The Auditory System

Name: 2: Frequency Selectivity and Nonlinearity in Hearing
Uploaded: 2026-03-30T14:51:54.343962+00:00
Duration: 1 h 17 min 23 s
Channel: MIT OpenCourseWare
Description: Summary and key takeaways on 2: Frequency Selectivity and Nonlinearity in Hearing — Summary, covering The Auditory System The ear separates into three

MIT OpenCourseWare

Mar 30, 2026

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77 min video

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The ear separates into three functional regions. The outer ear—pinna and eardrum—collects sound and directs it to the middle ear, where the ossicles match acoustic impedance and protect the inner ear from overload. The inner ear houses the cochlea, which performs frequency analysis. Approximately 3,500 inner hair cells and 12,000 outer hair cells occupy the organ of Corti in a 3:1 ratio. Outer hair cells act as reverse transducers, changing shape in response to electrical signals and providing level‑dependent amplification. About 30,000 auditory nerve fibers leave each ear, a number that contrasts with the visual system, where far fewer optic nerve fibers serve many photoreceptors.

Frequency Selectivity & Masking

Each auditory nerve fiber possesses a characteristic frequency, the tone that elicits the lowest threshold response. When two tones are presented together, they produce a beating sensation at the frequency difference; if the tones fall within the same cochlear filter bandwidth, listeners perceive roughness. Masking occurs when a second sound raises the audibility threshold of a target tone. By measuring how masking thresholds change with the bandwidth of a masking noise, researchers infer the shape of cochlear filters. The “critical band” marks the bandwidth beyond which further widening the noise no longer increases the masking threshold. Fletcher’s band‑widening method first identified this phenomenon in the 1940s. Modern studies favor the notched‑noise method because it better characterizes filter skirts and reduces off‑frequency listening.

Nonlinearity & Distortion

The cochlea amplifies low‑level sounds more than high‑level sounds, a property supplied mainly by outer hair cells. Consequently, tuning is narrow at soft intensities and broadens as level increases. The basilar membrane exhibits a compressive response function: its motion grows less than proportionally with rising sound pressure. This nonlinearity generates distortion products that are not present in the original stimulus. A classic example is the cubic distortion product 2f₁ – f₂, which can be measured as a physical vibration on the basilar membrane.

Hearing Loss

Presbycusis, the age‑related loss of hearing, typically appears as elevated thresholds at high frequencies. Postmortem otopathology shows that hair cell loss concentrates at the basal (high‑frequency) region of the cochlea. Comparative studies of industrialized versus non‑industrialized societies—such as the 1962 Mabaans survey and the 1954 Wisconsin State Fair investigation—suggest that environmental noise contributes substantially to hearing degradation. Acute noise exposure, for example from hunting, can produce localized damage to the organ of Corti. Audiograms distinguish conductive loss, which affects the outer or middle ear, from sensory or neural loss that reflects inner‑ear pathology.

“The outer hair cells are like the inner hair cells in reverse.”
“The cochlea can be thought of as a bank of bandpass filters.”
“Masking is determined by frequency selectivity.”
“The ear is a nonlinear system.”
“If there’s one thing that you take away from this class, wear earplugs.”

Takeaways

The cochlea functions as a bank of bandpass filters, with each auditory nerve fiber tuned to a characteristic frequency.
Masking experiments, especially the notched‑noise method, reveal the shape and bandwidth of cochlear filters through critical band analysis.
Outer hair cells provide level‑dependent amplification, creating a compressive response and generating distortion products such as 2f₁ – f₂.
Presbycusis manifests as high‑frequency threshold elevation, reflecting hair cell loss concentrated at the cochlear base.
Industrial noise exposure accelerates hearing loss, underscoring the importance of protective measures like earplugs.

Frequently Asked Questions

What is the critical band in auditory masking?

The critical band is the bandwidth of a masking noise at which increasing the noise’s frequency range no longer raises the masking threshold. It reflects the frequency width of a single cochlear filter and is identified through band‑widening experiments such as Fletcher’s method.

How do outer hair cells contribute to cochlear nonlinearity?

Outer hair cells act as reverse transducers that change shape in response to electrical signals, providing level‑dependent amplification. This amplification narrows tuning at low intensities and broadens it at high intensities, producing a compressive response and generating distortion products like the cubic 2f₁ – f₂ tone.

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Helpful resources related to this video

If you want to practice or explore the concepts discussed in the video, these commonly used tools may help.

High Fidelity Earplugs For Musicians Recommended

These earplugs reduce sound intensity while maintaining frequency clarity, helping to prevent the noise-induced hearing loss discussed in the lecture.

Amazon →

Anatomy Of The Human Ear Model

A physical anatomical model provides a 3D reference for the outer, middle, and inner ear structures described in the auditory system section.

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Textbook On Hearing And Auditory Perception

Academic texts on psychoacoustics provide deeper context on masking experiments, critical bands, and cochlear nonlinearity.

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Full Transcript YouTube

[SQUEAKING]
[RUSTLING] [CLICKING]
JOSH MCDERMOTT: All right.
So today, we will
continue our journey
into the auditory system.
Last time, we talked
about the ear.
And this time, we're going
to be talking about one
of the most important properties
of the ear, namely frequency
selective as well as the--
frequency selectivity,
as well as the fact
that the ear is nonlinear.
And then we're going to get
into hearing loss, which
will probably affect all of
you at some point in your life.
So just a refresher,
this is the ear.
Remember, sound enters here,
travels down the ear canal,
causes the eardrum to
vibrate back and forth.
Those vibrations are
transmitted via the ossicles
through to the cochlea,
which is the organ that
does the sensory
transduction for hearing.
And so remember,
we think of the ear
as having these three main
functional components.
There's the outer ear,
the pinna and the eardrum.
There's the middle ear,
which serves these two
main functions-- impedance
matching, which is necessary
because you go from air to
fluid, and overload protection.
Remember, there
are those muscles
on the bones of
the middle ear that
can contract in the presence
of high intensity sound.
And then we spent
most of our time
last time talking
about the inner ear.
And we think of one of the
main functions of the inner ear
as being frequency analysis.
And here are some numbers
that are worth knowing
and fun to think about.
So in each of your ears, there
are approximately 3,500 inner
hair cells.
Remember, the inner
hair cells are the cells
that move in response to sound.
And when they are moved, their
membrane potential changes.
So they transduce mechanical
energy into a voltage.
There are about 12,000
outer hair cells.
So remember that,
typically, you have
these three rows of
outer hair cells,
and then one parallel
row of inner hair cells.
So there's about a 3 to 1 ratio.
And the outer hair cells
are like the inner hair
cells in reverse.
So they get an
electrical signal.
And that causes their
shape to change.
Remember, we saw the
video of the outer hair
cell that was being supplied
an electrical signal, which
was music.
And you saw the outer
hair cell dancing.
The auditory nerve fibers
are these essentially wires
that are carrying information
from the inner hair
cells to the brain.
And there's about 30,000
auditory nerve fibers per ear,
so roughly about 10
per inner hair cell.
So just for
comparison-- and we'll
talk a lot more about the visual
system later in the class.
But these are analogous
numbers in each of your eyes.
So there are two types of
photoreceptors in the eye.
There are cones and rods.
The cones, there are
about 5 million of those.
There's far more of
the rods, 100 million.
The rods typically
function in conditions
where there are
low light levels.
But the interesting
discrepancy or difference
with respect to
the auditory system
is that there are actually
fewer optic nerve fibers
than there are receptors,
whereas, in the auditory system,
it's the opposite.
So in the visual system, you're
taking the super high bandwidth
signal and squeezing it
down into a narrow pipe.
And that's what gets
sent to your brain.
And there's probably
lots of consequences
for the neural coding from that.
And in the auditory system, it's
just the opposite relationship.
And we can talk in more detail
later on about why that is.
It's interesting to think about,
but it's a salient difference.
So one of the most
important attributes
of the auditory system
is frequency selectivity.
So you saw this
picture last time.
These are tuning curves
for auditory nerve fibers.
So each one of these lines
corresponds to a nerve fiber.
And remember, each line plots
the minimum sound intensity
at a given frequency that
is necessary to elicit
a response in the fiber.
So you hook an electrode
into a nerve fiber.
You're playing frequencies
of different intensities.
And you're looking at what the
threshold of the nerve fiber is.
And so for a particular
nerve fiber, say this one,
there is a special
frequency, which we normally
call the characteristic
frequency, to which it responds
best.
So the amplitude of
the sound doesn't
have to be very high in
order to get a response.
And if you change the
frequency, higher or lower,
the threshold goes way up.
So this empirical
result suggests
that the cochlea can
be thought of as a bank
of bandpass filters.
And this property of
frequency selectivity
has a whole host of
perceptual consequences.
So this is just one.
So how many of you are familiar
with the phenomenon of beating?
OK, a couple people.
So if you play a
string instrument
you probably take
advantage of beating
when you tune your instrument.
So beating is an
acoustic phenomenon,
and it happens anytime there
are multiple frequencies that
are present.
And what's shown on the
slide is an example of that.
So the slide shows you the
waveforms of two pure tones.
Remember, a pure tone
is a tone that just
consists of a single frequency.
It's a sinusoid.
So we've got the red pure
tone that's at one frequency.
And that sounds like this.
[PURE TONE]
Can everybody hear that?
OK.
And we've got the
blue pure tone,
which is a different frequency.
[PURE TONE]
It's a little bit higher.
So you can see that, because
those two pure tones are
different frequencies,
there's this point in time
here where the phases align.
So the peak of the red
curve aligns with the peak
of the blue curve.
And over time, they
drift out of phase.
And so you get to
this moment in time,
where the peak of the red
curve aligns with the trough
of the blue curve.
Now, if you play those two
pure tones at the same time,
the waveforms add in the air.
And so the sound
that would actually
occur if both of
those frequencies
were played at the same
time is the black curve,
which is just the sum of the
red curve and the blue curve.
And because of this
particular relationship
over time between
the phases, you
can see that the amplitude of
the black curve waxes and wanes.
So it's high here.
And then by the time
you get to this point
in time, the red and the blue
frequency, they cancel out.
So that's called beating, this
waxing and waning in amplitude.
And I mentioned that if you
play a string instrument,
you are probably familiar
with that because you actually
often listen to
beating if you're
trying to tune your instrument,
because it'll tell you
whether the notes that
are played on two strings,
if you play them
at the same time,
are exactly the same or
a little bit different.
So this is what it sounds
like in this particular case.
[PURE TONES]
So it sounds a little bit
like a telephone or something.
So that modulation
is perceptually
the corollary to beating.
And the word that we typically
use to refer to that sound
is roughness.
So we call a sound rough when it
contains amplitude modulation.
So beating is an
acoustic phenomenon.
It happens any time you have two
different frequencies that are
being played at the same time.
However, you only
hear the beating
as roughness under
particular conditions.
And they turn out to be
constrained by the cochlea.
So the beats are only
heard if the two frequency
components fall
within the bandwidth
of the filters in your cochlea.
And they also have to
be in the same ear.
So if we take the
red frequency--
if we use headphones, we
take the red frequency
and we apply that to your right
ear and the blue frequency
and we apply that
to your left ear,
you will not hear the beats.
So you only hear them if
they enter the same ear
and if the frequencies
are sufficiently
close that they stimulate
the same auditory filter.
So here's just a quick
demonstration of that.
So I'm going to play
you three sounds.
They each consist
of two frequencies.
But we're going to
vary the difference
between the frequencies.
All right.
So here, you have a one
semitone difference.
That's a 12th of an octave.
So that's like the
difference between a white
and a black key on the piano.
[ONE SEMITONE]
And you can hear that.
Here, it goes to
three semitones.
[THREE SEMITONES]
And the beating becomes
a lot more subtle.
And here, it's out at eight.
[EIGHT SEMITONES]
And so at eight semitones,
you can probably
hear those two frequencies
really as distinct things.
You can almost attend
to one or the other.
And you don't hear
the beating anymore.
And it's not because the
beating is not there.
It's out there in the world.
It's in the air.
It just doesn't make
it through your ear
because those two
frequencies get processed
by different parts
of the cochlea.
So this is one respect
in which the frequency
selectivity of the cochlea
really constrains what you hear.
OK.
So one of the most
important attributes
of the auditory system
is frequency selectivity.
The tuning that we observe
in the auditory nerve
suggests that the
cochlea can be thought
of as a bank of
bandpass filters.
But the problem is that,
in humans, we can't
measure the filters directly.
So this picture that
I just popped up,
this is probably from a
cat, or a rat, or a mouse,
or some critter in which you
can do an invasive experiment.
And we don't have the ability to
make these kinds of measurements
directly in humans, because the
auditory nerve is very, very
difficult to get to.
So in humans, if you want
to understand the frequency
selectivity in the
cochlea, you have
to infer it indirectly from
some other type of experiment.
And the principal way that
human frequency selectivity
has been explored is by making
use of what's called masking.
So what is masking?
Well, masking is
defined as the process
by which the threshold of
audibility for one sound
is raised by the presence
of another masking sound.
So let's suppose there's a
particular sound that you're
supposed to be detecting.
And you can hear it just fine.
And then we play another
sound at the same time.
Under some conditions,
that second sound
will make it much harder
to hear the first sound.
And that's called masking.
And this happens all the
time in everyday life.
And the reason for that is
that sounds add in the air.
And so any time there's
more than one thing that's
making sound, one
of them is probably
masking at least
part of the other.
So it's a very, very
common phenomenon.
And it turns out that masking
is very closely related
to frequency selectivity.
So this is a graph,
an old graph,
that shows the masking
of a target pure tone--
so it's a little
beep that you're
supposed to detect-- by
either a narrowband noise
masker or another pure tone.
And so what the graph is
plotting is the amount
of masking-- and I'll tell you
in a second what that means--
as a function of the
frequency of the target tone.
And there is a masker
that is present
at this particular frequency.
And it can either be a
noise band or a tone.
And so the caption of the
figure describes this in detail.
So the pure tone is at 400
cycles per second, 400 hertz.
And the narrow band of noise
is centered at 410 hertz.
So they're in this range here.
Now, the amount
of masking, that's
the amount by which you have to
increase the level of the target
tone in order to be able to
hear it when the masker is also
present.
All right, what does
the graph tell us?
Well, it tells us, when
the target tone has
a frequency that's either
much lower or much higher
than the masker, well, then the
amount of masking is very small.
You really don't have to
increase the level of the target
very much in order to be
able to tell that it's there.
But when the target is closer
in frequency to the masker,
you've got to crank up its
level fairly significantly.
And in particular, when it's
very similar to the frequency
of the masker, you might
have to elevate its level
by like 60 decibels.
That's highly significant
So in general, the
amount of masking
is determined by the
similarity of the frequency
between the signals.
Now, you might have noticed
that the curve for the pure tone
masker has got all these
funny bumps and dips.
And one of the
reasons for this is
that, when you
have two tones that
are present at
the same time, you
get this phenomenon of beating.
So if you're a participant
in this experiment,
trying to detect whether
the tone is there,
you can actually use the beating
to help you detect the tone.
So there are certain
places where the tone gets
a little bit easier to detect.
So that's why you get these
bumps and valleys in the graph,
whereas, for the noise
masker, you can't do that.
And so you get a
much smoother curve.
But the key concept
to take away from this
is that masking is determined
by frequency selectivity.
And so we can use it in order to
infer the shape of the filters
that you have in your ears.
All right.
And so the general model
by which we do this
is what's called the power
spectrum model of masking.
So this considers the cochlea
to be a bank of filters.
And you measure masking
by asking people
to detect a tone in the
presence of a noise masker.
And so the assumption is
that a signal is heard--
so a signal here is the tone.
It's heard when
the signal to noise
ratio at the output of the
filter that you're trying
to measure exceeds some value.
You're playing noise.
And then you're
playing the signal.
And the idea is that
some amount of the noise
gets through the filter.
And your ability
to detect the tone
will depend on the ratio
between the power of the tone
and the power of the noise
heard through the filter
that you're using to monitor
the presence of the tone.
All right.
So we assume that there
is a filter that's
characterized by a shape.
The masker is a
noise signal that
will be characterized
by some spectrum
So this is power as a
function of frequency.
And the filter's filters
got some response
as a function of frequency.
And so the power
of the noise signal
that gets through the filter
is given by this integral.
It's essentially the dot
product between the spectrum
of the noise and the
spectrum of the filter.
And so the model posits
that your ability
to detect the signal will be
a function of how much power
gets through the filter.
So let's just look at an example
to build up some intuition here.
So the idea is that there's
this red thing in your ear.
It's a filter.
And we want to infer
its properties.
The noise signal
is shown in gray.
So this is frequency.
So we're looking in
the frequency domain.
And this is plotting the masker
power or the filter response
as a function of frequency.
So we've got a broadband noise.
It's got all these
frequencies in it.
So the amount of noise power
that gets through the filter
will clearly be influenced
by the level of the masker.
So if we just increase the
intensity of the masker,
the noise power will increase.
But it will also be dependent
on the spectral properties
of the masker.
So here, we have a masker
that's very narrowband.
It's only got this narrow
band of frequencies.
And if we add low
and high frequencies
to make it more
broadband, you can
see that there's going to
be more frequencies here
that are hitting the filter.
So the dot product of the
filter and the noise will go up.
Now, the noise power will also
be affected by the filter shape.
So of course, we're assuming
that there's a fixed filter
shape in your ear.
But we don't know what it is.
And so one hypothesis might be
that it would have this shape.
Another hypothesis might be
that it would have this shape.
If the filter is wider, there
will be more noise power
coming through it.
And thus, it should make it
harder to detect the tone.
All right.
So the general model that
we're using here, in order
to try to understand frequency
selectivity via masking,
makes a whole bunch
of assumptions.
It assumes the filter is linear.
It assumes that, when you
are performing this detection
task of saying whether
you hear the noise or not,
you are only using one filter
that's centered at the signal
frequency.
So this is the signal.
It's a pure tone.
Remember, it's
got one frequency.
That's why there's
a spike there.
And in reality,
your ear consists
of this big bank of
filters because the cochlea
covers all frequencies.
But we assume that you're
just using one of them
in order to detect the tone.
And we also assume
that the detection
is based entirely on the overall
power at that filter's output.
And so none of these
assumptions are strictly true.
But they often
provide what we think
is a fairly reasonable
first approximation.
All right.
So the general
method that would be
used for measuring frequency
selectivity in a person
is to have some fixed
signal, and then
to manipulate the
characteristics of the masker
and to measure how
the signal detection
threshold will vary as the
masker characteristics vary.
And then we're going
to try to deduce
the characteristics of the
auditory filter in your ear
from the data.
So let me just
give you an example
I think will make
this pretty clear.
So this is like the
classic experiment
that was really the first
demonstration of this approach.
And it's attributed to Fletcher,
who was a scientist who worked
at Bell Labs back in the 1940s.
And so people that
were at phone companies
were very interested
in understanding
frequency selectivity
in the human ear
and also masking, in part
because masking really
determines the extent to which
you can compress an audio signal
and have it still
sound OK to a person.
And the essential concept
is that, if you've
got some sound with all these
different frequencies in it,
but you know that a whole
bunch of the frequencies
will be inaudible
because of masking,
you don't have to encode them.
And so you can save bits in
the signal that you're sending,
say over a phone line.
And so nowadays, all audio
compression algorithms
essentially have built into them
measurements of human masking.
So MP3 codecs have
that built into them.
So people were interested
in this for a long time.
All right.
So the experiment that
Fletcher conducted
involved measuring the
signal detection threshold
as a function of
the noise bandwidth.
So this is a noise that's got
a constant spectral level.
And we're just going to vary
the bandwidth of the noise
and measure how that
affects your ability
to detect a tone that's at
the middle of the noise.
And so the results of the
experiment are shown over here.
So this graph plots the
signal threshold in dB SPL
as a function of the masking
noise bandwidth in hertz.
So over here, the masker is very
narrow and the threshold is low.
As you increase the
bandwidth of the masker,
the threshold goes up.
And then there's
this magical point
at which, if you
continue to increase
the bandwidth of the masker,
the signal threshold does not
continue to increase.
And the intuition here
is that, at this point,
you've hit the
bandwidth of the filter
that you're using to
detect the signal.
So if you increase the
bandwidth of the masker
further, beyond the
edges of the red curve,
it's not going to
affect your ability
to detect the tone because
those frequencies don't
get passed through the filter.
And that's called
the critical band.
So we're going to
demonstrate this and measure
our own critical bands.
What we're going to
do is an experiment
where I will play you
a sequence of tones
that will decrease in level.
And your job is to count
how many of them you hear.
And the idea is
the number that you
can hear will be proportional
to your-- inversely proportional
to your threshold.
All right, so
let's check it out.
[AUDIO PLAYBACK]
- Critical bands by masking.
You will hear a 2,000 hertz
tone in 10 decreasing steps of 5
decibels.
Count how many
steps you can hear.
Series are presented twice.
[DECREASING TONES]
[END PLAYBACK]
JOSH MCDERMOTT:
Did you all get 10?
Yeah?
All right, good.
OK.
So you can hear 10.
Now, we're going to
do the same thing.
But there's going to
be a noise masker that
will be present throughout.
And so the tones will
get harder to hear.
And you won't be able
to hear quite as many.
[AUDIO PLAYBACK]
- Finally, the bandwidth is
reduced to only 10 Hertz.
[DECREASING TONES AND MASK]
[END PLAYBACK]
JOSH MCDERMOTT: I got eight.
Is that about right?
And I'm going to actually
let you watch this.
All right.
So that was a very
narrowband masker.
But it elevated your threshold.
So initially, you could hear 10.
Now, after that, you
could hear eight or nine.
Is that consistent?
Anybody disagree?
No?
All right.
I hear some complaints
from the crowd.
All right, let's
make it wider still.
[AUDIO PLAYBACK]
- Next, noise with a bandwidth
of 250 hertz is used.
[DECREASING TONES AND MASK]
[END PLAYBACK]
JOSH MCDERMOTT: I got five.
Yeah?
Is that about right?
OK.
All right, so the
threshold was elevated,
went from eight or
nine down to five.
What's going to
happen here, we're
going to keep making it wider.
And at some point, it's
going to stop getting harder
to hear the sounds.
[AUDIO PLAYBACK]
- Next, the noise has a
bandwidth of 1,000 hertz.
[DECREASING TONES AND MASK]
[END PLAYBACK]
JOSH MCDERMOTT: I
still got about five.
All right?
All right, so it's stable.
Now, we're going to go to
something that's a lot wider.
[AUDIO PLAYBACK]
- Now, the signal is masked
with broadband noise.
[DECREASING TONES AND BROADBAND]
[END PLAYBACK]
JOSH MCDERMOTT:
And what's kind of
cool about that is
that last noise is
way louder than the one
that came before it.
But it's no harder
to detect the tone.
And the explanation
for that is that you're
using the filters in your
ear to do that detection.
And the response of the filter
is not affected very much
by all those extra
frequencies that
get added above and below it.
So that's the critical band.
All right.
Any questions about this masking
experiment or the general logic?
Yeah?
STUDENT: Is it supposed
to be that you hear
more as it keeps getting wider?
Because at least
for me, I thought
I heard more for the last
one than the middle two.
But I don't know if that's
like an effect or not or just
happens to be like that.
JOSH MCDERMOTT: My
guess is it's a fluke.
I mean, there's no real reason
to think that that would happen.
The fact that you actually
hear a tone versus not
is somewhat subject
to random effects.
Sometimes, you're paying a
little bit more attention,
or had a little bit more
coffee, or whatever.
And so from trial to trial,
there'll be fluctuations.
But yeah, on average,
I don't think
we would expect that
you'd be any better there.
It typically flattens out, yeah.
Any other questions?
OK.
The experiment here, it's
conceptually very powerful.
It makes a really good demo.
And it's great for
teaching purposes.
But experimentally,
in terms of actually
using this to deduce the
properties of the ear,
it's actually not
all that useful.
And so nobody uses this anymore.
And the main issue here is
that the filter output power
is really dominated by
frequencies that are
near the center of the filter.
And so imagine you're
comparing this versus this.
And because the filter
has a weak response
here in the skirts, the
frequencies out there
actually don't have
a huge contribution
to the overall amount of power.
And so the technique
is actually not
super useful for providing an
accurate estimate of the filter
shape and bandwidth.
So we mostly just now use
this for teaching purposes.
So the standard modern
method for getting estimates
of frequency
selectivity is what's
called the notched-noise method.
So the idea is
what's shown here.
So you're still trying
to detect a signal.
But now, instead of
having noise that
has this continuous spectrum,
the noise has a notch in it.
So you're supplying frequencies
here and frequencies here.
And then you can change
the position of each
of the bands of frequencies.
So you can compare this,
to say this, to say this.
And so you measure
your threshold
for these different
types of maskers.
And so the idea is
that, in the black case,
the only noise power that's
coming through the filter
is really the things that
are out there in the skirts.
And so you isolate the response
at that particular point
in the filter.
And you can better
characterize it.
All right.
And so there's now been lots of
experiments along these lines.
I'm not going to work
through in detail
how you would go from the
results of an experiment
like this to inferring
the exact filter shape.
But you can work that out.
And this is just an example of
a derived filter function, where
you have the response
of this measured filter
as a function of frequency.
And so the notched-noise
method is generally
acknowledged to be better than
Fletcher's band-widening method.
So it gives you more information
about the filter skirts.
It's also got this
advantage that it
reduces the potential for what's
called off-frequency listening.
So when you're doing
this experiment,
the whole point
of the experiment
is to try to characterize
the red filter.
It's the one that's centered
at the signal frequency.
But the observer, the person
who's doing the experiment,
they have the option to
use their entire ear.
And in actuality, you
have these other filters
that are positioned at
slightly different frequencies.
And in principle, you might
actually get better signal
to noise ratios under
some conditions listening
to adjacent filters.
But the idea of the
notched-noise signal
is that the filter that's
actually centered at the signal
frequency is the one where
the signal to noise ratio
would always be the best.
And so the observer just
doesn't have any reason
to use anything other than that.
So that's considered
to be an advantage.
All right.
So this has now been used
fairly extensively in people
to characterize
frequency selectivity.
So one of the main findings that
comes out of these experiments
is that frequency
selectivity varies
as a function of the
center frequency.
So this is a graph that is
plotting absolute bandwidths.
And that's the equivalent
rectangular bandwidth.
So it's one measure of
how wide the filter is,
measured in hertz, as a function
of the characteristic frequency.
And so down here
at 100 hertz, you
can see that the bandwidth
is like maybe 35 hertz.
And then if you go up to a
kilohertz, it's about 150 hertz.
If you go up to 5
kilohertz, you can
see that it's like 500 hertz.
So as you move along the
cochlea, the bandwidths vary.
This is a pretty general
property biological auditory
systems, that the
bandwidths tend
to be higher at higher
frequencies in absolute terms.
Now, if you look at the
relative bandwidths,
so if you express the bandwidth
relative to the center
frequency, they actually
stay pretty constant
or even decrease.
And so these are filters plotted
on a logarithmic frequency
scale.
And you can now
see that they look
pretty similar at different
points along the spectrum
and, in fact, maybe
are a little bit
narrower here at
high frequencies
than at low frequencies.
And again, this is a
fairly general property
biological auditory systems.
The filters have that
property that, when
you look at them on
a logarithmic scale,
they looked pretty constant.
So as I mentioned, there's
lots of applications
of these measurements of
frequency selectivity.
One of them has to do with using
masking for audio compression.
Another is that this is a
pretty commonly used diagnostic
to tell whether somebody's
ears are healthy.
So as we'll discuss, when you
start to lose your hearing,
the filters tend to get broader.
And then another
application actually
involves comparing
the hearing of people
to the hearing of
non-human animals.
And that's interesting for
a whole bunch of reasons.
Oftentimes, we're stuck
with performing experiments
on non-human animals because
they're invasive methods that
are not possible in humans.
It's also really interesting,
from the standpoint
of thinking about
evolution, to understand
the relationship between
humans and non-human animals.
And indeed, out of
this type of work,
there's emerged this
interesting evidence
that humans appear to have
substantially better frequency
selectivity than
non-human animals.
So it's like our ears
are more tightly tuned.
And so this is one example graph
that shows an example of this.
So in this literature, they
tend to not plot bandwidths.
Instead, they plot
the tuning sharpness,
which is just reciprocally
related to the bandwidth.
So this is the tuning sharpness.
And this is the
characteristic frequency.
And there are measurements
that were made here
in cats and guinea pigs.
That's red and blue.
And then the black lines
plot two different estimates
of human tuning bandwidth.
And the point is that the
black lines are substantially
above the blue
and the red lines.
So the filters in the human
are thought to be more sharp.
Here's another graph that shows
cats, macaques, and humans.
And here, you can see
that the macaque monkey
seems to be somewhere
between cats and humans.
And it's interesting to
think about why this is.
And really, there isn't
widespread agreement on this.
It's just an
empirical observation.
You might imagine that some
of evolutionary pressure
for communication
might have driven this.
Other people think
it's just a function
of the size of the cochlea.
We don't really know.
But it's an
interesting difference.
All right.
Now, I told you a little bit
about some of these properties
that we find in biological
auditory systems.
And it's natural to wonder why
the ear is the way that it is.
And some recent approaches
that are now possible
have given us some
new ways of trying
to understand these questions,
where advances in machine
learning now make it
possible to optimize
machine systems to solve
interesting perceptual tasks.
And so this is a cool paper
that came out of Google
a few years ago now, where
they, as the title says,
learned the front-end
of a neural network that
had to recognize speech.
I mean, Google was
not really interested
in the scientific questions that
we're interested in this class.
They were just trying to build
a better speech recognition
system.
But the result of
the study actually
ends up being kind of
informative with respect
to thinking about
the auditory system.
So this is a big typical
system for recognizing speech.
So you start out with
a sound waveform.
And in this case, the system
convolves the waveform
with a bunch of filters.
And these filters,
critically, were learnable.
So there's convolution
with these filters.
There's some pretty
standard operations
of pooling and some
nonlinearities.
And then that's the input to
some convolutional layers.
And then these things called
LSTMs, long short-term memory--
the details of this
aren't really critical.
The point is it's a
system that was optimized
in order to recognize speech.
And part of that optimization
involved optimizing
this front-end filter bank.
And so you can do that.
And then you can ask,
well, what kind of filters
emerge as a good
engineering solution
to the problem of
recognizing speech?
So this is one way
of looking at that.
So these graphs are
plotting the set
of filters that are
in a standard model
of the cochlea that's based
on biological observations,
and then the filters that
were learned by the system.
So let's just focus on the model
of the biological cochlea first.
So these are the
filters ordered.
And there's about
40 of them here.
And you can see the frequency
response of each filter.
So this is frequency axis.
And the gray scale here plots
the response of that filter
to the corresponding frequency.
And the dashed green
line is a function
that's been fit to lots of
observations from the masking
experiments that we
just talked about.
And so what you can see is
that the filters in the ear
are arranged from low
to high frequencies
with this particular mapping.
But you can also see
the thing that I just
commented on earlier, which
is that the high frequency
filters are wider than
the low frequency filters.
So the point is that
there's a wider black region
here than here.
So that's the same
thing that we saw
on this graph, where we
saw that the bandwidth grew
with center frequency.
And so the interesting
result is that,
if you look at the
filters that emerged
as a consequence of optimizing
this system to recognize speech,
if you arrange them
in the same way--
I mean, it's a little bit
messy, but you can see
some traces of the same thing.
So if you look at
the filters that
are tuned to low
frequencies, they
tend to be pretty narrow,
whereas the ones that
are tuned for high frequencies
tend to be broader.
And the distribution
of frequencies
is a little bit different.
So you can compare the green
curve here to the black curve
here.
It doesn't fall exactly on it.
But it's not a million
miles away either.
All right.
So, so the inference that
we might make from this
is that the filters
that are in our cochlea
might be a good way to extract
information from sound.
Any questions about that?
STUDENT: What are
the alternatives,
like if you optimize it to
do some different task, will
it show a very
different kind of--
JOSH MCDERMOTT: Yeah,
that's a good question.
This hasn't been
looked at exhaustively.
I can tell you that we've done
a little bit of this in our lab
with some tasks.
And you can get-- if the
task is narrow enough,
you can get some unusual
solutions that come out.
And so I think it doesn't
have to turn out this way.
You could build a
filter bank that
wouldn't look like this at all,
where you could build one that
would just along the diagonal,
where everything would
be exactly the same bandwidth.
That's just not what emerges
from the optimization.
Yeah.
Any other questions?
OK.
Now, we talked very
briefly last time
about how the tuning
that you see in the ear
changes with sound intensity.
So in this respect,
it's nonlinear.
And this is another
couple graphs
that show the same of thing.
So cochlear filter shapes,
they change with sound level.
And we'll talk in some detail
about why that happens.
But these are just two
measurements that reflect this.
So this is physiological data.
This is actually
made from an animal
cochlea, where you cut a tiny
little hole in the cochlea.
And then you can look in at
the motion of the cochlea
in response to sound.
So you measure the motion
of the cochlea as a function
of frequency and intensity.
And the results
of the experiment
here are expressed
in terms of gain.
So the gain is the ratio between
the intensity of the stimulus
and the mechanical motion
of the basilar membrane.
So it's a measure of how much
the ear is amplifying sound.
And what this is showing is
that, when the sound intensity
is low-- so you can see the
sound intensity is labeled here.
That's what these numbers are.
So that's 5 and
10 dB, 20, 30, 40.
And so at low intensities,
you get this very, very narrow
tuning, where the gain is very
high at a particular frequency
range.
This is frequency.
And then it falls off.
Now, as the intensity
of the sound increases,
the gain overall drops.
But you can also see that
the tuning gets broader.
And so down by the time
that you're at 80 decibels,
the tuning is much, much broader
than it was at 30 decibels.
What do these pictures show us?
Well, they show us that the
ear is providing amplification.
And we believe that that's
supplied by the outer hair
cells.
And it's level-dependent.
So when your ear gets
a very quiet sound,
it's amplifying
the heck out of it.
When it gets a
much louder sound,
it's amplifying it much less.
And it's doing that in a way
that is frequency-dependent.
And so the consequence of that
is that, at low intensities,
the tuning tends to
be pretty narrow.
And at higher intensities,
it gets broader.
So this is a physiological
measurement, again,
made of the actual
motion of the cochlea.
This is psychophysical
measurements
made using the
masking experiments
that we've been discussing.
So each one of these
curves is the measurement
that's inferred from masking in
a human with a particular signal
frequency.
So this is one signal
frequency, this is another,
this is another,
this is another.
And the different curves here
are measured at different SPL
levels of the signal.
So this is dB SPL.
So that's pretty quiet.
And the highest
one is 70 dB SPL.
And you can see that the
low intensities give you
narrower tuning than
the high intensities.
So that's a psychophysical
analog of that phenomenon.
All right.
So in general, we
see sharp tuning
at low sound levels, broader
tuning at high sound levels.
And you can see this
both physiologically and
psychophysically.
So another way to look at this
level-dependent amplification
is with a graph
like this that shows
the response of the cochlea,
in particular the basilar
membrane, as a function
of sound pressure level.
And when you look
at it in this way,
the basilar membrane
exhibits what's
called a compressive
response function.
So what does this all mean?
So we've got sound
pressure here on the x-axis
and two different measures of
the basilar membrane response,
displacement and
velocity, which tell
the same story on the y-axis.
And they're both being
plotted on log scales.
This is in decibels.
And this is a logarithmic scale.
And for reference,
this line here
displays the motion
of the stapes.
Remember, the stapes
is the stirrup bone.
It's the last bone
in the ossicles
that connects to the cochlea.
So you can measure the
motion of the stapes.
And what you see there
makes perfect sense.
This is a line
with a slope of 1.
So that's a linear response.
So if you increase the sound
intensity by a certain amount,
the motion of the stapes
increases by the same amount.
Now, what happens on
the basilar membrane
is something that's
very different.
Instead, you increase the sound
pressure by a certain amount.
And the difference in the
motion of the basilar membrane
is substantially smaller.
So it's a compressive response.
Now, what's actually
happening here
is that there is
amplification that is
specific to very low intensity.
So when you have a sound
that's down here, 10 or 20 dB,
the cochlea is
amplifying the response
to a pretty enormous extent.
And one way to
think about this is
to compare the
response at the stapes
to the response on
the basilar membrane.
So at high levels, you can see
that the response at the stapes
and the response of the basilar
membrane are fairly comparable.
But they diverge.
So the point is
that, at the stapes,
the response to these
very low intensities
is like off the graph.
It's like down here.
But the response of the basilar
membrane is way up here.
That's because you have
this amplifier in your ear
that's boosting the response
to these low intensities.
And it doesn't boost the high
intensities nearly as much.
And that's what gives you this
compressive response function.
So this is called compression.
But really, it's
level-dependent amplification.
There's an amplifier
in your ear.
And it acts specifically when
the sounds are low in intensity.
And again, we believe this is
the outer hair cells, which
provide this kind of
feedback system, whereby
they get a little bit of
input, and then they move,
which, in turn, increases the
motion of the basilar membrane.
It's a little
amplifier in your ear.
All right.
Now, the story is a little bit
more complicated than that.
And that is that the
amplification really only occurs
for frequencies that are
near the preferred frequency
of a place on the cochlea.
So these are,
again, measurements
of the basilar membrane motion.
So it's the same kind of
graph we were just looking at.
But now, the different
lines here-- and this
is all made at one
place on the cochlea.
And the different
lines correspond
to different frequencies.
So this is made
at the place that
corresponds to 10
kilohertz, which
is shown in the open symbols.
And so at 10 kilohertz, you
see this very shallow slope
here for the cochlea's response.
If you increase the frequency
a little bit to 11 kilohertz,
you still see a
pretty shallow slope.
But then as you go
to 12 and to 13,
the slope shifts to
being pretty close to 1.
So as the frequency
moves away from
the characteristic
frequency, the response
becomes much more linear.
So you stop getting this
nonlinear amplification.
So this picture is
actually telling you
really the same thing
seeing as this picture.
There are two different ways of
looking at the same phenomenon.
So at low intensities,
you're getting
this massive amplification.
But it's very
frequency-selective.
And so that's why,
at low intensities,
you get this very narrow
tuning, because it's only
the frequencies that the
characteristic frequencies that
get boosted.
So at higher intensities,
there's much less amplification
happening.
And as a consequence, the
tuning gets much, much broader.
Any questions about this?
You're going to have to
go over this a few times.
It just takes a little while
to wrap your head around this.
And so there's going
to be a problem
on the problem set where
you think a little bit more
about this.
But the big picture here is
that the ear is nonlinear.
You've got this
amplifier in your ear.
And that is helping you hear
these very low intensity sounds
that we have to deal
with on a daily basis.
Yeah?
STUDENT: What is the
characteristic frequency
[INAUDIBLE]?
JOSH MCDERMOTT: So the
characteristic frequency
is the frequency to which a
given place on the cochlea
is most sensitive,
responds the best.
STUDENT: [INAUDIBLE]
JOSH MCDERMOTT: In this
graph or in this graph?
It would be 10 kilohertz.
So it's like you're getting
the biggest response here
at 10 kilohertz.
So on this graph, it would
be it would be 10 kilohertz.
On this graph, each
one of these fibers
has a different
characteristic frequency.
It gives you the tip
of the tuning curve.
And it corresponds to the
place along the cochlea.
Yeah, go ahead.
STUDENT: [INAUDIBLE]
JOSH MCDERMOTT:
Ah, that I don't--
you mean like with
this converged
to being right on
the dashed line?
I'm not sure.
You might have--
there's probably
some baseline level
of amplification
that you get throughout.
Yeah, I'm not
positive about that.
But it gets pretty close,
as you can see, yeah.
Yeah, any other questions?
All right.
Now, one of the consequences
of the fact that you
have these nonlinearities
in your ear
is that your ear
creates frequencies
that are not necessarily
present in the input to the ear.
And these are called
distortion products.
So the idea is that
sinusoids are eigenfunctions
of a linear system.
So that means that, if you
have a linear system, if you
put in two frequencies,
the output of the system
will contain those same two
frequencies, potentially scaled
in amplitude and
shifted in phase.
But if the system is
nonlinear, then you
can get additional
frequencies that come out.
And that's, in fact,
what happens in the ear.
So here's a situation
where we've got f1 and f2.
So we're supplying these
two frequencies to the ear.
And there are these
other frequencies
that we might
potentially observe
depending on the type of
nonlinearity that's in the ear.
So if it's a quadratic
nonlinearity,
it involves a squaring.
You'd get f1 minus f2.
If it's a cubic nonlinearity,
you'd get 2 f1 minus f2.
And so you can think
of any nonlinearity
as being approximated
by a Taylor series.
So there'd be a quadratic
term and a cubic term.
And those tend to be pretty
prominent in our ears.
So we would expect
that, if you've
got this like powerful
nonlinearity in your ear,
it's going to cause these new
frequencies to be present.
How would we potentially
detect these?
So this is a classic
demonstration.
That's one of the main
ways in which we actually
measure distortion products.
And it's going to make use
of beating, which we just
talked about at the
start of the lecture.
All right.
And we'll listen to
this demonstration.
But I'm going to
explain it first.
So we're going to play you a
sound that contains two pure
tones, one at 1,000 hertz
and one at 1,200 hertz.
So the cubic distortion
product, which we would predict
would be present in
your ear if there
is a cubic component to the
nonlinear function in your ear--
the cubic distortion product
would be 2 times f1 minus f2.
So 2 times f1 would be
2,000 minus f2 is 800 hertz.
So the theory
predicts there should
be this additional frequency
that's being created in your ear
by its nonlinear
properties at 800 hertz.
So to probe for the
presence of that,
we're going to add a
pure tone at 804 hertz.
Now, the logic here is that, if
your ear is creating 800 hertz
and we add an 804 hertz,
there's going to be beating.
Now, what I didn't
tell you before
is that beating always happens
at the difference of two
frequencies.
So if we've got 800
hertz and 804 hertz,
there should be beating at 4
hertz, four times a second.
So you'll hear this low
frequency fluctuating wobble.
And so we're going
to actually do this.
And you can see
whether you hear this.
And I'm going to show
you this, so you can
see what you're listening to.
[AUDIO PLAYBACK]
- Aural combination tones--
in this demonstration, two tones
of 1,000 and 1,200 hertz are
presented.
When an 804 hertz
probe tone is added,
it beats with the 800 hertz
aural combination tone.
[AURAL COMBINATION TONES]
[END PLAYBACK]
JOSH MCDERMOTT: All right,
so the point is that,
when you just have the two
primaries present at 1,000
and 1,200, you shouldn't
hear this subtle fluctuation.
Then we add in the
third tone at 804 hertz
and you should hear
this subtle pulsation.
So that's how you're supposed
to tell whether you've got
the distortion product or not.
So we can just try it again.
[AUDIO PLAYBACK]
[AURAL COMBINATION TONES]
[END PLAYBACK]
JOSH MCDERMOTT: All right.
So it's pretty subtle,
but it's there.
And in a second, I'll play you
something that's not as subtle.
So this is actually
one of the ways
that people actually
measure these things.
And there's something
even crazier that you do,
if you actually want to infer
the amplitude of the distortion
product.
And that is-- so you do
what we just did, all right?
So you've got your two
primaries, and then
the beating tone.
And then you add in
a tone at 800 hertz.
And the participant has to
adjust the amplitude and phase
of the 800 hertz tone that
you're piping into their ear.
And the idea is that, if they
can get it exactly out of phase
with the frequency that
your ear is creating,
it cancels out,
destructive interference.
And then the beating goes away.
And so you do these incredibly
painful experiments,
where you're
twiddling these knobs,
adjusting the amplitude and
phase of this 800 hertz thing
to make the beating go away.
And so we did this
once in our lab.
And it's a paper that has
only 1 and 1/2 participants.
One of the participants was the
grad student who led the study.
And he did it in
both of his ears.
And then the other participant
was another student.
And he could only bear
to do one of his ears
because it's really,
really draining to do.
But you can do it.
And you can measure
these things.
But we have an even
cooler demonstration
of this, which is
that we're going to--
let me turn down
the volume here.
All right.
So we expect that
there is a distortion
product that's 2 f1 minus f2,
the cubic distortion product.
And so the idea is that, because
there's a minus sign in front
of the f2, if we actually
induce a frequency sweep--
so we cause f2 to sweep up--
the distortion product should
sweep down in frequency.
And so that actually
makes it really easy
to hear because you
can tell that there's
this thing that you're
hearing that's going down
when the other stuff is either
staying stationary or going up.
So this is what you'll hear.
[F1 TONE]
So that's f1.
[F2 TONE]
That's f2.
And now, the both.
[F1 AND F2 TONES]
You hear it going down?
OK.
OK, let's do it again.
[F1 AND F2 TONES]
So you can see how the
stimulus is going up.
That thing that was going
down is in your ear.
It's not in the signal.
So that's a distortion product
that your ear is creating.
Any questions about
distortion products?
Yeah?
STUDENT: I don't
understand what it
means to have something
created in the ear.
Is it like a perceived thing?
Are we creating it
not in our minds?
Like, how does it have physical
tangibility in the ear?
JOSH MCDERMOTT: Well, yeah,
I use the word created
because the nonlinearity
in your ear,
it actually is reflected in the
motion of the basilar membrane.
So your basilar
membrane will actually
be vibrating at the frequency
of the distortion product.
STUDENT: [INAUDIBLE]
JOSH MCDERMOTT:
That's correct, yeah.
Yeah.
Yeah, any other
questions about that?
OK.
So take-home messages are the
ear is frequency selective.
You can't measure it
directly in humans.
You have to infer
it from masking.
So we talked a little bit
about how you do those masking
experiments.
The results of the
masking experiments
show that frequency selectivity
varies with frequency.
So at high frequencies,
it tends to be broader
than at low frequencies.
We talked about some evidence
that maybe that's a good way
to design an ear in order to
help you perform auditory tasks.
We also talked about how
frequency selectivity changes
with level.
And that's because there
is amplification that's
happening in your ears that
is both level-dependent and
frequency-specific.
So it happens at
low sound levels
at frequencies that are close
to the characteristic frequency.
And the consequence of
that is that your ear
is a nonlinear system.
And that is evident in
these distortion products
that you can hear if
you do clever things.
And so I should also emphasize
about these distortion
products--
I mean, these are
there all the time.
It's just that most of the
time you don't notice them.
It's just part of the way
the world sounds to you.
And you have to do these
funny experiments in order
to see very, very
clear evidence of them.
OK, let's start talking
about hearing loss.
So this is a graph that shows
normal auditory sensitivity.
So this is plotting detection
thresholds expressed
as the sound intensity that
you can just barely detect
as a function of frequency.
So it has this U shape.
So you're most
sensitive typically
around 2 or 3 kilohertz.
And then when
frequencies get lower,
you become less sensitive.
And when they become higher,
you're less sensitive.
So this is just what somebody
with normal hearing looks like.
This is what gets measured
when you go to the doctor.
You want to pass those out?
Yeah, sure.
STUDENT: [INAUDIBLE]
JOSH MCDERMOTT: Ah, we have
some hard copies of slides.
There's a few people
that wanted those, yeah.
OK, so this is
what gets measured.
If you go to the audiologist and
you have your hearing checked.
We do this in our lab.
This is me getting my audiogram
measured this morning thanks
to a grad student who
helped me do this.
And so this is what
it looks like if you
go to the audiologist.
These are frequencies here.
And this is the threshold here.
And I mentioned in
the previous lecture
that we often talk
about hearing level.
So there's often
SPL measurements
that are absolute
level measurements
relative to the standard.
And then hearing level is
expressed relative to what's
considered normal hearing.
So 0 would mean that you
have perfect hearing.
And my hearing is not perfect.
But it's not terrible.
It could be worse.
And you can see here that,
at higher frequencies,
I've got some significant
threshold elevation, especially
in the left ear.
So at 4,000 hertz, my threshold
is like 35 dB higher than
presumably it was
when I was born.
So if you go to the doctor,
this is the kind of thing
that they'll do.
If you're a hearing
scientist, you often
do this before you run
somebody in an experiment,
just to make sure their
hearing is normal.
And this is what they look like
as a function of age on average.
So this is that same thing, but
now averaged within age groups.
So we've got the threshold
expressed in dB HL.
So again, 0 is
considered normal.
And you can see
that, in your 20s,
which is the black curve
and 30s, the red curve,
life is pretty good.
On average, there's very, very
little threshold elevation.
But as you move beyond that--
40, 50, 60-- there
starts to, on average,
be some fairly significant
threshold elevation.
And it's just
systematic with age.
And it's really
quite significant.
So you can see that
people in their 80s,
like at these high
frequencies, 4 and 8 kilohertz,
we're talking decibels
of threshold elevation,
so pretty substantial.
So this is a massive
public health problem
because it basically
happens to almost everybody.
And there's lots
and lots of interest
in trying to understand both why
this occurs, how to treat it,
whether to prevent
it, things like that.
Yeah?
STUDENT: So does this
graph-- as you go higher,
does it gradually go up?
Or does it asymptote
at some point
once you get like,
higher [INAUDIBLE}.
If you extended this
frequency all the way to like
20 kilohertz does is it--
is it an asymptote?
JOSH MCDERMOTT: No.
So it would--
STUDENT: [INAUDIBLE]
JOSH MCDERMOTT:
Yeah, it'll look--
STUDENT: [INAUDIBLE]
JOSH MCDERMOTT: Oh,
well, you just--
that would be hard to measure.
But yeah, no, you
wouldn't really
bother measuring anything
that's more than 80 decibels
because it's just not really
practically very relevant.
But yeah, I mean,
it'll look worse.
So I mean, typically if you
take somebody in their 30s,
they will have threshold
elevation in the high teens
of kilohertz.
Yeah, the very high frequencies
are the most vulnerable.
And that's where you see the
biggest threshold shifts.
Did you have a question?
STUDENT: Yeah, I
was going to ask
if there's any hearing loss
that's characterized with losing
lower frequency sounds, and
then still being able to hear
the higher frequencies.
JOSH MCDERMOTT: Yes.
It's more unusual and
typically associated
with particular genetics.
But yeah, you do you do
find people like that.
Yeah?
STUDENT: What's the deal
with the 40 and 50-year-olds?
JOSH MCDERMOTT: I think
that's a midlife crisis.
No.
I mean, I think the
sample size here
is just-- it's not infinite.
And so there are
error bars on these.
But yeah, we would
certainly expect
that this would be
monotonic with age
if you had enough data, yeah.
Yeah?
STUDENT: [INAUDIBLE]
JOSH MCDERMOTT: So we'll
talk about conductive losses
in a second.
Those are not so common.
So this is really
just reflecting
typical age-related
hearing loss that just
happens to almost everybody.
There are specific diseases that
would have different phenotypes
that are less common.
Yeah?
STUDENT: Is this true for
people living in all places
or if you're rural--
JOSH MCDERMOTT: Stay tuned.
Yeah, great.
That's a great question, yeah.
OK.
So just to give you a sense
of the significance of this,
this is the amount
of attenuation
that you would get from
having earplugs in your ears
or just putting your
hands over your ears.
So this is sound frequency
and the amount of attenuation.
So earplugs maybe give you
20 or 30 dB attenuation more
at high frequencies
than at low frequencies.
Putting your hands over
your ears gives you that.
So this is on par with or
maybe not even as extensive
as what you would have if you
just get older on average.
So there's two kinds
of hearing loss
that we will typically
distinguish between.
I hope you don't do
that the whole lecture.
So there's conduction
loss, which
we were just talking about.
So that's an impairment in
the mechanical transmission
of sound energy
to the inner ear.
So it's typically a problem
with the outer or middle ear.
So for instance, if
the bones in your ear
don't move as well
as they should,
you won't get as much energy
into the cochlea as you should.
And your hearing will be worse.
So that's contrasted with
sensory/neural loss, which
is an impairment in the
transduction of sound energy
to electrical signals or in
their transmission to the brain.
And that's usually due to
problems with the inner ear.
So conduction loss can
involve the puncturing
of the eardrum-- for instance,
via an ear infection.
There's also otosclerosis,
which was just asked about.
So that's a disease
that involves
the gradual immobilization
of the stapes bone
and the ossicles.
So it just doesn't move as well.
It's inherited.
And the good news is
that this can usually
be treated pretty effectively.
So they can perform
surgeries that
will replace the stapes bone.
And that's a pretty common
surgery for an ear surgeon
to perform.
Yeah?
STUDENT: [INAUDIBLE]
JOSH MCDERMOTT: I forget.
I'm not sure.
Yeah, I can find out.
So sensory/neural loss is
the more vexing problem
that most of us deal with.
So one aspect of this
is what's normally
referred to as presbycusis.
So that's the thing that
was just on that graph
that we were showing,
which refers to the fact
that, as people age, they become
less sensitive and particularly
less sensitive to
high frequencies.
So we didn't see
this on the graph.
But as I was alluding
to, most people over 30
typically can't hear
above 15 kilohertz.
Most people over 50 can't
hear above 12 kilohertz.
So did any of you-- like when
maybe you were in high school,
did you have those high
frequency ringtones
that your parents couldn't hear?
Or you've heard of them?
Your friends have them?
Anyhow, this is a thing, right?
You can program your phone
to have a very high frequency
ringtone, if you don't want
your parents to know that you're
getting phone calls.
And it's because older
people can't hear
these really high frequencies.
OK, so it's unclear
what causes presbycusis.
There appears to be
a genetic component.
And part of what makes this--
part of what makes
this hard to understand
is that while people
are alive, it's
really hard to actually
see inside their ears.
So you can measure the fact that
somebody's hearing is worse,
but you can't really look inside
their ear, their auditory nerve,
and actually
directly observe what
would be different
about somebody
who has poor hearing compared to
somebody who has great hearing.
So one of the main ways
that this has been studied
is what is called otopathology.
This is postmortem
studies of the cochlea.
So when people die, if they
donate their bodies to science,
the cochlea can be removed.
You can chop it up, put
it under a microphone,
and then look at it in all
kinds of different ways.
And so one of the classic
things that has been done
is to actually count
the number of hair cells
that are present in a
person when they die.
So this is an example of
a slice of the cochlea.
This is the organ of Corti,
so basilar membrane here.
And we've got outer hair
cells here and an inner hair
cell here.
So you look at these
things under a microphone
and you count them up.
And so these would
be different slices
along the cochlear spiral.
And you just count the presence
or absence of outer hair cells.
So you see three here.
And inner hair cells,
you see one there.
So present, absent as a function
of distance from the base.
In fact, our neighbors across
the river at the Mount Sinai Ear
Institute are a worldwide
leader in this kind of thing.
So they have lots and
lots of data on this.
And these slides are
actually borrowed
from my colleague, Charlie
Lieberman, who works there.
So these are results of a
couple studies that did this.
So they get these
cadaver cochlea.
And they know the age at
which the person died.
And it can be just
anywhere on this range.
So each dot here is a person.
And the graph here is plotting
the percent of hair cells
that are present in that
individual at death.
And we have IHC-- that's
inner hair cells--
on the left and OHCs--
that's outer hair
cells-- on the right.
And the different colors are
just two different studies,
one in 1968 and one from
a couple of years ago.
And what these
graphs show is that,
as the age of an individual
increases, at death,
they have fewer hair cells.
So there's a few
people here who,
unfortunately, died very young.
And you can see that
they have almost all
of the hair cells remaining.
And then it, on average,
gradually drops off with age.
So this is a graph that
plots the hair cell
survival as a function of
position on the cochlea.
So the previous graph is just
pulling everything together.
And here, we have
hair cell survival
as a function of
position on the cochlea.
And what this shows is
that, for inner hair cells,
there's considerably
more hair cell loss
at the base of the cochlea.
And which frequencies get
transduced at the base?
High or low?
High, that's right.
So base transduces
high frequencies.
So that's consistent, in
principle, with the fact
that people tend to lose their
hearing at high frequencies more
than low.
You can see that outer hair
cells also tend to be lost,
but it's more distributed
across the cochlea.
So both the base and the apex
have outer hair cell loss
and even in the middle.
So this is a study.
So you can also look
at this in lab animals.
And these are graphs that plot
five different species of lab
animal-- gerbils, chinchillas,
mice, rats, and guinea pigs.
And this is their
outer hair cell
survival as a function of
position along the cochlea.
And if you compare
that to humans,
there's this
interesting difference,
that humans seem to have
considerably more outer hair
cell loss at the
base of the cochlea.
Now, what is it that's different
about humans than all these lab
animals?
Well, the lab animals
lead very quiet lives.
They sit in a
boring room in a lab
and are not exposed to
all of the noise and rock
concerts and stuff that
normal humans get exposed to.
So you might imagine that this
is consistent with the idea
that some component of this
is related to noise exposure.
So there's this hypothesis that
prolonged exposure to noise,
possibly even that which occurs
Incidentally in industrialized
societies, likely plays a role.
And so this gets
back to the question
that was asked a little
bit earlier, which is
what happens in other places.
So there's a couple
of intriguing studies
that have been done that suggest
that, in non-industrialized
places, there's quite a bit less
of age-related hearing loss.
So this is one study that
was done in 1962 in a fairly
remote area in Africa.
So it says, in the
description here,
the area chosen is about 650
miles southeast of Khartoum,
the capital of the
Republic of the Sudan,
a few miles from
the Ethiopian border
and 10 degrees
above the equator.
Until 1956, this area
was a closed one,
untouched by any foreign
culture or civilization.
So they went to this place
and measured audiograms.
And the results are shown here.
So this is this group of
people called the Mabaans.
And they compared the
results to a very large study
of hearing that was conducted
at the Wisconsin State
Fair in 1954.
They set up a booth at
the Wisconsin State Fair.
And all these people came and
had their hearing measured.
And so people in Wisconsin
in the '50s show something
that's consistent with the
graph that I showed you earlier.
So as a function of age,
hearing gets worse, especially
at high frequencies.
So the Mabaans,
on the other hand,
show much less of this
age-related hearing loss.
Yeah?
STUDENT: What does it mean
when [INAUDIBLE] negative?
JOSH MCDERMOTT: Yeah.
I mean, the 0 is just--
it's like a standard.
It's supposed to be like
the average person who has
good hearing, normal hearing.
So you can do better
than that, yeah.
So you might think this
is circumstantial evidence
that, well, there's
presumably some difference
between the people in
Wisconsin and the Mabaans
that accounts for this.
And there could
be lots of things.
But one candidate is the fact
that industrialized society
is very noisy.
We're around noisy
machinery all the time.
And that might not be
good for our hearing.
So the other study that
was done along these lines
was conducted on Easter Island.
This is an island that's off
the coast of South America.
It has been called the most
isolated inhabited place
in the world.
And I guess, at some point--
I don't know if this
is still the case.
But it was known as the
Island of the Great Silence
because it's non-industrialized.
So you don't have modern
day machinery there.
At least, you didn't at the
time when this was done.
And so what they
did is they went
to Easter Island and measured
audiograms of people there.
Now, people who live on
Easter Island, I guess,
would occasionally go to
mainland South America
for some period of time, like
to work for a little bit,
and then sometimes come back.
And so the researchers divided
the participants in this study
into those that had
never left Easter Island,
and to those that had been
away on mainland South
America for three to five years,
and those that had been away
more than five years.
And so this is the average
audiogram for those three groups
of people.
So what this shows is
that the people that
had been on mainland South
America for some period of time
had worse hearing than the
ones that had never left.
Interestingly, if you take the
group of people that had never
left and you subdivide
them according to age,
you still see signs of
age-related hearing loss.
So the older participants
have worse hearing
than the younger participants.
But this, again, is
circumstantial evidence
that something about living
on mainland South America
causes your hearing
to deteriorate.
And it could be noise exposure.
So there's this hypothesis that
the incidental noise exposure
that happens with modern
life may contribute
to age-related hearing loss.
And I think it's plausible
that we evolved in conditions
that were just much less noisy.
And so the ears are
just ill-equipped
for the sound levels that
we encounter in life today.
That seems possible.
Now, what's much
less controversial
is that acute noise exposure
can cause hearing loss
through damage to
the organ of Corti.
So if you get
exposed to something
that's really, really loud--
it could be gunshots,
could be an airplane,
if you're an airplane mechanic--
we have pretty clear
evidence that that's not
good for your hearing.
And some of the
clearest evidence
actually comes from this really
interesting study of hunters.
So this is a person
holding a rifle.
And in this
particular study, they
recruited people who, I
guess, were aspiring hunters.
And they measured
their audiograms
before they learned
how to hunt, and then
after they had been
hunting for a while.
So the person's
holding the rifle--
and the idea is that there's
some-- you fire the gun.
And there's an explosion in
here that causes a big sound
wave to come out.
And there's a direct
path from the source
of the sound wave
and the left ear,
whereas the right ear is
shielded from the sound.
And what you can see here are
the pre-exposure audiograms.
Those are the solid lines.
So the x's are the left ears
and the o's are the right ears.
And then the post-exposure
audiograms-- so
you can see that
post-exposure-- so
that means after the person
started hunting-- the thresholds
are elevated.
But they're substantially
more elevated
on the left than the right,
consistent with what you would
expect from the noise exposure.
OK.
Eventually, the people
who became hunters
passed away and donated
their ears to science.
And this is the result of
otopathology done on their ears.
So we've got the left
ear and the right ear.
And these are the counts of
inner hair cells and outer hair
cells.
And so there's three
lines, because there's
three rows of outer
hair cells typically,
along the length of
the basilar membrane.
And you can see that, at
the basal end of the basilar
membrane in the
left ear, there's
this precipitous drop in
the presence of hair cells.
And certainly, the right ear
also doesn't look normal.
But it's not nearly
as pronounced
as what you see in the left ear.
And we, again, think that's
because the right ear is
protected by the
acoustic shadow.
Any questions about that?
Yeah?
STUDENT: So have
there been studies
where lab animals have
been exposed to noise
and their hearing is measured?
JOSH MCDERMOTT: Yeah,
there's lots of those.
In fact, that is what we are
going to talk about next.
Yeah, so we know quite a lot
about the temporary or transient
effects of noise exposure from
these studies of lab animals,
yeah.
Any other questions about this?
So OK, before we
wrap, if there's
one thing that you take away
from this class, wear earplugs.
You're going out to hear music?
Wear earplugs.
You'll be happy
when you're older.
And in fact, the
thing that I'm going
to tell you next, which will
have to wait until next time,
is going to be some
particularly sobering evidence
that actually hearing
protection is important,
because one of the other
things that can happen
is, in addition to these
threshold shifts that show up
in the audiogram, so where
your thresholds get elevated,
there are also temporary
threshold shifts.
So if you get exposed to
moderately loud sounds--
this is like the
rock concert effect.
You go out to a
nightclub or a concert.
You probably have
this experience
that you leave and you can tell
that your hearing is not normal.
It's harder to hear.
Maybe you have some ringing.
And that's measurable.
So these are temporary
threshold shifts.
So if you went and measured
your audiogram right
after you went to the
nightclub, the thresholds
would be elevated.
But then they go back to normal.
You wait a day or
even a few hours
and they go back to normal.
But as we will see
next time, there's
reason to believe that, even
though your thresholds return
to normal, your auditory
system has potentially
been altered by this.
And we will hear
about that next time.