisfy all four Maxwell's
equations. The electric field results from
a changing magnetic field, and a magnetic field results
from a changing electric field. So one exists at the mercy of
the other, and the other exists at the mercy of one.
Together, they propagate through space -- they can even
propagate through vacuum, where there are no charges,
and where there are no currents.
Very mysterious. I will write down a possible
solution of an electromagnetic wave which meets all four
Maxwell's equations, and this is the graphical
display of those waves that I'm going to write down.
But I will discuss that with you in a minute.
The electric field is only in the direction of X -- this is
the magnitude, the largest value of the
electric field -- it's only in the direction of X.
Cosine K Z minus omega T. This is the frequency,
and the minus sign tells you that it is
traveling in the plus Z direction.
B, the associated magnetic field, is B zero,
only in the Y direction, with exactly the same cosine
minus omega T term. So if I plot this at time T
equals zero, then you see this curve right here.
And you see the magnetic field curve here.
The magnetic field is only in the Y
direction, and the electric field is only in the X
direction. And this is a package that,
together, moves in the direction of plus Z with this
speed, which is omega divided by K.
And the wavelength from here to here is N two pi divided by K.
We call then plane waves, and the reason why we cal them
plane waves is that, if you take a plane,
anywhere perpendicular to Z, that no matter where you are in
that plane, at that moment in time, the E and the B vector are
everywhere in that plane the same.
So think of this as a plane perpendicular to the Z axis,
and then this whole train passes by you.
And so you see the electric field vector like this,
becomes zero, like this, becomes zero,
like this. And the magnetic field vector,
maximum, zero, this direction,
and so on. But that's why they're called
plane waves. These equations only satisfy
Maxwell's equations under two conditions.
And one condition is that B zero is E zero divided by C,
and the other condition is that omega divided by K,
which is the velocity, with which it propagates,
I will call that C -- in vacuum,
we call the velocity of electromagnetic radiation C --
that is one divided by the square root of epsilon zero,
mu zero. If that's the case,
my two equations will satisfy Maxwell's equations.
Imagine the victory for Maxwell.
Maxwell was not only able to predict the existence of
electromagnetic waves, but he was even able to predict
that they would move through vacuum
with that speed. What an unbelievable victory,
when you come to think of it, that epsilon zero can be
measured -- in a static way, if follows from Coulomb's law,
has nothing to do with the B dT, has nothing to do with the E
dT. Has nothing to do with
traveling waves. Epsilon zero is about eight
point eight five times ten to the minus twelve in SI units.
Mu zero is equally static, can be measured from the force
at which two wires, through which you run a
current, attract each other. No dB dT, no dE dT,
there's nothing to do with electromagnetic waves.
Mu zero is about one point two six times ten to the minus six
in SI units. And if you multiply them,
and substitute them in this equation, you will find that C
equals two point nine nine times ten to the
eight meters per second. Unbelievable.
What a success for that theory. It always baffles me how two
quantities so static, an seemingly so unrelated to
moving waves, with dB dTs and dE dTs all over
the place, how they can predict the speed of light.
Suppose I ask you to measure the pressure in your tires of
your car, and I would ask you to also
measure the voltage of your battery, and then to predict the
speed of the car. It's almost something like
that. It is bizarre.
But it works, and it was a great victory,
and of course, it justified entirely this one
term, which is this displacement current term.
Together, you and I will prove that this is,
indeed, a necessary condition so
that these equations satisfy Maxwell's equations.
We will do it together. I will do 50 percent,
and you will do the other 50 percent at assignment number
nine. So we split this bill
fifty-fifty. I will make a new drawing,
and I will do something that I rarely ever do in lectures,
I will give you eight minutes of hardcore math.
You're going to hate it. I'm going to make a new
drawing, which is not too different from what you have
there. So this is Z,
this is X, and this is Y. And at T equals zero,
I'm going to draw here the electric field like so.
So this is E zero, electric field is this
strength, and now I'm going to apply
Ampere's Law -- that's my half of the bargain -- closed-loop
integral of B dot D L -- you see there -- equals epsilon zero
times mu zero times D phi E D T. We're dealing with vacuums,
so kappa is one, and the dielectric constant is
one. And there is no such thing as a
current I, because we are in empty space,
so this whole term does not exist.
What does Ampere's Law require? I need a closed loop,
and I need a surface that I attach an open surface to that
closed loop. I'm going to choose a closed
loop in the plane Y Z. And this is going to be my
closed loop. This here is going to be my
closed loop. This length is L,
and the length -- or the width, of this side,
is lambda divided by four. I have to do a closed loop
integral of B dot D L, I will do that last.
I will first do the hardest part, which is the time
derivative of the electric flux through this surface.
The problem is that the electric field is not constant.
The electric field is zero here, and has a maximum here,
and falls off in this way. So I have to do an integral.
So I'm going to make a slice here, and this slice here has a
width D Z. And in that very narrow slice,
the electric field is approximately constant.
Right here, the electric field ahs this value.
But everywhere in that slice, it has the same value,
because remember, it's a plane wave.
And so I will draw here a line parallel, and so everywhere in
that slice, the electric field has exactly this value.
And that value is given by this equation.
If you tell me what Z is at time T equals zero,
I know what that value is, that's this value.
So now I have to calculate the electric flux.
So phi of E -- I have to take the dot product between D A and
the electric field. Remember, flux is a dot
product, E times D A. I will choose D A up,
because E is also up, so that makes life easy -- I
have to remember that later, then, when I do the closed loop
integral of B dot D L, then looking from below,
I have to go clockwise, because I remember the
right-hand corkscrew rule.
So I get all my minus signs and plus signs just right.
So D A an E are in the same direction.
So what is D A of this little slice?
That is L times D Z. So I get L times D Z.
What is the local electric field in this slice?
Well, that's that equation. So I get E zero times the
cosine of K Z minus omega T. This X roof,
of course, is gone, because the A and E are in the
same direction, I have already taken that into
account. But I have to integrate this
now, from Z equals zero to lambda over four,
because I have to integrate it over this whole surface.
So that's the -- the answer. But I'm not interested in phi
E. I have to know the phi E D T.
So it's going to be worse for you.
I told you, eight minutes,
pain in the neck. So I'm going to take the time
derivative of that function, so D phi E D T.
L and E zero can come out, that's no problem,
they are constants. I tae the time derivative of
cosine K Z minus omega T, then minus omega pops out,
and the cosine becomes a minus sign.
So I get minus the sine of K Z minus omega T.
And I have to do an integral -- here is my D Z,
zero to lambda over four. This minus sign eats up this
minus sign. I have to do the integral,
but I do that at T equals zero. In other words,
this thing goes away, because T equals zero.
So I'm getting close. So I'm going to continue here,
so I get L times E zero, I have an omega,
and now I have to do the integral of sine K Z D Z.
Well, the K Z means I have to get a K out, which is here,
and then the integral of sine D Z is simply minus the cosine of
K Z, and I have to evaluate that between zero and lambda over
four. If I evaluate cosine K Z
between zero and lambda over four, that's minus one.
I'm sure you can do that alone. Times this minus one makes it
plus one. And so the answer is L times E
zero times omega divided by K, but we call that C,
in vacuum, that is the speed of electromagnetic radiation.
So this is the answer to the phi E D T.
Now, we have to do the closed loop integral of B dot D L.
And that is easy. At this moment in time,
B is the maximum here, which is B zero,
and then it falls off to zero here.
You can see the same there. Suppose I start here,
and I go this way, this way, this way,
and this way. Closed loop integral.
If I go from here to here, my B and D L are at ninety
degree angles. B is coming to you,
and B L i- D L is like this. So there is no contribution
here. If you go from here to here,
well, B is zero everywhere along the line.
So integral B dot D L from here to here is zero.
It's a plane wave, remember?
B is zero here, it's also zero here,
it's also zero here.
If you go from here to here, B and D L are,
again, at ninety-degree angles, so there is no contribution,
so there's only a contribution due to this portion.
And that I B zero times the length L.
And now you see why I chose the width lambda over four,
so I get a very easy result. So I find, then,
that B zero times L, which is the left part of
Ampere's Law -- well, it's too much to give Ampere
credit -- all the credit, because it's really Maxwell who
added that term, the phi E D T.
And so this, now, is epsilon zero mu zero,
which you see upstairs there, times the result that we have
here. Oh, by the way,
this is E zero. Times L, times E zero,
times C. And I lose my L.
And you see here a result that is quite remarkable,
even though it doesn't look so remarkable to you,
yet. The reason is,
that you are going to do the other half.
You are going to apply Faraday's Law for me.
I only used Ampere's Law, you're going to -- in
assignment nine, use this relationship,
which will allow you to prove this.
And once you have this, substitute for B zero,
E zero divided by C, and you see immediately that
the speed of light, then, has to be this.
This is your task. I did this end.
Yours is not easier than mine, and I advise you also,
use this quarter-wavelength trick.
All right, so you can demonstrate that this is a
necessary condition for Maxwell's equations to satisfy
the, um -- this is not what I want -- to -- that these
equations actually satisfy all four Maxwell's equations.
Traveling electromagnetic waves always have the following
properties. This is on the Web,
so you can download that. E is perpendicular to V.
Notice that that's what I chose.
E is perpendicular to V. V is in the Z direction,
and E is like this, so that's obviously why I chose
that. B is also perpendicular to V.
B is in the Y direction here. Only in the Y direction.
It's also perpendicular to V, which is in the Z direction.
E is also perpendicular to B. That's what I did.
E in the X direction, B in the Y direction.
E and B are in phase. That is like saying,
if this is cosine K Z minus omega T, this also has to be
cosine K Z minus omega T. They simultaneously go through
zero, and they simultaneously reach a maximum.
What is also a necessary condition, that E cross B,
the unit vector, is in the direction of V.
Ha, look at that, that's exactly what I did.
If you take E and you cross it with B, you go into the
direction Z. In fact, whenever you make
drawings like this, you should always
what we call a right-handed coordinate system,
which is that X roof crossed with Y roof is always Z roof.
If you don't do that, you got yourself into muddy
water. And then, in case you are in
vacuum, there is a correlation between -- a relation between B
zero and E zero that you are going to prove with Faraday's
Law, and then, combined with my results,
the speed of electromagnetic radiation in vacuum is one over
the square root of epsilon zero mu zero.
If you know the frequency of the electromagnetic radiation,
then the wavelength follows immediately, and so you see here
a few examples that I've calculated for you.
If you start out with a low frequency of thousand Hertz,
you get a wavelength of three hundred kilometers,
radio waves, megaHertz, still talk about
radio waves, but when you go up in frequency,
the wavelengths, of course, get shorter and
shorter, we would call these radar
waves, microwaves. If you go to ten to the
fourteen, ten to the fifteen Hertz, you get into the domain
of infrared and visible light, and the ultraviolet,
and if you go even higher, then you end up with X-ray and,
ultimately, gamma rays. All of these are members of the
electromagnetic family, electromagnetic waves.
This A with a little zero there stands for angstroms.
That means ten to the minus ten meters.
So, a whole family of electromagnetic waves,
and we give them names so we can talk about them without ever
mentioning the specific frequency or the -- or the
wavelength. So given the fact that
electromagnetic waves then travel with three hundred
thousand kilometers per second, one foot would take one
nanosecond. Twenty six one hundred,
thirty meters deep. The light, for me,
to Professor Bertozzi all the way at the end would take about
oh point one microseconds.
One second, light, radio waves to the moon.
Eight minutes it takes the light from the sun to reach us.
The light from the nearest stars will take five years.
And the nearest large galaxy to the Earth would take two million
years for that light to reach us.
So when you look at that galaxy, then you see the galaxy
the way it was two million years ago.
In astronomy, we use as our meter
stick, a light-year, which is the distance that
light travels in one year, which is about ten to the
sixteen meters. If you study a galaxy which is
at a distance of ten billion light-years, you're looking at
the universe the way it was ten billion years ago.
So in astronomy, you can look back minutes,
you can look back years, you can look back millions of
years, but you can also look back in time
billions of years. Most forms of electromagnetic
radiation -- certainly light, and radio waves,
and radar -- can reflect off surfaces.
At least, to some degree, it depends on the surface.
And this is the basis behind the distance determination.
When you send a radar pulse to an airplane, or to a rainstorm,
some of that radiation comes back at you, and you know the
speed, and so that allowed you to calculate the
distance. If the distance to the plane is
D, and you send a brief pulse, and it comes back -- they call
it the echo -- and it takes a certain amount of time to come
back, which you can measure, then that signal has traveled
twice the distance, so that is the speed of light
times T, this is what you measure, the distance in time
from the moment you sent the signal until you get the
reflection back, and so you can calculate the
distance. The distance to the moon can be
measured this way. There are five corner
reflectors on the moon. Three were left there by the
Americans and two were left by the Soviets, in the days that it
was still the Soviet Union. An optical telescope from Earth
can send a very brief pulse, laser pulse,
to these corner reflectors. The l- the time,
the length in time of this pulse is only one-quarter of a
nanosecond. Just imagine,
light only travels seven centimeters in one-quarter of a
nanosecond. So the kind of wave that you
get is really not very much of a plane wave, the way we envision
it. But in any case,
this pulse goes to the moon, and then some of it comes back,
it's reflected off these radar -- these corner reflectors,
not radar, it's light. Laser light.
There are two times ten to the seventeen photons,
roughly, in one of these pulses, and only one comes back
per ten pulses. So not much comes back.
But it's enough, if you integrate it to get an
accurate distance determination between us and the corner
reflectors, the accuracy is about ten centimeters.
And the goal is really to get a handle on the precise orbit of
the moon. I can show you these
corner reflectors the way they were built on Earth,
and then I will also show an optical observatory as it is
sending out these quarter-nanosecond pulses,
laser light, to the moon.
So this is, uh, one of those corner
reflectors. They are designed in such a way
that if light strikes it in a certain direction,
that it reflects the light in exactly the same direction
backwards, hundred eighty degrees, very clever design.
And so the next slide will show you, in Texas,
McDonald Observatory is sending, here,
these short, brief pulses,
laser light, to the moon,
and what you see here is simply some scattered light of the dust
in the Earth atmosphere.
And then only a teeny weeny little bit of that comes back,
but that is enough to get the distance to the moon.
There are, on the moon -- this is enough for this slide to --
John -- there are, on the moon,
several cameras. They were left there by a
surveyor, they are small cameras.
The lens, I think, is only two inches across.
And they keep an eye on the Earth all the time.
Something that you may never have thought of,
if you were on the moon, and you look at the Earth,
and the Earth is there, say, that an hour from now,
the Earth will still be there. And ten hours from now,
the Earth will still be there, and ten years from now,
the Earth will still be there. As seen from the moon,
the Earth never moves. Of course, it rotates about its
axis. You will see that.
You will also see that certain parts of the Earth are at night
and others are at day, that's different,
but it's always in the same direction.
So it's very easy for these cameras to keep an eye on us,
so to speak. All you have to do is aim them
in one direction, and you never have to change
that direction. Imagine that you and I were now
on the moon, and we were looking at the Earth.
And you, for instance, would see the Earth as you see
it here. Here is North America,
and this part of the Earth happens to be daylight,
and here it's night. And this is the moment that
these cameras are going to take a
picture of the Earth. So you expect to see a lot of
light here, and you expect this to be night, here is New York.
You may think that there is so much light coming from New York
that you may actually see New York, that a picture taken by
these cameras actually may show you New York.
Well, you won't, but you see something else
which is very dramatic, that's why I show this to you
-- because the picture you're going to see next -- John,
you can show it -- is at the time that two observatories on
Earth were both sending these laser pulses to the moon.
And here you see one in Arizona, and here you see one in
California. But you don't see New York.
Isn't that amazing? That you're on the moon,
and you know there's really life on Earth,
someone is blinking at you. Well, you don't see the
blinking, but you see these lights.
Very dramatic shot.
Thanks, uh, John, that's fine.
Radio waves can be generated by oscillating charges.
I will talk about that a great deal the next lecture.
So you run alternating current through wires called antennas --
this is an antenna -- and then you create electromagnetic
waves. And radio stations transmit at
a well-defined frequency. For instance,
WEEI transmits at eight hundred and fifty kiloHertz,
wavelength three hundred and fifty three meters.
Eight hundred and fifty kiloHertz is an extremely high
frequency. How come I can hear things,
that I can hear music, and that k- I hear someone
speak? Well, this signal -- we call
this the carrier wave -- is being modulated.
The strength of that signal is modulated with the frequency of
audible sound, we call that,
therefore, amplitude modulation.
So, for instance, if you looked at this signal as
a function of time, then this would be the audio
modulation of that signal. But the transmitter would
transmit eight hundred fifty kiloHertz -- here,
the signal would be a little stronger, here a little weaker,
here a little stronger - and if this were a thousand Hertz tone,
then this would be one millisecond.
At the receiving end, you tune your radio,
you change a capacitor somewhere in your radio,
you have an LRC circuit, so that you
are exactly on resonance at eight hundred fifty kiloHertz,
and you're not on resonance at eight hundred and forty
kiloHertz, so you don't hear other stations,
but you really tune in on that one station, and you can receive
this signal, then. And then you do some
demodulation to only hear the audio envelope,
and you hear speech and you hear music.
That's the idea. Right here in twenty six one
hundred, we have a transmitter, and I can transmit sound at
almost any frequency that we choose.
We have decided in honor of you, to transmit a one kiloHertz
audio signal at eight zero two kiloHertz.
The eight zero two is in honor of you.
At eight hundred and two kiloHertz, there is no radio
station, so this is a nice thing to do.
We're not interfering with anyone.
We're going to transmit it here, and then we have a radio
here, and we are going to search for that signal at eight hundred
and two kiloHertz. That's what we're going to do
first before we're going to do some other things which are not
so nice. Now, Marcos is an expert,
in order to get the frequencies right, so Marcos has promised to
help me with this, very nice.
[tone] Oh, boy, you're already on,
[laughs], we are already transmitting at eight hundred
and two kiloHertz, and the station is already
receiving it, the station meaning our radio.
[tone] Marcos, let me convince the students
that, indeed, [tone] that it -- oh,
you changed the frequency. [tone] Yeah.
[tone] So he changed the audio signal.
[tone] So I want you [tone] to appreciate that we really are
transmitting from this antenna, by unplugging it.
[tone] [static] So now the radio doesn't see the
electromagnetic waves, [tone] at eight hundred and two
kiloHertz. [tone] So the radio is
receiving now, [tone] the radio waves that we
are producing. [tone] Now, we're going to do
something that is not so nice. [tone] We're going to change
our frequency to eight hundred fifty KiloHertz.
[tone] So now what are we going to do is jamming the WEEA sport
channel. [tone] So you may hear our one
kiloHertz [tone] tone but you may not hear [tone] what they
are saying. [tone] Can we first listen to
WEEI, [tone] before we do this nasty thing?
[tone] Radio: [static] Radio:
uh, not the, you know, Larry Dominique
matchup, but he says it was not -- now what -- what was the date
of Clemens' -- This is WEEI? Radio: -- dig that up.
Do we know the date? Now be a naughty boy.
Radio: I've got all the, uh, the Celtics playoffs dates
here -- [tone] We're doing something
very illegal here. [tone] In fact,
we can do even worse. [tone] I can be on the radio.
[laughter] I'll have to turn off my microphone,
because otherwise, you wouldn't know whether it
comes from the radio, or whether it comes from my
microphone. Hello, hello?
Can you hear me? This is radio WHTL,
it's a pirate station in the Cambridge area,
we're now transmitting at eight hundred fifty kiloHertz.
Our weekly programs will be on the latest excitement in
science. Of course, we realize that this
is illegal as hell, [laughter] but that's why we
like it so much. [laughter] We start our first
program next Monday at ten AM,
and if you have any questions, feel free to contact the
Physics Department of Harvard University.
[laughter] See you next Wednesday.
[applause]