7. Waves

including UFOs, earthquakes, and music

Two strange but true stories

The following two anecdotes, Flying Saucers and Rescuing Pilots, are actually closely related, as you will see later in this chapter. They both will lead us into the physics of waves.

Flying saucers crash near Roswell, New Mexico

In 1947, devices that the U.S. government called “flying disks” crashed in the desert of New Mexico. The debris was collected by a team from the nearby Roswell Army Air Base, which was one of the most highly classified locations in the United States. The government put out a press release announcing that flying disks had crashed, and the story made headlines in the respected local newspaper, The Roswell Daily Record. Take a moment to look at the headlines for July 8, 1947:

Serious newspaper headlines from the respected Roswell Daily Record, RAAF stands for “Roswell Army Air Force”.

The next day, the U.S. government retracted the press release, and said their original announcement was mistaken. There were no flying disks, they claimed. It was only a weather balloon that had crashed. Anybody who had seen the debris knew it wasn’t a weather balloon. It was far too large, and it appeared to be made from some exotic materials. In fact, the object that crashed was not a weather balloon. The government was lying, in order to protect a highly classified program. And most people could tell that the government was lying.

The story I have just related sounds like a fantasy story from a supermarket tabloid--or maybe like the ravings of an anti-government nut. But I assure you, everything I said is true. The story of the events of Roswell, New Mexico is fascinating, and not widely known, since many of the facts were classified until recently. In this chapter I’ll fill in the details so that the Roswell story makes sense.

Incidentally, if you are unfamiliar with the name Roswell, that means you have not watched the TV program “The X Files” or read any of the other voluminous literature about flying saucers and UFOs. Try doing an Internet search on Roswell in 1947 and see what you find. Be prepared to be astonished.

Now for the second anecdote.

Rescuing Pilots in World War II

The true story of the flying disks began with an ingenious invention made by the physicist Maurice Ewing near the end of World War II. His invention involved small objects called “sofar” spheres that could be placed in the emergency kits of pilots flying over the Pacific Ocean. If a pilot was shot down, but he managed to inflate and get on to a life raft, then he was instructed to take one of these spheres and drop it into the water. If he wasn’t rescued within 24 hours, then he should drop another.

What was in these miraculous spheres? If the enemy had captured one and opened it up, they would have found that the spheres were hollow with nothing inside. How could hollow spheres lead to rescue? How did they work?

Here’s the answer to the sofar question: Ewing had been studying the ocean, and he was particularly interested in the way that sound travels in water. He knew that the temperature of the water got colder as it got deeper--and that should make sound travel slower. But as you go deeper, the pressure gets stronger, and that should make the sound travel faster. The two effects don’t cancel. When he studied it in detail, he concluded that the sound velocity would vary with depth. His most interesting conclusion was that at a depth of about 1 km, the sound travels slower than at any other depth. As we will discuss later, this implies the existence of a “sound channel” at this depth, a layer that tends to concentrate and focus sound and keep it from escaping to other depths. Ewing did some experiments off the coast of New Jersey and verified that this sound channel existed, just as he had predicted.

The sofar spheres were hollow and heavier than an equal volume of water. They sank but were strong enough to hold off water pressure until they reached the depth of the sound channel. At that depth the sphere suddenly collapsed with a bang. That sent out a pulse of sound that could be heard thousands of kilometers away. From these sounds, the Navy could figure out the approximate location of the downed pilot, and send out a rescue team.

It turns out (this wasn’t known back then) that Ewing’s little spheres used the same phenomena that whales use to communicate with other whales: the focusing of sound in the sound channel. We’ll discuss this shortly.

At the end of World War II, the same Maurice Ewing proposed a second project based on the same idea. This project was eventually given the name Project Mogul. It used “flying disks” for a highly classified purpose: to detect nuclear explosions. It made use of a sound channel in the atmosphere. But the flying disks crashed in Roswell, New Mexico in 1947, made headlines, and became part of a modern legend.

To explain these stories, we have to get into the physics of sound. And to understand sound, we have to talk about waves.

Waves

All waves are named after water waves. Think for a moment about how strange water waves are. Wind pushes up a pile of water, and the pile creates a wave. The wave moves and keeps on moving, carrying energy far from the place where the wave was created. Waves at the coast are frequently an indicator of a distant storm. But the water from that distant storm didn’t move very far, just the wave. The wind pushed the water and the water pushed other water and the energy traveled for thousands of miles, even though the water only moved a few feet.

You can make waves on a rope or with a toy called a slinky. (If you’ve never played with a slinky, you should go to a toy store as soon as possible and buy one.) Take a long rope or a slinky, stretch it across a room, shake one end, and watch the wave move all the way to the other end and then bounce back. (Water waves, when they hit a cliff, also bounce.) The rope jiggles, but no part of it moves very far. Yet the wave does travel, and with remarkable speed.

Sound is also a wave. When your vocal cords vibrate they shake the air. The air doesn’t move very far, but the shaking does. The shaking moves as far as the ear can hear and further. The initial shaking air around your vocal cords makes the air nearby shake also, and so on. If the shaking reaches someone else, then it causes his eardrums to shake, which sends signals to his brain and causes him to hear you.

For a nice animation of a sound wave, showing how the molecules bounce back and forth but create a wave that moves forward only, see http://www.kettering.edu/~drussell/Demos/waves/wavemotion.html

If the sound wave hits a wall, it bounces. That’s what gives rise to echoes. Sound waves bounce just like water waves and rope waves.

A remarkable thing about all these kinds of waves is that the shaking leaves the location where it started. Shake some air and you create a sound, but the sound doesn’t stay around. A wave is a way of transporting energy long distances without actually transporting matter. It is also a good way to send a signal.

It turns out that light, radio, and TV signals also consist of waves. We’ll get to that in the next chapter. What is waving for these? The traditional answer is “nothing” but that is really misleading. A much better answer is that there is a “field” that is shaking – the electric and magnetic fields. Another correct answer is that “the vacuum” is what is shaking. We’ll discuss this further in the chapter on quantum mechanics.[1]

Wave packets

Waves can be long with many vibrations, as when you hum, or they can be short, as in a shout. We call such short waves “wave packets.” You may have noticed water waves often travel in packets. Splash a rock into a pool and you’ll see a bunch of waves moving out, forming a ring that contains several up and down oscillations. That’s a packet. A shout contains many oscillations of the air, but these oscillations are confined to a relatively small region. So that too is a wave packet.

Now think about this: short waves act in a way very similar to particles. They move and they bounce. They carry energy. If the packet were extremely short, maybe you wouldn’t notice that it was really a wave. Maybe you would think it was a small particle.

In fact, the theory of quantum mechanics is really a fancy name for the theory that all particles are really little packets of waves. The packets for an electron and proton are so small that we don’t normally see them. What is waving in an electron? We think it is the same thing that is waving for light: the vacuum.

So when you are studying sound, water, and earthquakes, you are really learning the properties of waves. That will be most of what you need to understand quantum mechanics.

Sound

Sound in air results when air is suddenly compressed, for example by a moving surface (such as a vibrating vocal cord or bell). The compression pushes against adjacent air, and that pushes against the air in front of it, and so on. The amazing thing about sound is that the disturbance travels, and the shaking of the original air stops. The energy is carried away very effectively.

Sound is generated in air when something compresses it in a local region. This could be the vibrating of vocal cords, a violin string, or a bell. The compressed air expands, and compresses the air next to it. The air never moves very far, but the compression is passed on from one region to the next. This is depicted in the following diagram. Each little circle represents a molecule. The wave consists of compression and expansion of regions of the gas.

Each molecule shakes back and forth, and doesn’t travel very far. But the waves travel forward. Look at the diagram, and imagine that you are looking at a series of water waves from an airplane. But the waves in sound don’t come from up and down motion, but from compression and dilation. When these compressions reach your eardrum, they make it vibrate. Those vibrations are then passed on through the rest of your ear to nerves and then to the brain, where the vibrations are interpreted as sound.

To understand this, it is easiest to watch a movie. A very nice one is posted at www.kettering.edu/~drussell/Demos/waves/wavemotion.html. A wave is moving from the left to the right. But if you watch one molecule, you’ll see that it is shaking back and forth, and never travels very far. It bangs into a nearby molecule, and transfers its energy.

That is the key aspect of waves. No individual molecule travels very far, but the energy is transferred. They pass on the energy, from one to the next. It is the energy that travels long distances, not the particles. Waves are means for sending energy without sending matter.

Sound waves can travel in rock, water, or metal. All those materials compress slightly, and this compression travels and carries away the energy. If you hit a hammer on a railroad rail, then the metal rail is momentarily distorted and the distortion travels down the rail. If someone puts her ear to the rail a mile away, she will hear the sound. The best way to hear the sound is to put your head against the rail. The vibration in the rail will make your skull vibrate, and this will make the nerves in your ear respond--even if none of the sound is actually in air.

Because steel is so stiff, it turns out that sound travels 18 times faster in steel than in air. In air, sound takes 5 s to go 1 mi; in steel, sound will go that same distance in less than 1/3 s. In the olden days, when people lived near railroad tracks, they could listen to the track to hear if a train was coming, and they could even estimate the distance to the train by the loudness of the sound.

For sound to travel, the molecules of air have to hit other molecules of air. That’s why the speed of sound is approximately equal to the speed of molecules. We discussed this fact in Chapter 2. But in steel, the molecules are already touching each other. That’s why sound in steel can move much faster than the thermal velocity of the atoms in the steel.

Sound travels in any material that is springy, i.e. which returns to its original shape when suddenly compressed and then released. The faster it springs back, the faster the wave moves. The speed of sound in water is about 1 mi/s, but it varies slightly depending on the temperature and depth of the water.

Note that a sound wave in water is a different kind of wave than the water wave that moves on the surface. In water, sound travels under the surface, in the bulk of the water. It consists of a compression of the water. Water waves on the surface are not from compression, but from movement of the water up and down, changing the shape of the surface. So although they are both in water, they are really very different kinds of waves. You can see surface waves easily. You usually cannot see sound waves. Surface waves are slow and big. Sound waves are microscopic and fast.

The speed of sound in air doesn’t depend on how hard you push, that is, on how intense the sound is! No matter how loud you shout, the sound doesn’t get there any faster. That’s surprising, isn’t it?

Why is that true? Remember, at least for air, the speed of sound is approximately the speed of molecules. The signal has to go from one molecule to the next, and it can’t do that until the air molecule moves from one location to another. (The added motion from the sound vibration is actually very small compared to the thermal motion of the molecules.) When you push on the air, you don’t speed up the molecules very much; you just push them closer to each other.

But the speed of sound does depend on the temperature of the air. That’s because the speed depends on the velocity of the air molecules, and when air is warmer, the velocity is greater.

The table below gives the speed of sound in several materials:

material and temperature	speed of sound
air at 0 C = 32 F	331 m/s = 1 mi for every 5 s
air at 20 C = 68 F	343 m/s
water at 0 C	1402 m/s = 1.4 km/s
water at 20C	1482 m/s = almost 1 mi/s
Steel	5790 m/s = 3.6 mi/s
Granite	5800 m/s

There is no need to memorize this table. But you should remember that sound moves faster in solids and liquids than in air. And you should know that the speed of sound in air is about one mile every five seconds.

Sound traveling in rock gives us very interesting information about distant earthquakes. We’ll come back to that later in this chapter. Observations of the surface of the sun show sound waves arriving from the other side, traveling right through the middle of the Sun. Much of our knowledge of the interior of the Sun comes from the study of these waves. (We detect them by sensitive measurements of the surface of the Sun.) Sound has been detected traveling through the Moon, created by meteorites hitting the opposite side. On the Moon we use instruments that were left behind by the Apollo astronauts.

There is no sound in space because there is nothing to shake. A famous tag line from the science fiction movie Alien (1979) is, “In space, nobody can hear you scream.” Astronauts on the moon had to talk to each other using radios. Science fiction movies that show rockets roaring by are not giving the sound that you would hear if you were watching from a distance--since there would be no sound.[2]

Transverse and longitudinal waves

When you shake the end of a rope, the wave travels down its length, from one end to the other. However, the shaking is sideways, i.e. the rope vibrates sideways even thought the direction that the wave is moving is along the rope. This kind of wave is called a transverse wave. In a transverse wave, the motion of the particles is along a line that is perpendicular to the direction the wave is moving.

For an illustration of a transverse wave, go back to:

http://www.kettering.edu/~drussell/Demos/waves/wavemotion.html

and look at the second illustration on that page.

A sound wave is different. The vibration of the air molecules is back and forth, in the same direction that the wave is moving. This kind of compressional wave is called a longitudinal wave. In such a wave, the motion and direction of the wave are both along the same line.

This may seem peculiar, but water waves are even stranger.

Water surface waves

Water waves (the term we will use when we mean the ordinary surface water waves--as opposed to water sound waves) gave all waves their name. If you are swimming or floating and a water wave passes by, you move slightly back and forth as well as up and down. It is worthwhile to go swimming in the ocean just to sense this. In fact, for most water waves, the sideways motion is just as big as the up and down, and you wind up moving in a circle! But when the wave is past, you and the water around you are left in the same place. The wave, and the energy it carries, passes by you.

For a nice illustration of the motion of particles in a water wave, take a look again at

http://www.kettering.edu/~drussell/Demos/waves/wavemotion.html

but this time scroll down to the third animation. Look at one particle, maybe one of the blue ones, and watch how that particle moves. Does it move in a circle?

When there is a series of waves following each other, we call that a wave packet. The distance between the crests (the high points of the waves) is called the wavelength. Waves with different wavelengths travel at very different speeds. Those with a short wavelength go slower, and those with a long wavelength go faster. In deep water (when the depth is greater than the wavelength), the