Video: Sound Waves

In this lesson, we will learn how to describe sound wave propagation, define audible frequencies, and explain the applications of reflections of sound waves.

14:00

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.

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