Video Transcript
In this video, the topic we’re
talking about is sound waves. Sound waves of course are
responsible for all the music we hear as well as the speech we hear. And as we get into it, we’ll see
that sound waves are interesting not just for the information they carry, but what
they do to the medium in between the source of the sound wave and the person
listening.
We can begin our discussion with
the age-old question: if a tree falls in the forest and no one’s there to hear, then
does it make a sound wave? Well, on second thought, how about
we start out with an easier question? Let’s consider what is a sound
wave. One of the first and most
interesting things to know about sound waves is that they can’t exist on their
own. They need some sort of medium, some
sort of material to move through. Otherwise, they can’t exist.
So let’s say we start out with some
material. Let’s say that each one of these
blue dots is an air molecule. And let’s also say that this is air
at ground level, so at standard temperature and pressure. Under normal conditions like these,
these molecules are moving in all directions randomly. They are bouncing into one another
and in general moving every which way. So we have this randomly moving but
fairly evenly distributed massive air. And let’s say at one end of this
air mass, we set up a gigantic speaker. We turn the speaker on and it
starts to energize the air molecules nearby it. Not only this powered-on speaker
distribute energy to the air molecules it comes in contact with, but it does this
energy distribution in a particular way, in a wave or a sinusoidal pattern.
Here’s what starts to happen. These individual air molecules
start to move left and right within this mass. If we could see it with our eyes,
we would notice that the molecules start to bunch up in lines. The molecules collect at these
regularly spaced intervals. And we see that in between these
points — in between the high-density points — there are far fewer air molecules. So whereas before all these air
molecules were fairly evenly spread out, now we see they’re bunching together and
creating gaps between the bunches. And this isn’t all that takes place
when we power on the speaker. We would also start to see these
bunches of air molecules start to move in the direction away from the speaker.
What we have then is an alternating
series of high-concentration areas of air molecules with low-concentration areas
that’s moving left to right; it’s moving in a wave. And then, if we could look even
closer, we would see something really amazing going on at the level of individual
air molecules. Let’s say we pick this molecule
right here and we keep our eye on that as the wave moves from left to right. As that happens, what we would
notice about this particular air molecule or any specific air molecule we looked at
individually is that its net motion, its overall motion as these areas of high
concentration and low concentration pass by is actually zero. These bunches of molecules pass by
and pass through this point. And the molecule we’ve highlighted
is part of that overall motion. And yet, if we kept an eye on this
molecule over many cycles of this wave, we would see that even as the wave moves
forward left to right, this molecule overall stays in place.
In answer to the question what is a
sound wave, we can say that a sound wave is what we’ve drawn here. It’s a regularly alternating series
of high- and low-concentration areas of a given material. Now, it turns out that these
high-concentration and low-concentration areas of a sound wave have particular
names. Each high-concentration area where
all the molecules are bunched closely together is called a compression. That makes sense since it looks
like all the molecules are compressed together into a small space. And then in between those
compressions, in between the high-concentration areas, the low-concentration areas
are called rarefactions. One way to help with remembering
what this word means rarefactions is to see the word rare in it and to realize it
indicates an area where the material that the sound wave is passing through is
rare. It’s a low-density area.
Now that we know these two terms,
we can update our definition of what a sound wave is. We can now say that a sound wave is
a regularly alternating series of compressions and rarefactions of a material. And if we consider just what kinds
of materials our sound waves can travel through, it really runs the gammon. Solids, liquids, and gases are all
candidate materials for sound waves. The main requirement for a sound
wave is that there be a material of some type, whatever type it is. Imagine what would happen to this
sound wave, for example, if we were to erase all the blue dots, that is get rid of
all the air molecules. There wouldn’t be any material to
make a wave from. So the wave would disappear.
Now we’ve been using this word
“wave” to describe sound. But what we’ve drawn here on screen
doesn’t perhaps look like a wave to our eye. Often when we think of a wave, in
our minds eye it looks something like this, like something that goes up and down
perpendicular to the direction of the wave motion. It turns out though that this
picture of a wave is just one kind of wave. Not all waves have this property,
where the amplitude of the wave goes up and down, while the motion of the wave goes
left to right. In fact, sound waves are great
examples of a wave type that isn’t like this.
The sound wave that we’ve drawn
here does indeed move left to right, just like this other type of wave we sketched
in. But for the sound wave, the peaks
and the troughs, where our compressions are peaks and the rarefactions are troughs,
instead of moving up and down, these peaks and these troughs move left and right
along the same axis as the wave motion. Sometimes, we may see sound waves
represented by a wave that looks like this. But strictly speaking, that’s not
entirely accurate. In a way, representing a sound wave
like this is familiar and therefore a bit helpful. But the problem with this
representation is that it has parts of the wave as we sketched in moving up and down
perpendicular to the direction that the wave moves. And as we said, sound waves don’t
behave this way.
For a sound wave moving left and
right, the peaks and troughs move on the same axis or along the same dimension left
and right as well as the wave itself. Now considering this sound wave,
what would you say one wavelength of the wave is? We know that in general the
wavelength of a wave is the distance it takes for the wave to go through one
complete cycle of its own motion. For the type of wave we just
sketched in then, this would be one wave length. And note that we could also
represent the wavelength as the distance from one peak to an adjacent peak or one
trough to an adjacent trough and so on.
Now, that’s helpful to us when it
comes to sound waves because these kinds of waves have compressions as their peaks
and rarefactions as their troughs. We could measure the wavelength of
this sound wave starting at a compression then and moving one compression over. That distance — we could call it 𝑑
— is equal to the wavelength of this wave. In a similar way, we could also
start at a rarefaction — the midpoint between two compressions — and then go one
rarefaction over. And that distance would also be 𝑑
one wavelength.
Now if this is a sound wave, that
means if a person stood here and listened, they could hear this sound, right? Well, it turns out that the answer
to this depends on a property of the wave, known as its frequency. Here is the idea with
frequency. Let’s say we were to put an
observer right here and the observer had a counter. As this sound wave moved along left
to right and the compressions and rarefactions pass to the stationary observer, the
observer would count every time a compression moved past. Now let’s imagine that in one
second of elapsed time, the observer measured three full cycles of this wave, three
compressions that passed by. In other words, there were three
wave cycles in this one second. Now if we were to divide the number
of cycles by the number of seconds, we can see that we get a result of three
complete wave cycles passing that point of the observer every second.
This unit cycles per second can be
expressed another way. One cycle per second is known as
one hertz, a unit named after the famous physicist Heinrich Hertz and abbreviated
capital Hz. So instead of saying that our wave
has three cycles that pass a point every second, we can instead say that it has a
frequency of three hertz. When it comes to human hearing,
sounds with a lower number of hertz, a lower frequency, sound lower and sounds with
a higher frequency sound higher. That’s how our ear perceives lower
and higher frequencies. Our ears aren’t sensitive to all
sound wave frequencies, but instead operate within range. Roughly speaking, if a sound has a
frequency of at least 20 hertz, that is it goes through at least 20 wave cycles
every second, then our ears are able to hear it.
Assuming that the wave frequency
isn’t higher than about 20000 hertz or 20000 cycles per second, now these numbers
the lowest and the highest frequencies the ear can hear are a little bit different
for each person and they also change as we age. But roughly speaking, if the sound
coming out of this speaker is between 20 hertz and 20000 hertz, then this person
standing by the speaker would be able to hear it. Of course, the range of human
hearing doesn’t limit the types of sound waves that are out there in the world. There are waves for example that
have lower frequencies than 20 hertz. These are called “infrasonic
waves,” where infra means below, that is below the human hearing range. And then on the other end of
things, for waves with frequencies higher than 20000 hertz, those waves are
sometimes referred to as “ultrasonic waves” where ultra stands for above or
beyond.
Now just because a sound is beyond
the range of human hearing, that doesn’t mean there no other animals that can hear
that sound. For example, dogs, cats, and
dolphins are all capable of hearing sounds with higher frequencies than we are able
to hear. And at the other end of the
spectrum, animals like elephants, whales, and alligators can hear sounds that are
infrasonic to our ears. Now when we talk about the
frequency of a sound wave or any wave for that matter, that frequency is typically
represented using a lowercase 𝑓. And we’ve seen that the wavelength
of a wave is represented using the Greek letter 𝜆.
Now there’s something interesting
that happens if we multiply 𝜆 by 𝑓, that is the wavelength of a wave by its
frequency. To see what that might be, consider
that the wavelength of a wave has units of meters, whereas the frequency of a wave
has units of hertz which is the same as cycles per second. Multiplying these two values
together then, we get a result with the overall units of distance, a length, divided
by a time. Going further, we know that the
speed of an object is equal to the distance that object travels divided by the time
it took to travel that distance. When we multiply wavelength by wave
frequency, we indeed do get a speed often represented as 𝑣.
So if we know the wavelength of a
wave and we know its frequency, then we can take their product and solve for the
wave speed. And like we said, this is true not
just for sound waves but for any waves. Now knowing all this about sound
waves, let’s get a bit of practice with these ideas through an example.
A submarine’s sonar scanner uses
sound waves that reflect from objects around the submarine. The submarine emits sound waves
vertically downward and detects their reflection 6000 milliseconds later. The sea beneath the submarine is
4713 meters deep. What is the speed of the sound
waves? Answer to the nearest meter per
second.
Okay, so we have this
submarine. And we’re told that it emits sound
waves vertically downward. We know that the way sonar works is
when these sound waves run into something — in this case the seafloor — they’ll
bounce back and be received by the source that emitted them, the submarine. We’re told two things about this
scenario. First that the submarine is 4713
meters above the sea floor and then second we’re told that the time it takes to emit
and then receive back that sonar signal is 6000 milliseconds. Based on this, we want to figure
out what is the speed of the sound waves as they travel through the sea.
To start working toward our
solution, let’s make an assumption. Let’s assume that the speed of the
sound waves is constant as they travel from the submarine to the seafloor and
back. Under that assumption, we can use
the fact that the average speed of an object — we’ll call it 𝑣 — is equal to the
distance the object travels divided by the time taken. Now if we call the speed of the
sound waves we want to solve for 𝑣, then that’s equal to the total distance
travelled by the waves divided by the time taken to travel that distance.
Looking at the waves in our sketch,
we know that they go down 4713 meters until they run into the seafloor and then they
reflect off the floor and go back up that same distance until they reach the
submarine. That means the distance they travel
is two times 4713 meters. And then when it comes to time,
we’re told that the total elapsed time for these reflected sound waves to be
detected by the submarine is 6000 milliseconds. But instead of using units of
milliseconds in our calculation, we’d like to use units of seconds. To make that conversion, we can
recall that 1000 milliseconds is equal to one second. Therefore, 6000 milliseconds is
equal to six seconds.
Now, solving for wave speed 𝑣 just
involves calculating this fraction: two times 4713 meters divided by six
seconds. To the nearest meter per second, 𝑣
is 1571 meters per second. That’s the speed of this sound wave
through the sea.
Let’s take a moment now to
summarize what we’ve learned in this lesson on sound waves.
First off, we learned that a sound
wave is a regularly alternating series of high- and low-concentration areas in a
given material. We saw that these areas of high
concentration also considered the peaks of the sound wave are known as compressions
and that the low-concentration areas we can considered them the troughs of the sound
wave are called rarefactions. Another learning point is that
sound waves cannot travel through empty space. They need a medium, some kind of
material to move through. When it comes to human hearing, our
ears are sensitive to sound waves with frequencies from about 20 to 20000 hertz or
20 to 20000 cycles every second. And lastly, we saw that the speed
of a sound wave and indeed the speed of any wave is equal to the frequency of that
wave multiplied by its wavelength.
