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So far, we analyzed...

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We calculated the periods
of lots of oscillators:

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pendulums, springs,
rulers, hula hoops.

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We gave them a kick,
moved them off equilibrium,

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and then they were oscillating

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at their own
preferred frequency.

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Today, I want
to discuss with you

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what happens if I force upon
a system a frequency of my own.

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So we call that
forced oscillations.

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I can take a spring system,
as we have before.

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This is x equals zero,
this is x,

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and we have the spring force,
very familiar, minus kx.

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But now this object here,
which is mass m,

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I'm going to add
a force to it, F zero,

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which is
the amplitude of the force,

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times the cosine of omega t.

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So I'm going to force it
in a sinusoidal fashion

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with a frequency that I choose.

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This frequency is not

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the frequency with which
the system wants to oscillate.

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It is the one that I choose,
and I can vary that.

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And the question, now, is
what will the object do?

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Well, we have
Newton's Second Law--

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ma equals minus kx plus that
force, F zero cosine omega t.

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a is x double dot,
so I get x double dot,

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plus-- I bring this in--

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k over m times x equals
F zero divided by m

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times the cosine omega t.

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Now, the question is

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what is the solution
to this differential equation?

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It's very different
from what we saw before,

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because before,
we had a zero here.

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Now we have here
a driving force.

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It's clear that if you wait
long enough that sooner or later

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that system will have to start
oscillating at that frequency.

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In the beginning, it may be
a little different.

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In the beginning, it may want
to do its own thing,

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but ultimately,
if I take you by your arms

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and I shake you back and forth,
in the beginning you may object,

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but sooner or later,
you will have to go

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with the frequency
that I force myself upon you.

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And when we reach that stage,
we call that the steady state

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as opposed to the beginning,

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when things are
a little bit confused,

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which we call
the transient phase.

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So in the steady state,
the object somehow must have

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a frequency which is
the same as the driver,

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and it has some amplitude A.

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And I want to evaluate with you
that amplitude A.

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So this is my trial function

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that I'm going to put
into this differential equation.

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x dot equals minus A
omega sine omega t.

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x double dot equals minus A
omega squared cosine omega t.

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And so now I'm going
to substitute that in here,

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so I'm going to get minus A
omega squared cosine omega t

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plus k over m times A
cosine omega t, and that equals

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F zero divided by m
times the cosine of omega t.

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And that must always hold.

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So therefore I can divide out
my cosine omega t.

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I can bring the A's together,

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so I get A times k over m
minus omega squared

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equals F zero divided by m.

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Now, this k over m is something
that we are familiar with.

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If we let the system do
its own thing--

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we bring it away
from equilibrium

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and we don't drive it--

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then we know that omega squared,
which I will give the zero,

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equals k over m.

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This is the frequency
that we have dealt with before.

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This is the driving frequency--
it's very different.

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And so I'm going to substitute
in here for k over m

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omega zero squared,

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and so I find, then,
that the amplitude

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of this object here at the end
of the spring will be

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F zero divided by m

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divided by omega zero squared
minus omega squared.

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And this amplitude has
very remarkable characteristics.

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First of all, if I drive the
system at a very low frequency

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so that omega is much,
much smaller than omega zero,

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we call omega zero often
the natural frequency.

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It is the one that it likes.

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If you have omega much,
much less than omega zero,

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this goes--
omega zero squared is k over m--

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so you get an amplitude A
which is F zero divided by k.

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If you go omegaway
above the natural frequency

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or, let's say,
omega goes to infinity--

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it becomes very, very large--

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then downstairs becomes very,
very large, so A goes to zero.

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But now, what happens when
omega is exactly omega zero?

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Then the system goes wacky.

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Look what happens.

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The downstairs becomes zero and
the amplitude goes to infinity.

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And that's
what we call resonance.

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So if we drive it
at that frequency,

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the system goes
completely berserk.

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I can make a plot of A
as a function of frequency.

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When I say "omega,"

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you can obviously always change
to hertz, if you prefer that,

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because omega is two pi times F,
so you can do it either in hertz

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or you can do it in radians
per second, of course.

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So if I make a plot

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of the amplitude versus
frequency omega,

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then at low values-- I have here
F zero divided by k--

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is the amplitude.

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When I hit
the resonant frequency,

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the natural frequency
of the system,

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it goes out of hand,
it goes to infinity.

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The moment that omega is
larger than omega zero,

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notice that
the amplitude becomes negative.

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A negative amplitude
simply means

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that you get all of a sudden
a phase change of 180 degrees,

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so the object is 180 degrees
out of phase with the driver.

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I will not expand on that too
much today, but it is negative,

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and so it comes up here,
and then it goes here to zero

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for very high frequencies
of omega.

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So something very spectacular
is going to happen

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at the resonant frequency
of the system.

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In practice, of course,

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the amplitude will not go
to infinity,

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and the reason for that is

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that there is always friction
of some kind.

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There is always damping, but
you get a very high amplitude

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but not infinitely high.

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So if I make you a more
realistic plot of the amplitude,

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and I will take now the
absolute value, the magnitude,

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so we don't have to worry
about it getting negative--

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we don't have to worry about
the 180-degree phase shift--

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then you would get a curve
that looks like this.

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And here, then,
if this is frequency F,

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then here you would get

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the natural frequency
when things go out of hand.

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And depending upon
how much damping there is,

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this curve would look either
very narrow and very spiky--

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it goes very, very high,

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then there is
very little damping--

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or if there is a lot
of damping in the system,

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it's more like this.

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So the narrower this...

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We call this
the resonance curve.

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The narrower that is,
the less damping there is.

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I have here a system
on the air track

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which is an object
that I can drive

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with a frequency
that I can choose.

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Here is a spring...
object mass m,

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and here is another spring.

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It's fixed on this side,
right there,

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and here I'm going to drive it,

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so I have here this variable
force that you see there.

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And what I want to show you now
is that first I will drive it

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at a frequency which is way
below the resonant frequency.

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Then you will see an amplitude,
not very large.

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I will then drive it way
above the resonant frequency.

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Again, you will see an amplitude
which is very low.

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If I can go very high frequency,

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you will see
that it almost stands still,

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and then I will try to hit
the resonant frequency,

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and that will be...

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It's about one hertz,
the resonant frequency,

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if I just let this object
do its own thing, just this.

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Now you see
the natural frequency--

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it's about one hertz--

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but now I'm going to drive it
here with a system,

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and we are going to pull
on this spring

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with a frequency
that we control.

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So let me start.

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You see here the frequency.

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You see an indicator, very low,
way lower than one hertz.

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And when you look at the way
that the system responds,

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if you wait long enough when
the transients are died out,

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you will see
that they go hand in hand,

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that the amplitude is
in phase with the driver.

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That's why we have
plus amplitude here.

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But the phase is
not so important today.

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See, they go hand in hand.

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Very small amplitude,
roughly at zero divided by k,

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which is the spring constant
of the spring.

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Now I'll go way above resonance,
and this system will slip here,

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so don't pay attention
to the arrow anymore.

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Way above resonance.

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You see, it starts to slip.

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Look at the amplitude--
very modest, very small.

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But we went over this curve,

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so first we probed it here
and now we're probing it here.

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Look, it's almost not moving
at all, almost standing still,

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and I'm driving it
at a high frequency now.

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And now I'm going to find you
this resonance,

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which is near one hertz...

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which is somewhere here.

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And look-- very high amplitude.

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If we're not careful, then we
can actually break the system.

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Very high amplitude--
I'm trying to scan over it now,

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go a little bit off resonance.

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Now I'm back on resonance.

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See what a huge amplitude!

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Better turn it off.

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So you see here the response
when I drive a system.

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When my system is
a little bit more complicated--

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for instance,
if I had two masses here

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so I would add one here,

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spring constant k,
spring constant k--

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I could repeat this experiment,

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and if I did that, I would find
two resonant frequencies.

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And if I do it
with three objects,

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I would find
three resonant frequencies.

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If I did it with five, I would
find five resonant frequencies.

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And when I make, then,

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this curve of A amplitude
as a function of frequency--

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either hertz or in radians per
second, whichever you prefer--

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then if I had three objects
there in a row,

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you would see
something like this.

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And depending upon how many
of these objects you have,

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you get more
and more resonances.

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And these resonances
can all be found

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by driving the system
and searching for them.

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If I go to a system
whereby I have

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an infinite number
of these masses...

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We call them
coupled oscillators;

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these oscillators are coupled
through the springs.

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An infinite number
of coupled oscillators

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would be a violin string.

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Here's a violin string.

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And the reason why I call it

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"infinitely" number
of oscillators

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is that I can think
of each atom or each molecule

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as being driven,

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as being connected by springs
to the neighbor.

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And so it's an infinite number
of coupled oscillators.

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And so when I start to shake
this system,

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I would expect
a lot of resonances,

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and that's what I want
to explore with you now.

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In the case here,

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that the objects move in the
same direction of the spring...

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I call this the y direction and
I call this the x direction,

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so the spring is
in the x direction,

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the objects, the beats
are in the x direction,

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and the oscillations are
in the x direction.

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We call those
longitudinal oscillations.

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There is also a way
that you can have

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transverse oscillations,
transverse...

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whereby the motion is
in the y direction,

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whereas the beats are
in the x direction.

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I could even do that
with this system--

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I could make them
oscillate like this,

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because the springs will
obviously also work

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if I do this with the system.

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And that's the way I want
this violin string

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or piano string
to oscillate now,

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because that's
the only meaningful way

259
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that I can make it oscillate.

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And so I wonder--

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if I'm going to drive it here
by shaking it up and down,

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searching for
the resonant frequencies--

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what I will be seeing.

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If I go with
very low frequencies,

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the string laughs at me,
the string does nothing.

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It's just bored,
doesn't respond to me.

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I am somewhere here
in the resonance curve.

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But then when I increase
the frequency slowly,

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I hit the very first frequency
at which it likes to oscillate.

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I call that f1.

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And when I look at the string,
and you will see that shortly,

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the string will oscillate
like so.

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It will go up here,
and it will go down here.

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And all it will do is this.

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(makes swishing sounds )

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That's its first resonance.

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And I call this n equals one,
often called the first harmonic.

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And then I go
to higher frequencies,

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and it will not do very much.

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It's very unhappy.

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And then all of a sudden,
I hit a second resonance.

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I call that f2.

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And the second resonance
will show up like this.

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This point of the string
will not move at all.

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When this part is up,
this part will be down.

286
00:15:41 --> 00:15:47
I call that s... n equals two.

287
00:15:43 --> 00:15:49
And it oscillates like so.

288
00:15:45 --> 00:15:51
(makes swishing sounds )

289
00:15:47 --> 00:15:53
And this point
which is not moving at all,

290
00:15:50 --> 00:15:56
we call that a node.

291
00:15:51 --> 00:15:57
I go a little bit
beyond that second resonance,

292
00:15:55 --> 00:16:01
and nothing happens-- the
string will be quite unhappy,

293
00:16:00 --> 00:16:06
sort of flutters a little bit

294
00:16:02 --> 00:16:08
until I hit
another resonance, f3,

295
00:16:05 --> 00:16:11
and then is the next resonance.

296
00:16:08 --> 00:16:14
I will see two nodes appear,
one here and one here,

297
00:16:15 --> 00:16:21
and the string
will oscillate like so.

298
00:16:18 --> 00:16:24
This goes up and down,
180 degrees out of phase,

299
00:16:23 --> 00:16:29
and these two ends are in phase.

300
00:16:26 --> 00:16:32
This is n equals three.

301
00:16:28 --> 00:16:34
And I can go on like that
and add nodes,

302
00:16:32 --> 00:16:38
and I will show you
some of that very shortly.

303
00:16:36 --> 00:16:42
The frequency that I generate--

304
00:16:39 --> 00:16:45
I call that f of n,
n is an integer; 

305
00:16:42 --> 00:16:48
it could be one, two, three
or four-- is linear in f1.

306
00:16:48 --> 00:16:54
In other words,
if f1 were 100 hertz,

307
00:16:52 --> 00:16:58
then f2 would be 200 hertz
and f3 would be 300 hertz.

308
00:17:02 --> 00:17:08
We call n equals one-- we call
that the first harmonic.

309
00:17:07 --> 00:17:13
Some books also call it
the fundamental.

310
00:17:10 --> 00:17:16
I will call it
the first harmonic.

311
00:17:13 --> 00:17:19
 

312
00:17:15 --> 00:17:21
And we call n equals two
the second harmonic.

313
00:17:19 --> 00:17:25
And so on-- n equals three
is the third harmonic.

314
00:17:24 --> 00:17:30
So we're going to get a series
of discrete frequencies

315
00:17:27 --> 00:17:33
which were equally spaced.

316
00:17:30 --> 00:17:36
f1 depends on the length
of the string, on the tension--

317
00:17:37 --> 00:17:43
I will write "tension"; don't 
confuse this with period--

318
00:17:41 --> 00:17:47
and it depends
on the mass of the string.

319
00:17:44 --> 00:17:50
Without going into the detail
how the dependence is,

320
00:17:46 --> 00:17:52
these are the parameters that
determine the first harmonic.

321
00:17:54 --> 00:18:00
I have here a very special
violin string or piano string,

322
00:17:59 --> 00:18:05
whatever you want to call this.

323
00:18:01 --> 00:18:07
And we can generate
these resonant frequencies

324
00:18:05 --> 00:18:11
by searching for them,

325
00:18:06 --> 00:18:12
and I would need assistance
from a student.

326
00:18:10 --> 00:18:16
Would you be willing to help me?

327
00:18:12 --> 00:18:18
So, you hold one end of
the piano string in your hand.

328
00:18:19 --> 00:18:25
Don't let it go, please,
don't let it go.

329
00:18:22 --> 00:18:28
I promise you
I won't let it go either.

330
00:18:24 --> 00:18:30
Okay, so I put
a certain tension on it,

331
00:18:27 --> 00:18:33
and I start to shake
at a very low frequency.

332
00:18:30 --> 00:18:36
Look how low, and look how happy
this string is-- nothing.

333
00:18:36 --> 00:18:42
It just laughs at me,
ignores me, it doesn't like me.

334
00:18:40 --> 00:18:46
Now I'm going to increase
the frequency.

335
00:18:43 --> 00:18:49
 

336
00:18:46 --> 00:18:52
And now I'm hitting the first
resonance-- it's coming up.

337
00:18:48 --> 00:18:54
There it is, and that's exactly

338
00:18:51 --> 00:18:57
the shape that you see
on the blackboard-- very clear.

339
00:18:55 --> 00:19:01
I shake it here.

340
00:18:56 --> 00:19:02
I have exactly
the resonance at one.

341
00:19:01 --> 00:19:07
Let me now try to hit
the second harmonic.

342
00:19:07 --> 00:19:13
If I go up a little over the f1,
then nothing much happens.

343
00:19:12 --> 00:19:18
 

344
00:19:15 --> 00:19:21
It's hard for me to see.

345
00:19:17 --> 00:19:23
Is this... is this
the second harmonic,

346
00:19:19 --> 00:19:25
or is this already the third?

347
00:19:21 --> 00:19:27
(chuckling ):
It's already the third.

348
00:19:23 --> 00:19:29
Let me see
whether I can get the second.

349
00:19:26 --> 00:19:32
 

350
00:19:30 --> 00:19:36
I think I got it now; do I?

351
00:19:33 --> 00:19:39
Okay, so here you see
the second harmonic.

352
00:19:36 --> 00:19:42
You see, indeed, that node,
that point standing still,

353
00:19:40 --> 00:19:46
and the amplitude is enormous.

354
00:19:42 --> 00:19:48
That's a characteristic
for a resonant frequency.

355
00:19:45 --> 00:19:51
We call it also
a normal mode frequency

356
00:19:48 --> 00:19:54
or a natural frequency.

357
00:19:49 --> 00:19:55
It's all the same thing.

358
00:19:51 --> 00:19:57
Let me now try to generate
one that is very high,

359
00:19:53 --> 00:19:59
as high as I possibly can,

360
00:19:55 --> 00:20:01
and you tell me
which harmonic it is.

361
00:19:57 --> 00:20:03
All you have to do is count
how many nodes there are,

362
00:20:00 --> 00:20:06
not counting my hand
and his hand,

363
00:20:03 --> 00:20:09
and you add one, and that is
the harmonic that I generate.

364
00:20:07 --> 00:20:13
 

365
00:20:11 --> 00:20:17
The system is not too happy.

366
00:20:13 --> 00:20:19
You see, you feel it sort
of when it comes... (yells ).

367
00:20:15 --> 00:20:21
No, no, no, no, no.

368
00:20:16 --> 00:20:22
See, now I'm off resonance.

369
00:20:18 --> 00:20:24
 

370
00:20:24 --> 00:20:30
It's very hard for me to hit
resonance, but I will get it.

371
00:20:27 --> 00:20:33
There it comes, there it comes,
there's no question now!

372
00:20:30 --> 00:20:36
I got it, I'm on resonance now!
Look at it!

373
00:20:32 --> 00:20:38
Clearly I'm on resonance!

374
00:20:34 --> 00:20:40
So, how many did you count?

375
00:20:36 --> 00:20:42
STUDENT:
Six.

376
00:20:37 --> 00:20:43
LEWIN:
Six harmonic?

377
00:20:39 --> 00:20:45
Looked 12 to me, but okay,
you count better than I can.

378
00:20:42 --> 00:20:48
Okay, thank you very much.

379
00:20:44 --> 00:20:50
So, you see here how
the system responds to a driver,

380
00:20:48 --> 00:20:54
and a complicated system
like a string

381
00:20:51 --> 00:20:57
has many, many
of these resonant frequencies,

382
00:20:55 --> 00:21:01
which we call the normal modes.

383
00:20:58 --> 00:21:04
Now, when you have a violin,
you have four strings.

384
00:21:03 --> 00:21:09
They all have the same length.

385
00:21:05 --> 00:21:11
There are musical instruments
like a piano,

386
00:21:07 --> 00:21:13
whereby the length is different.

387
00:21:09 --> 00:21:15
Violin-- four strings,
all the same length.

388
00:21:12 --> 00:21:18
You can set the tension so you
have something to play with.

389
00:21:16 --> 00:21:22
The tension is changed,
normally,

390
00:21:18 --> 00:21:24
when you tune the instrument
before you start playing,

391
00:21:21 --> 00:21:27
but these four strings
all have a different mass,

392
00:21:24 --> 00:21:30
and that gives them
a very different frequency.

393
00:21:27 --> 00:21:33
Now, if you play the violin,

394
00:21:29 --> 00:21:35
you cannot change the tension,
of course, during the playing.

395
00:21:31 --> 00:21:37
That would be
a little difficult,

396
00:21:33 --> 00:21:39
although there are
instruments that exist

397
00:21:35 --> 00:21:41
where actually
the playing depends

398
00:21:36 --> 00:21:42
on the tension of the string.

399
00:21:38 --> 00:21:44
With the violin, that's not
the case, so with the violin,

400
00:21:41 --> 00:21:47
the only option you have
while you are playing it

401
00:21:43 --> 00:21:49
is to make
the string length shorter,

402
00:21:45 --> 00:21:51
and you do that by moving
your finger along the string.

403
00:21:49 --> 00:21:55
By making it shorter,
the frequency goes up,

404
00:21:52 --> 00:21:58
and by making it longer,
the frequency goes down.

405
00:21:55 --> 00:22:01
Now, how do you excite
a musical instrument

406
00:21:58 --> 00:22:04
like a piano string
or a violin string?

407
00:22:03 --> 00:22:09
There is nothing
that is driving it

408
00:22:05 --> 00:22:11
exactly at
that resonant frequency,

409
00:22:07 --> 00:22:13
so if you want to get a 440
hertz out of a violin string,

410
00:22:10 --> 00:22:16
then you are not driving it
exactly at the 440 hertz,

411
00:22:14 --> 00:22:20
like we are doing.

412
00:22:15 --> 00:22:21
Well, that's true,
but if you take a bow

413
00:22:18 --> 00:22:24
and you rub the string
with a bow,

414
00:22:21 --> 00:22:27
then in a way what you're doing
is you're exposing that string

415
00:22:24 --> 00:22:30
to a lot of possible
frequencies, not just one.

416
00:22:27 --> 00:22:33
But it is a rubbing action.

417
00:22:29 --> 00:22:35
I could also rub it
with my finger,

418
00:22:31 --> 00:22:37
or I could pluck it, or I could
kick it, and what it does is

419
00:22:35 --> 00:22:41
it ignores all the frequencies
which are not at resonance,

420
00:22:38 --> 00:22:44
but it picks out the ones
which are at resonance.

421
00:22:41 --> 00:22:47
So striking it with a bow
is effectively exposing it

422
00:22:44 --> 00:22:50
to a whole large spectrum
of frequencies,

423
00:22:47 --> 00:22:53
and it picks out
the ones that it likes.

424
00:22:50 --> 00:22:56
In fact, if you strike
a violin string with a bow,

425
00:22:53 --> 00:22:59
you may excite it simultaneously

426
00:22:55 --> 00:23:01
in the first harmonic
and in the second,

427
00:22:57 --> 00:23:03
and even in the third harmonic,
or even higher harmonics.

428
00:23:00 --> 00:23:06
And that makes the difference
between the various instruments.

429
00:23:03 --> 00:23:09
That gives it
the special tone quality.

430
00:23:05 --> 00:23:11
Depends upon the cocktail,

431
00:23:08 --> 00:23:14
the combination of the various
harmonics that you excite.

432
00:23:12 --> 00:23:18
Now, if you go
to woodwind instruments,

433
00:23:16 --> 00:23:22
then the situation is
quite different.

434
00:23:21 --> 00:23:27
I have here a sound cavity.

435
00:23:23 --> 00:23:29
It's a box that has length l,
and there is air inside here.

436
00:23:28 --> 00:23:34
And I want to see

437
00:23:30 --> 00:23:36
whether this system has
resonant frequencies.

438
00:23:33 --> 00:23:39
So I put in here
a little loudspeaker

439
00:23:37 --> 00:23:43
to generate sound
with different frequencies

440
00:23:40 --> 00:23:46
and search for resonances,
and there are.

441
00:23:43 --> 00:23:49
The resonances
of this system, however,

442
00:23:47 --> 00:23:53
are different from the string
in that sense.

443
00:23:50 --> 00:23:56
It's not the box
that will resonate here,

444
00:23:52 --> 00:23:58
but it is the air itself
that starts to resonate.

445
00:23:54 --> 00:24:00
Air acts like a spring.

446
00:23:56 --> 00:24:02
In fact, in that sense,

447
00:23:58 --> 00:24:04
it is very parallel
to our spring system.

448
00:24:01 --> 00:24:07
It is also
a longitudinal oscillation,

449
00:24:03 --> 00:24:09
whereas that is
a transverse oscillation.

450
00:24:06 --> 00:24:12
So you make
pressure waves inside,

451
00:24:07 --> 00:24:13
and if you do that
at the right frequency,

452
00:24:10 --> 00:24:16
the air acts like a spring

453
00:24:12 --> 00:24:18
and then you get
strong reactions,

454
00:24:14 --> 00:24:20
which are the resonances.

455
00:24:17 --> 00:24:23
In this case, the nth mode,
the nth harmonic,

456
00:24:22 --> 00:24:28
is given by n times the velocity
of sound divided by 2L.

457
00:24:29 --> 00:24:35
And v is about 340 meters per
second at room temperature,

458
00:24:35 --> 00:24:41
so it is the sound speed.

459
00:24:39 --> 00:24:45
Notice it's again linear in n.

460
00:24:42 --> 00:24:48
In other words, if an instrument
produces a certain frequency--

461
00:24:49 --> 00:24:55
let us say that
L equals 25 centimeters--

462
00:24:54 --> 00:25:00
then you can calculate
the frequency f1.

463
00:24:57 --> 00:25:03
You know what the speed
of sound is, 340,

464
00:25:00 --> 00:25:06
so we take n equals one,

465
00:25:02 --> 00:25:08
so the frequency
that we would get

466
00:25:05 --> 00:25:11
equals 340 divided by 2L,
which is 0.5 in meters,

467
00:25:11 --> 00:25:17
and so that gives me 680 hertz.

468
00:25:15 --> 00:25:21
So that would be this big,
it would give you 680 hertz,

469
00:25:19 --> 00:25:25
but the second harmonic, f2,
will be double that.

470
00:25:24 --> 00:25:30
So it will be 1,360 hertz,
and so on.

471
00:25:28 --> 00:25:34
 

472
00:25:30 --> 00:25:36
Now, this system which
is closed on both sides

473
00:25:33 --> 00:25:39
wouldn't be
a very good musical instrument

474
00:25:35 --> 00:25:41
because your sound
would not come out.

475
00:25:38 --> 00:25:44
So what people do,
they make them open,

476
00:25:40 --> 00:25:46
a sound cavity which is
just open on both sides.

477
00:25:44 --> 00:25:50
Like this, for instance--
this is open on both sides.

478
00:25:50 --> 00:25:56
And even though
it may surprise you,

479
00:25:52 --> 00:25:58
if we put a little
loudspeaker here,

480
00:25:54 --> 00:26:00
we can excite the air column,
even in this open system,

481
00:25:58 --> 00:26:04
in a complete similar way

482
00:26:00 --> 00:26:06
than we do it here
in this closed system,

483
00:26:02 --> 00:26:08
and we get exactly
the same series of frequencies

484
00:26:05 --> 00:26:11
that I put here
on the blackboard.

485
00:26:08 --> 00:26:14
There are also
musical instruments

486
00:26:10 --> 00:26:16
which are open on one side
and closed on the other.

487
00:26:13 --> 00:26:19
So this is called
an open-open system,

488
00:26:18 --> 00:26:24
and this would be called
a closed-open.

489
00:26:20 --> 00:26:26
A clarinet is closed-open.

490
00:26:23 --> 00:26:29
Here I can also get a series
of resonant frequencies,

491
00:26:26 --> 00:26:32
even though here, the series
wouldn't be exactly like this; 

492
00:26:30 --> 00:26:36
it's a little different.

493
00:26:31 --> 00:26:37
It doesn't matter now
how different,

494
00:26:32 --> 00:26:38
but it is a little different.

495
00:26:35 --> 00:26:41
But you get, again, a whole
series of resonant frequencies.

496
00:26:39 --> 00:26:45
So, again, you see that
if I make the system longer,

497
00:26:43 --> 00:26:49
then I get lower frequencies.

498
00:26:46 --> 00:26:52
So if I make the length
one meter, yay big,

499
00:26:51 --> 00:26:57
then I would get a frequency f1,

500
00:26:54 --> 00:27:00
which is about four times lower
than the one that I have there,

501
00:26:57 --> 00:27:03
which is 170 hertz.

502
00:26:59 --> 00:27:05
 

503
00:27:02 --> 00:27:08
And if the second harmonic were,
then, 340 hertz, and so on...

504
00:27:08 --> 00:27:14
So when you see an organ
in a church,

505
00:27:10 --> 00:27:16
you see all these organ pipes,
different lengths.

506
00:27:13 --> 00:27:19
The long ones have
the very low tones,

507
00:27:15 --> 00:27:21
and the short ones have
the very high tones.

508
00:27:17 --> 00:27:23
And that is the way
that these instruments work.

509
00:27:22 --> 00:27:28
I have here a wind organ which I
have demonstrated to you before.

510
00:27:28 --> 00:27:34
It is open on both sides,

511
00:27:30 --> 00:27:36
and because it is corrugated
in a very special way,

512
00:27:33 --> 00:27:39
when I blow wind past this,
it will go into resonance.

513
00:27:37 --> 00:27:43
That's to say,

514
00:27:39 --> 00:27:45
wind here is like a spectrum
of all possible frequencies.

515
00:27:43 --> 00:27:49
It's like the bow on the violin.

516
00:27:45 --> 00:27:51
And then it picks out
the frequencies that it likes.

517
00:27:49 --> 00:27:55
However, if I increase
the speed of the wind,

518
00:27:52 --> 00:27:58
I can try to force it
into higher frequencies.

519
00:27:56 --> 00:28:02
So at low wind speeds,

520
00:27:57 --> 00:28:03
I am more likely to hit
the lower harmonics.

521
00:28:00 --> 00:28:06
At high wind speeds,

522
00:28:02 --> 00:28:08
I am more likely to hit
the higher harmonics.

523
00:28:05 --> 00:28:11
This one is 75 centimeters long,
it's open-open; 

524
00:28:08 --> 00:28:14
and if I were able to hit
the first harmonic,

525
00:28:12 --> 00:28:18
that would be a frequency
of about 240 hertz.

526
00:28:17 --> 00:28:23
I may not be able to excite

527
00:28:19 --> 00:28:25
the lowest harmonic, the
first harmonic, but I'll try.

528
00:28:22 --> 00:28:28
But certainly

529
00:28:23 --> 00:28:29
the higher harmonics
are very easy to excite,

530
00:28:26 --> 00:28:32
and I can make you
even listen simultaneously

531
00:28:28 --> 00:28:34
to more than one frequency,

532
00:28:30 --> 00:28:36
just like the violin string,
when you strike it,

533
00:28:33 --> 00:28:39
can simultaneously oscillate
in a combination of these modes.

534
00:28:38 --> 00:28:44
So let me swirl this around.

535
00:28:40 --> 00:28:46
I'll first start low.

536
00:28:41 --> 00:28:47
(tube hums medium tone )

537
00:28:45 --> 00:28:51
This may be 240.

538
00:28:48 --> 00:28:54
(tube hums higher tone )

539
00:28:49 --> 00:28:55
This is definitely way higher.

540
00:28:52 --> 00:28:58
(tube hums even higher )

541
00:28:54 --> 00:29:00
(tube hums higher,
then starts going back down )

542
00:28:59 --> 00:29:05
(tube returns to first tone )

543
00:29:01 --> 00:29:07
I think this is the 240.

544
00:29:03 --> 00:29:09
This is the lowest,
this is the first harmonic.

545
00:29:06 --> 00:29:12
Were there times that
you heard two simultaneously?

546
00:29:10 --> 00:29:16
(tube hums two tones )

547
00:29:13 --> 00:29:19
I hear two.

548
00:29:15 --> 00:29:21
(tube hums two tones )

549
00:29:16 --> 00:29:22
 

550
00:29:18 --> 00:29:24
If you play a flute,
that... you do the following:

551
00:29:22 --> 00:29:28
You make holes in here,

552
00:29:24 --> 00:29:30
and when you take
your fingers off both holes,

553
00:29:28 --> 00:29:34
then the effective length
of the flute is this long

554
00:29:32 --> 00:29:38
and you get a high tone.

555
00:29:33 --> 00:29:39
If you put your finger
on this one,

556
00:29:36 --> 00:29:42
then the effective length
of the flute is this long

557
00:29:39 --> 00:29:45
and you get a lower tone.

558
00:29:40 --> 00:29:46
When you put your finger
on both,

559
00:29:42 --> 00:29:48
the effective length
of the flute is this long

560
00:29:45 --> 00:29:51
and you get an even lower tone.

561
00:29:47 --> 00:29:53
I have here a very special
flute, open on both sides,

562
00:29:51 --> 00:29:57
and here you see the two holes.

563
00:29:53 --> 00:29:59
We will first close the two.

564
00:29:55 --> 00:30:01
That gives us
the lowest frequency...

565
00:29:57 --> 00:30:03
(plays low tone,
then up and down triad )

566
00:30:06 --> 00:30:12
(plays short tune
on low tones )

567
00:30:12 --> 00:30:18
...that you play the flute.

568
00:30:14 --> 00:30:20
So it's simply a matter
of making the instrument

569
00:30:17 --> 00:30:23
longer or shorter.

570
00:30:18 --> 00:30:24
I have another example
here of an instrument

571
00:30:22 --> 00:30:28
which is open here
and here is closed.

572
00:30:26 --> 00:30:32
This is my version
of a trombone.

573
00:30:29 --> 00:30:35
There's a piston here.

574
00:30:31 --> 00:30:37
So this is a system
that is like this,

575
00:30:34 --> 00:30:40
but I can move this in and out,

576
00:30:36 --> 00:30:42
and so when I have it far in,
the frequency would be high...

577
00:30:41 --> 00:30:47
(plays high tone )

578
00:30:44 --> 00:30:50
and when I have it here...

579
00:30:45 --> 00:30:51
(plays low tone )

580
00:30:48 --> 00:30:54
(tones gradually get higher )

581
00:30:57 --> 00:31:03
So you see,
it's directly related

582
00:30:59 --> 00:31:05
to the length of this trombone.

583
00:31:01 --> 00:31:07
And if you learn how to play,
you can try to play a tune.

584
00:31:05 --> 00:31:11
I'll try.

585
00:31:07 --> 00:31:13
(plays "Jingle Bells" )

586
00:31:17 --> 00:31:23
(class laughs quietly )

587
00:31:19 --> 00:31:25
(tune continues )

588
00:31:25 --> 00:31:31
(tune ends )

589
00:31:26 --> 00:31:32
(class applauds )

590
00:31:32 --> 00:31:38
LEWIN:
Thank you.

591
00:31:34 --> 00:31:40
Resonances are all around us.

592
00:31:37 --> 00:31:43
When you drive your car,
you may have noticed

593
00:31:40 --> 00:31:46
that all of a sudden, you hear
some crazy rattle somewhere.

594
00:31:43 --> 00:31:49
It could be your mirror,
or it could be something else,

595
00:31:45 --> 00:31:51
it could be an ashtray,

596
00:31:47 --> 00:31:53
because you are driving it,
and you are exciting it

597
00:31:48 --> 00:31:54
with the frequency
with which the wheels go around

598
00:31:50 --> 00:31:56
and you may hit
a resonant frequency.

599
00:31:52 --> 00:31:58
You go a little slower
and the rattle stops,

600
00:31:54 --> 00:32:00
but something else
may start to rattle.

601
00:31:56 --> 00:32:02
The reason
why the first rattle stopped,

602
00:31:59 --> 00:32:05
because you go off resonance,

603
00:32:00 --> 00:32:06
but you may go on resonance
of another object.

604
00:32:03 --> 00:32:09
All objects that you have
in your room

605
00:32:06 --> 00:32:12
have preferred
resonant frequencies.

606
00:32:08 --> 00:32:14
Whether they are
the pots or the pans

607
00:32:09 --> 00:32:15
or whether it is
your refrigerator,

608
00:32:11 --> 00:32:17
or anything you can think of,

609
00:32:12 --> 00:32:18
everything has
resonant frequencies.

610
00:32:14 --> 00:32:20
Your body has
resonant frequencies.

611
00:32:16 --> 00:32:22
If I took you in my hands
and I would start to shake you,

612
00:32:19 --> 00:32:25
then if I do it
at low frequency,

613
00:32:21 --> 00:32:27
not much would happen,
but there would be one frequency

614
00:32:24 --> 00:32:30
that your arms begin
to move like this,

615
00:32:26 --> 00:32:32
like they're
physical pendulums, right?

616
00:32:28 --> 00:32:34
And if I hit that frequency,

617
00:32:29 --> 00:32:35
then indeed there would be
a strong response,

618
00:32:32 --> 00:32:38
and so your body has
many resonant frequencies:

619
00:32:34 --> 00:32:40
your arms, your legs,
your head, everything.

620
00:32:38 --> 00:32:44
We also experience, all of us,
emotional resonances--

621
00:32:43 --> 00:32:49
a small input, a huge output.

622
00:32:45 --> 00:32:51
Falling in love is
an emotional resonance.

623
00:32:50 --> 00:32:56
If someone touches a sensitive
nerve, that is a resonance.

624
00:32:55 --> 00:33:01
Someone could say
something to you

625
00:32:58 --> 00:33:04
and it could be
a very sensitive issue for you,

626
00:33:02 --> 00:33:08
and you go nonlinear!

627
00:33:03 --> 00:33:09
Your response is
unbelievably strong!

628
00:33:06 --> 00:33:12
That, in my view,

629
00:33:07 --> 00:33:13
is also a form
of an emotional resonance.

630
00:33:13 --> 00:33:19
I have here two tuning forks.

631
00:33:15 --> 00:33:21
And these tuning forks
are designed in such a way

632
00:33:18 --> 00:33:24
that all I would have to do
is just bang them

633
00:33:21 --> 00:33:27
and they will pick out
their own resonant frequencies.

634
00:33:25 --> 00:33:31
The tuning fork is
very simple, like this.

635
00:33:30 --> 00:33:36
I give it a kick, and the kick

636
00:33:32 --> 00:33:38
is like dumping a whole spectrum
of frequencies on it,

637
00:33:35 --> 00:33:41
and it picks out the ones that
it likes, which is this one,

638
00:33:38 --> 00:33:44
and that's the one
at which it will resonate.

639
00:33:40 --> 00:33:46
It's possible that I can excite
it at higher frequencies,

640
00:33:43 --> 00:33:49
at higher harmonics,

641
00:33:44 --> 00:33:50
but that's a little hard,
even, with a tuning fork.

642
00:33:47 --> 00:33:53
So this one is 256 hertz.

643
00:33:49 --> 00:33:55
(plays low tone )

644
00:33:55 --> 00:34:01
So the prongs move
256 times per second,

645
00:33:58 --> 00:34:04
and this one is 440 hertz.

646
00:34:00 --> 00:34:06
(plays higher tone )

647
00:34:02 --> 00:34:08
And you hear no overtones--
you don't hear higher harmonics.

648
00:34:05 --> 00:34:11
 

649
00:34:08 --> 00:34:14
If I take something as simple
as a wineglass like this,

650
00:34:11 --> 00:34:17
it has many, many
normal-mode frequencies,

651
00:34:14 --> 00:34:20
many resonant frequencies.

652
00:34:15 --> 00:34:21
The lowest one is
very easy to excite,

653
00:34:17 --> 00:34:23
and I will do that.

654
00:34:19 --> 00:34:25
I will rub it with my finger.

655
00:34:20 --> 00:34:26
Rubbing is like striking
a string with a bow.

656
00:34:23 --> 00:34:29
It's all the same-- I expose it
to lots of frequencies,

657
00:34:26 --> 00:34:32
it ignores them all, it picks
out the one that it likes,

658
00:34:29 --> 00:34:35
the resonant frequency,

659
00:34:30 --> 00:34:36
the normal mode,
the natural frequency.

660
00:34:32 --> 00:34:38
And what the glass will do,

661
00:34:34 --> 00:34:40
in its lowest harmonic--
in its first harmonic--

662
00:34:37 --> 00:34:43
it will sort of oscillate,
like this,

663
00:34:39 --> 00:34:45
and I will show that to you
later in this lecture

664
00:34:42 --> 00:34:48
in slow motion.

665
00:34:44 --> 00:34:50
But let me first make you
listen to the frequency.

666
00:34:47 --> 00:34:53
It's around 430... 470 hertz.

667
00:34:48 --> 00:34:54
I have to wash my hands because
I have chalk on my fingers

668
00:34:52 --> 00:34:58
and because of the chalk,
I will not be able to excite it.

669
00:34:55 --> 00:35:01
I have to really rub it
with some liquid,

670
00:34:58 --> 00:35:04
and therefore
my hands have to be chalk-free.

671
00:35:01 --> 00:35:07
Chalk is just too greasy--
let me try.

672
00:35:05 --> 00:35:11
(plays high tone )

673
00:35:12 --> 00:35:18
Very clear.

674
00:35:14 --> 00:35:20
I remember when I was a student,
we had after-dinner speakers.

675
00:35:18 --> 00:35:24
If we got bored,
we would all do this.

676
00:35:20 --> 00:35:26
Let me tell you,
that makes a lot of noise.

677
00:35:23 --> 00:35:29
 

678
00:35:26 --> 00:35:32
So, again, I'm not exciting it
with the 470 hertz.

679
00:35:28 --> 00:35:34
I'm dumping
the whole frequency...

680
00:35:30 --> 00:35:36
the whole spectrum
of frequencies on it,

681
00:35:33 --> 00:35:39
and it picks out
the one that it likes,

682
00:35:35 --> 00:35:41
which, in this case,
is the 470 hertz.

683
00:35:38 --> 00:35:44
Resonances can be destructive,

684
00:35:40 --> 00:35:46
and rumor has it
that there are singers,

685
00:35:44 --> 00:35:50
women who take a wineglass
and they do exactly what I did.

686
00:35:48 --> 00:35:54
They do this.

687
00:35:50 --> 00:35:56
(plays high tone )

688
00:35:51 --> 00:35:57
They listen carefully,

689
00:35:52 --> 00:35:58
they generate that frequency
with their voice,

690
00:35:55 --> 00:36:01
they increase the
volume of the voice,

691
00:35:57 --> 00:36:03
and then the rumor has it
that bang, the glass goes.

692
00:36:00 --> 00:36:06
In other words, the amplitude
of the glass becomes so large

693
00:36:04 --> 00:36:10
that you get so high
so close to resonance

694
00:36:06 --> 00:36:12
and so much power goes into it

695
00:36:08 --> 00:36:14
because of the volume
of the voice

696
00:36:10 --> 00:36:16
that the glass breaks.

697
00:36:12 --> 00:36:18
I'm going to try to break
a glass with you,

698
00:36:15 --> 00:36:21
and you'll see
that it is not easy.

699
00:36:17 --> 00:36:23
I have here a wineglass.

700
00:36:21 --> 00:36:27
It's almost the same
as the one I have there.

701
00:36:24 --> 00:36:30
And we can illuminate
that glass with a strobe light,

702
00:36:27 --> 00:36:33
which you see here.

703
00:36:29 --> 00:36:35
And I'm going to show you there

704
00:36:31 --> 00:36:37
the display
of that strobe light.

705
00:36:33 --> 00:36:39
And the reason why we strobe it
is that we want you to see,

706
00:36:37 --> 00:36:43
as we excite the exact
frequency of the glass,

707
00:36:40 --> 00:36:46
we want you to see
the motion of the glass.

708
00:36:42 --> 00:36:48
And the way we can make you see
the motion is by strobing it

709
00:36:46 --> 00:36:52
not exactly at the frequency
of the sound

710
00:36:48 --> 00:36:54
but a little bit
different frequency.

711
00:36:50 --> 00:36:56
So you will see
the stroboscopic motion, then,

712
00:36:54 --> 00:37:00
of the glass.

713
00:36:56 --> 00:37:02
So I can... already
I will make it darker shortly,

714
00:36:59 --> 00:37:05
but I want you to see
at least most of this.

715
00:37:02 --> 00:37:08
I can generate, then,
the 470 hertz,

716
00:37:04 --> 00:37:10
which is very close
to the resonant frequency.

717
00:37:07 --> 00:37:13
(plays high tone )

718
00:37:09 --> 00:37:15
This is the tone
that we will use.

719
00:37:11 --> 00:37:17
We will increase the volume,

720
00:37:12 --> 00:37:18
and then we will try to hit
that resonance just right.

721
00:37:15 --> 00:37:21
We may be off by a few hertz.

722
00:37:17 --> 00:37:23
We have to be right on
within a hertz,

723
00:37:19 --> 00:37:25
and then we'll see whether
we can make the glass break.

724
00:37:22 --> 00:37:28
Now, I want to warn you,

725
00:37:23 --> 00:37:29
the sound is going
to be very strong,

726
00:37:26 --> 00:37:32
so you may... as the time goes
on, as we go to higher volume,

727
00:37:29 --> 00:37:35
you may want to turn, you
may want to close your ears.

728
00:37:32 --> 00:37:38
In fact, I will use this
to protect my ears,

729
00:37:35 --> 00:37:41
and I will even use this
to protect my eyes

730
00:37:38 --> 00:37:44
in case the glass might break,

731
00:37:39 --> 00:37:45
which I doubt whether it will,
but who knows?

732
00:37:42 --> 00:37:48
 

733
00:37:46 --> 00:37:52
All right,
so let's make it very dark.

734
00:37:48 --> 00:37:54
 

735
00:37:54 --> 00:38:00
(tone continues )

736
00:37:56 --> 00:38:02
 

737
00:37:58 --> 00:38:04
So, you see here the glass.

738
00:38:00 --> 00:38:06
It's not doing very much.

739
00:38:02 --> 00:38:08
And I'm now going to increase
the volume of the sound.

740
00:38:06 --> 00:38:12
(high tone gets louder )

741
00:38:12 --> 00:38:18
I'm going to cover my ears now.

742
00:38:15 --> 00:38:21
We already begin
to see some motion.

743
00:38:18 --> 00:38:24
 

744
00:38:22 --> 00:38:28
I'm not sure
that I am on resonance.

745
00:38:25 --> 00:38:31
(high tone continues,
becomes louder )

746
00:38:36 --> 00:38:42
We increase the volume.

747
00:38:38 --> 00:38:44
(high tone continues, louder )

748
00:38:41 --> 00:38:47
 

749
00:38:54 --> 00:39:00
(tone continues )

750
00:38:57 --> 00:39:03
 

751
00:39:11 --> 00:39:17
(tone continues )

752
00:39:13 --> 00:39:19
 

753
00:39:27 --> 00:39:33
I'm now changing the frequency.

754
00:39:29 --> 00:39:35
(similar tone playing )

755
00:39:31 --> 00:39:37
 

756
00:39:45 --> 00:39:51
Getting very close.

757
00:39:46 --> 00:39:52
 

758
00:39:59 --> 00:40:05
(tone continues,
getting slightly louder )

759
00:40:05 --> 00:40:11
Gettingvery close.

760
00:40:08 --> 00:40:14
(shatters loudly )

761
00:40:09 --> 00:40:15
(tone continues )

762
00:40:13 --> 00:40:19
(tone fades away )

763
00:40:15 --> 00:40:21
(lower tone plays
as slow-motion replay begins )

764
00:40:18 --> 00:40:24
(shatters slowly )

765
00:40:21 --> 00:40:27
 

766
00:40:27 --> 00:40:33
I mentioned that resonances
can be very destructive,

767
00:40:30 --> 00:40:36
and there are some striking
examples in history.

768
00:40:33 --> 00:40:39
In fact, you may have...

769
00:40:34 --> 00:40:40
When there's a storm, you may
have seen the traffic signs,

770
00:40:37 --> 00:40:43
which... just a sign on a pole,

771
00:40:40 --> 00:40:46
that the traffic sign
starts doing this.

772
00:40:42 --> 00:40:48
This is strange,
because there's a wind.

773
00:40:45 --> 00:40:51
Wind is like a spectrum
of all kinds of frequencies.

774
00:40:48 --> 00:40:54
It's like blowing air
into a musical instrument.

775
00:40:50 --> 00:40:56
And then this traffic sign
just picks out

776
00:40:53 --> 00:40:59
the frequency that it likes,
and then,

777
00:40:55 --> 00:41:01
if the wind is strong enough,
it could be very destructive.

778
00:40:59 --> 00:41:05
And the most striking example
of destruction

779
00:41:02 --> 00:41:08
is that of a bridge
which was built.

780
00:41:04 --> 00:41:10
And that is the Tacoma Bridge,
on the West Coast,

781
00:41:07 --> 00:41:13
which is very dramatic,

782
00:41:08 --> 00:41:14
and, of course, I will have
to show you that movie.

783
00:41:11 --> 00:41:17
You will see what
the wind can do to a bridge.

784
00:41:15 --> 00:41:21
 

785
00:41:19 --> 00:41:25
So we'll start this movie,
and then we'll make it dark.

786
00:41:22 --> 00:41:28
 

787
00:41:28 --> 00:41:34
FILM ANNOUNCER:
On the first of July, 1940,

788
00:41:32 --> 00:41:38
a delegation of citizens met
in Washington State.

789
00:41:37 --> 00:41:43
The weather was beautiful,
the occasion historic,

790
00:41:42 --> 00:41:48
and the speechmaking and fanfare
altogether appropriate.

791
00:41:47 --> 00:41:53
This was the grand opening
of the Tacoma Narrows Bridge.

792
00:41:52 --> 00:41:58
From the beginning, the bridge,

793
00:41:55 --> 00:42:01
which spanned Puget Sound
between Seattle and Tacoma,

794
00:41:59 --> 00:42:05
was traveled in style,
as well it should have been.

795
00:42:04 --> 00:42:10
The Tacoma Narrows Bridge

796
00:42:06 --> 00:42:12
was one of the longer
suspension bridges on earth.

797
00:42:10 --> 00:42:16
And if somebody hadn't
overlooked something,

798
00:42:13 --> 00:42:19
it probably would have remained

799
00:42:16 --> 00:42:22
one of the longer
suspension bridges on earth.

800
00:42:20 --> 00:42:26
The problem wasn't that
right from the beginning,

801
00:42:22 --> 00:42:28
a lot of people didn't pay
a lot of attention

802
00:42:25 --> 00:42:31
to details-- they did.

803
00:42:29 --> 00:42:35
But somewhere along the line,
and this was obvious in the end,

804
00:42:36 --> 00:42:42
it looks as if someone forgot
the significance of resonance.

805
00:42:43 --> 00:42:49
(low rumbling as wind blows )

806
00:42:46 --> 00:42:52
 

807
00:42:49 --> 00:42:55
Among other things,
the Tacoma Narrows Bridge

808
00:42:52 --> 00:42:58
was the most spectacular
Aeolian harp in history.

809
00:42:56 --> 00:43:02
Unfortunately,
its first performance

810
00:42:59 --> 00:43:05
was destined to run
only about four months.

811
00:43:03 --> 00:43:09
(sirens wailing )

812
00:43:04 --> 00:43:10
In the meantime, she was
a beautiful bridge...

813
00:43:09 --> 00:43:15
beautiful, but a little strange.

814
00:43:13 --> 00:43:19
Even before construction
was completed,

815
00:43:16 --> 00:43:22
people observed
its peculiar behavior.

816
00:43:20 --> 00:43:26
That was because
even in a light breeze,

817
00:43:23 --> 00:43:29
ripples ran along the bridge.

818
00:43:26 --> 00:43:32
After a while,

819
00:43:27 --> 00:43:33
one of the local humorists
called her "Galloping Gertie."

820
00:43:32 --> 00:43:38
And for fairly obvious reasons,
the name stuck,

821
00:43:35 --> 00:43:41
at least until
the seventh of November, 1940.

822
00:43:39 --> 00:43:45
 

823
00:43:41 --> 00:43:47
Then as now, Seattle and Tacoma
were sports-minded cities.

824
00:43:47 --> 00:43:53
For four months,
a regional sport

825
00:43:50 --> 00:43:56
was to drive across
the bridge on a windy day.

826
00:43:54 --> 00:44:00
While some claimed it was
like riding a roller coaster,

827
00:43:57 --> 00:44:03
others found it
a little disconcerting

828
00:43:59 --> 00:44:05
to see the car
in front disappear.

829
00:44:02 --> 00:44:08
 

830
00:44:04 --> 00:44:10
How popular
this bridge sport was,

831
00:44:06 --> 00:44:12
or to what extent it might have
spread across the country,

832
00:44:09 --> 00:44:15
is anybody's guess.

833
00:44:11 --> 00:44:17
On November 7, 1940, the winds
were relatively moderate,

834
00:44:17 --> 00:44:23
about 40 miles per hour.

835
00:44:19 --> 00:44:25
 

836
00:44:21 --> 00:44:27
A new mode appeared.

837
00:44:23 --> 00:44:29
Rather than ripple,
the bridge began to twist.

838
00:44:27 --> 00:44:33
(wind blowing )

839
00:44:31 --> 00:44:37
A wind of 40 miles per hour
is not too strong,

840
00:44:34 --> 00:44:40
but it was strong enough

841
00:44:36 --> 00:44:42
to start the bridge
twisting violently.

842
00:44:39 --> 00:44:45
 

843
00:44:42 --> 00:44:48
And at 11:00 a.m., it fell.

844
00:44:45 --> 00:44:51
(low roaring )

845
00:44:50 --> 00:44:56
(loud crashing )

846
00:44:52 --> 00:44:58
(rumbling as wind blows )

847
00:44:57 --> 00:45:03
(rumbling continues )

848
00:45:03 --> 00:45:09
LEWIN:
Amazing-- amazing
what resonance can do.

849
00:45:07 --> 00:45:13
 

850
00:45:10 --> 00:45:16
With musical instruments,
we have...

851
00:45:13 --> 00:45:19
we're stuck to the speed
of sound in air,

852
00:45:17 --> 00:45:23
which is 340 meters per second.

853
00:45:20 --> 00:45:26
And when I speak to you,
I have here a sound cavity

854
00:45:24 --> 00:45:30
which has a certain size,
a certain shape.

855
00:45:27 --> 00:45:33
And while I speak, this size and
this shape changes all the time.

856
00:45:33 --> 00:45:39
And that gives my voice
a very characteristic sound

857
00:45:37 --> 00:45:43
that makes it possible for me
to make a low sound.

858
00:45:40 --> 00:45:46
It makes it possible for me
to make a high sound.

859
00:45:42 --> 00:45:48
And no matter how I speak,

860
00:45:43 --> 00:45:49
you will say,
"Yeah, there's no question.
 

861
00:45:45 --> 00:45:51
That's Walter Lewin--
that's clear."

862
00:45:48 --> 00:45:54
It's very recognizable.

863
00:45:49 --> 00:45:55
Each one of you and I have
a very well recognizable voice.

864
00:45:53 --> 00:45:59
The situation would change

865
00:45:55 --> 00:46:01
if I could change the speed
of sound in my system.

866
00:46:01 --> 00:46:07
And helium, which has

867
00:46:04 --> 00:46:10
a very different
molecular weight from air,

868
00:46:07 --> 00:46:13
has a way higher speed
than the speed of sound in air.

869
00:46:11 --> 00:46:17
It's about 2.7 times higher,
2.7 times 340 meters per second.

870
00:46:19 --> 00:46:25
 

871
00:46:21 --> 00:46:27
So if I fill my system
with helium--

872
00:46:24 --> 00:46:30
apart from the fact that
there's no oxygen in helium,

873
00:46:27 --> 00:46:33
so I wouldn't survive very long;
that's a detail...

874
00:46:30 --> 00:46:36
(class laughs )

875
00:46:31 --> 00:46:37
LEWIN:
If I fill my system with helium,

876
00:46:34 --> 00:46:40
then, of course, my vocal cords
and my sound cavity here,

877
00:46:39 --> 00:46:45
they don't know that.

878
00:46:40 --> 00:46:46
So they do the same thing

879
00:46:42 --> 00:46:48
that they normally do
when they speak to you.

880
00:46:45 --> 00:46:51
However, since the speed
of sound is much higher

881
00:46:47 --> 00:46:53
here in my sound cavity,

882
00:46:49 --> 00:46:55
the frequency that it
will produce is way higher,

883
00:46:53 --> 00:46:59
and I sound very differently.

884
00:46:55 --> 00:47:01
The problem, however,
is, as I mentioned,

885
00:46:57 --> 00:47:03
there is no oxygen in helium,

886
00:46:59 --> 00:47:05
and yet if I only take
a little bit of helium,

887
00:47:02 --> 00:47:08
it doesn't work very well and
you don't hear much difference,

888
00:47:05 --> 00:47:11
so I have to really take a lot
of helium, and I will try that.

889
00:47:09 --> 00:47:15
But for that I pay
a small price,

890
00:47:11 --> 00:47:17
and the small price
is that you can faint.

891
00:47:14 --> 00:47:20
I'll try just to stay away
from the fainting level.

892
00:47:18 --> 00:47:24
So, here is helium, and I have
to let my air out first

893
00:47:22 --> 00:47:28
and then get helium in and maybe
let the helium out again

894
00:47:25 --> 00:47:31
and let the helium in again.

895
00:47:26 --> 00:47:32
And during that time
I can't speak,

896
00:47:28 --> 00:47:34
but then, when I think
I'm full enough with helium,

897
00:47:31 --> 00:47:37
I will say a few words to you.

898
00:47:35 --> 00:47:41
So, let's get the pressure up
to the level that I like.

899
00:47:40 --> 00:47:46
(exhaling )

900
00:47:41 --> 00:47:47
(helium hissing from hose )

901
00:47:43 --> 00:47:49
(inhales )

902
00:47:46 --> 00:47:52
(helium hissing again )

903
00:47:48 --> 00:47:54
(inhales again )

904
00:47:50 --> 00:47:56
(in very high voice ):
I told you it would sound
very differently.

905
00:47:52 --> 00:47:58
(class laughs and applauds )

906
00:47:54 --> 00:48:00
LEWIN:
Well, I hope you enjoyed this,
and I'll see you Wednesday.

907
00:47:55 --> 00:48:01
Thank you.

908
00:47:57 --> 00:48:03
(class laughs )

909
00:47:58 --> 00:48:04