Thank you. Oscillations can travel through a medium such as air or water without carrying matter along with them. These mechanical disturbances are called waves.
In any era, there are certain experiments which are just barely possible. These are experiments at the state of the art. They're a test of the skill and ingenuity of the very finest experimental physicists. An example today might be the attempt to detect gravity waves coming from distant stars. At the end of the 17th century, a state-of-the-art experiment was to measure the speed of sound.
Sound normally comes to us through the air. If there were no air in this room, you wouldn't be able to hear me speaking. Of course, if there were no air in this room, you would have more serious problems, but that's another story.
Sound travels very fast, but its speed is not infinite. We can tell that it takes some time because we can hear echoes, for example, sound reflecting from distant walls. And also, we can see lightning before we hear thunder because light travels much faster than sound. 300 years ago, one of those who tried to measure the speed of sound was Isaac Newton himself.
His measurement was not the very best in his own era. Experimental physics is a special art, and it was not Newton's. strong point.
But of course he was very clever and it's interesting to see how he tried to make the measurement. At Trinity College where he lived and worked there was a long corridor that was known to have an echo. and he tried to measure the amount of time that it took for sound to get down the corridor and return. As a timing device, he used a simple pendulum.
Now you remember that the time it takes for a pendulum to make one full swing depends on its length. He arranged for a sharp noise to go off at just the moment that the pendulum was released. If the pendulum returned before the sound, it was too fast and had to be made longer. If the sound returned first... the pendulum was too slow and had to be made shorter.
And in that way, he could get closer and closer to the exact amount of time that it took the sound to go down the corridor and come back, and thereby measure the speed of sound. Today I would like to give you an intuitive understanding of what sound is. Sound is a wave, a disturbance that travels at a definite speed, like the waves in this machine.
And a good point to start our discussion of waves is with two harmonic oscillators like these, which are coupled together. Water, light, sound, even pressure, they all travel in waves. In fact, throughout the physical world, waves are one of the most common natural phenomena. And nature isn't the only one who can make waves. People can make waves of their own, and they've been doing it for a very long time.
New York City. 1926. A big welcome for Gertrude Ederly, the first woman to swim the English Channel. But there's more going on here than meets the eye, much less the guest of honor. This is a human shockwave, with the circular wave front like the molecular motions of a sound wave in a gas.
Notice how the wave moves from one person to the next, leaving a partial vacuum in its wake. This non-recurrent wavefront was harmless. This one was not.
NOETOC 1952 The first hydrogen bomb test. The world at large feels the heat of the first nuclear shock wave in the Cold War. But the phenomenon of spreading waves goes back considerably farther than 1952. Much farther back than 1926. It goes back to the very beginning of time, and the universe itself, in fact.
The Big Bang. And from the very beginning of it all, a disturbance in one place, natural or otherwise, inevitably causes a reaction in another. And so it goes.
Disturbed weather in a polar region causes trouble in the paradise of a tropical isle halfway around the globe. The chain of earthly events and phenomena, which are hooked together by infinitely complex links, is often better seen at a distance, but it can be better understood close up. That's because no matter how complex the system appears, an underlying principle begins to explain its physical aspects.
When simple mechanical systems are joined, a disturbance in one will pass on to the next. Thank you. When any stable mechanical system is disturbed, nature's response is simple harmonic motion. For a single oscillator, that's as far as it goes. But when oscillators are linked, from one to the next and to the next, a disturbance in one.
passes on to the next, and continues on down the line. This is the essence of a mechanical wave. Sometimes, individual mechanical oscillators are easy to discern.
In other cases, the wave itself is easier to see than the individual oscillators. Perhaps more surprising, waves propagate not only along the surface of water, but even through the interior of a crystal. to lean solid. A disturbance's speed depends on the medium through which it passes and on the connection between one bit of matter and the next.
If the linkage is weak, the disturbance passes slowly. If it's strong, the disturbance travels rapidly. But no matter the speed or the medium, water, air, or even a solid, all waves that propagate through any medium are called mechanical waves. Mechanical waves, or impulses, pass through a crystal from atom to atom because each atom is bound to an equilibrium position by electrical forces.
When disturbed, they act mechanically, exactly like masses connected by springs. When an impulse moves through a system, no single oscillator goes very far. But the disturbance moves right along.
Sometimes mechanical oscillations can be more moving than disturbing. Can be art as well as science. And it can be enjoyed as well. Musical instruments send continuous waves through the air that can be visualized as well as heard.
Masses connected by springs may not look like beautiful music, but the principle is the same. And it can be described using a few handy terms. Each wave has an amplitude, the size of the disturbance, which is preserved as the wave moves along. It also has a definite time for each complete cycle, called the period.
The inverse of the period is called the frequency. The tone of music depends on its frequency. The higher the frequency, the higher the tone or pitch of the sound. And the loudness of music depends on the amplitude.
But no matter how loud, sounds are always on the move. And regardless of pitch or loudness, all sound travels through the air at exactly the same speed. If it didn't, every listener would hear a different performance. Whether it's short and sweet or loud and long, every wave has a definite distance from one compression to the next called the wavelength. The wavelength equals the period times the speed of the wave.
Or in other words, frequency times wavelength equals speed. Lower frequency generates a longer wavelength, but the speed remains the same. For sound waves in air, the speed is always the same, regardless of the frequency, the wavelength, or even the amplitude.
But in this world, all waves don't get an even break. Sound and water waves travel at different speeds. And unlike sound waves, water waves can travel at speeds different from each other.
At a considerable distance from a continent, way out there in the deep blue sea, long waves travel faster than short ones. But closer to the shore, waves travel together. And no matter their length, all waves decrease in speed as they approach the shore. In the mechanics of waves, that's the long and the short of it. Because on land, or at sea, in fact anywhere at all, All mechanical waves follow the same basic principles.
Wherever anything makes waves, harmonic oscillators respond and then spring back. The oscillators are linked in such a way that every cycle of one excites the oscillator beside it. But what determines how fast the wave moves? For masses connected by springs, the speed of the wave depends on the stiffness of the spring, the mass of each oscillator, and the equilibrium distance between them.
In water, gravity is the force that makes the water spring back. That's why gravity determines the speed at which a water wave travels. But so too does the length of the wave itself.
If the water is much deeper than the wavelength, the wave speed is approximately equal to the square root of g, the acceleration of gravity, times the wavelength, divided by 2 pi. In other words, long ocean waves move rapidly, while short ripples move more slowly. The result is that in deep water, long waves pass right under the surface ripples.
And whether they're long waves or ripples, water waves differ from simple mechanical ones in some other ways. For example, masses and springs can oscillate along the direction that connects them. These are called longitudinal waves.
And they can also be made to wave sideways. These are called transverse waves. But water waves are neither longitudinal nor transverse.
Instead, each bit of water on the surface moves around in a little circle, each circle slightly offset from the next, all together giving the familiar undulation of the watery surface. As a water wave approaches the shore, it comes into ever-increasing contact with the seabed, which slows it down. The closer the surface is to the bottom, the slower the wave. In shallow water, the wave speed is approximately equal to the square root of the acceleration of gravity times the depth of the water. When this happens, the thick part of the wave moves faster than the thin part, spoiling its sine wave form and ultimately causing the wave to break.
Sound waves can be heard, but not seen. Waves of sound are generated by something vibrating the air. A vibrating object.
sets the air next to it into motion, compressing and expanding its density with each vibration. That's why a generated sound wave carries the same frequency as its source. The force that drives a sound wave is due to the change in pressure as the density of air increases or decreases. Just as the speed of water waves depends on gravity, the speed of sound depends on the pressure and density of air.
In air, the speed of sound is approximately equal to the square root of the pressure divided by the density of the air. Around the world. In the most gentle setting, or the most violent, countless bits of matter vibrate in unison.
According to the principles of harmonic motion, they create the phenomenon of the mechanical wave. And so, now we're in a position to understand why Isaac Newton was playing with a pendulum in a corridor at Trinity College. He had worked out his theory of the speed of sound and decided that it ought to be equal to...
the square root of the pressure of the atmosphere divided by the density of air. And when he put in those values to find out how big it should be, the result was 979 English feet. Newton was trying to measure the speed in order to test his theory to see if it was right.
Now, as I told you, Newton's measurement was not the very best of the time. The best was made by a man named William Durham, who got a result of 1,142 feet per second. Now at this point, Newton had to do what every scientist must do all the time. He had to make a value judgment.
His theory predicted this number. The experiment measured this result, and the question is... Is that good or bad?
Is the agreement or disagreement between these two numbers satisfactory or unsatisfactory? Now we know, in retrospect, looking back, that what Newton had done was an absolutely stale... stunning intellectual accomplishment.
Because before Newton, nobody had the foggiest notion of what the speed of sound should be. Newton came along, had the right idea of what sound was, and calculated a speed that was correct to within 20%. And so he should have been satisfied.
Newton considered this situation, and he found it totally, completely unacceptable. The reason was because the entire thrust of the scientific revolution from the time of Copernicus on was to cast magic and the occult out of science. Newton had introduced into science his theory of gravitation, in which invisible forces acted between bodies at vast distances with nothing in between.
between. And that smelled to Newton and his contemporaries like magic. Newton's defense of his own theory of gravity was it had to be right because it worked so well. That is to say, it gave precisely correct numerical predictions.
And that, he said, is the true test of the correctness of a scientific idea. But if precise agreement is the true test of his theory of gravity, it had to be also the true test of gravity. of his theory of the speed of sound. And the speed of sound was wrong by 20%. And so, Newton set out to make his theory correct.
What he did has a special name in science. It's called fudging, and it's something that no scientist ever does. And this is no ordinary fudging. This is fudging by the great Sir Isaac Newton in the ultimate classic of science, the Principia itself.
I'm going to tell you what he did. Listen carefully. The first thing he said was, look, sound travels 979 feet each second, not through the air, but through the space between the molecules of the air.
It actually goes a larger distance. It goes further in each second because the molecules themselves take up some space. How much space do the molecules take up?
Well, he said, we know that the density of the molecules The density of air is 470 times less than the density of water. In other words, if we imagine a volume like this containing air, all of that air could be condensed down to 1 470th of that volume, a little thing like that. And if we did that, the linear distance that it took up would be 1 9th of the original linear distance.
So the extra distance that the sound travels in one second, is 979 divided by 9, which is an extra 108. And if he adds that to this, we get 1,088 feet per second. Well, that's a little closer, but it's not good enough. enough for Newton. And so he says, well, look, air is 10% water vapor. How does he know that?
He doesn't say. And of course, the water doesn't participate in this process. Why not?
He doesn't bother to tell us. But he says, when we divided by the square root of the density of air, we made a mistake. We should have divided by the square root of 9 tenths of the density, because the other tenth is water. So we must add to this number 1,088 divided by the square root of 9 tenths of the That's about an additional 5%, about 55 feet. And so if he adds 55 to this, he gets a result of 1,143 feet per second compared to the measurement of 1,142 feet per second, and now Newton was satisfied.
And that's the way the great Sir Isaac Newton made science and reason triumph over magic and the occult. I'll see you next time. The real reason for the discrepancy between Newton's calculation and the measured speed of sound is that air is heated when it's compressed, causing it to spring back slightly faster than expected.
The effect is so subtle, it would not be discovered until a century after Newton's death. The For information about this and other Annenberg Media programs, call 1-800-LEARNER and visit us at www.learner.org.