The Doppler Effect|
Posted April 1, 2001
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Catherine called in a couple of weeks ago and asked if I could explain a phenomenon called "red shift." Well, first of all, red shift is really just the Doppler effect, applied to light instead of sound.
The doppler effect is the change in pitch that you hear when the police drive past with their sirens on. When they're coming toward you, you hear a high pitched siren; and when they drive away from you, you hear a low pitched siren.
For the same reason, if a star is moving toward you, its light is a higher frequency; and if it's moving away from you, its light is a lower frequency. Lower frequency light is more red, so you see red shift when the star moves away from you; and higher frequency light is more blue, so you see blue shift when the star moves toward you.
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You're listening to Mostly Mozart, a unique children's show.
We're here to find out a few things about red shift, which is the doppler effect as it applies to light.
If a car drives toward you with its horn on, well, first of all, you should probably get out of its way. Let's assume that the horn is generating a 400 Hz tone. That just means that in one second, it will generate 400 sound pressure pulses, which will soon be received by your ears. During that one second, the car also moves 25 metres closer to you. That means the first pulse had to travel 25 metres further than the 400th pulse. Sound travels at 330 metres per second, so the first pulse takes an extra thirteenth of a second to get to you, compared to the 400th pulse.
If the first pulse takes a thirteenth of a second longer to get to you than the 400th pulse, and all 400 pulses were generated in a one-second interval, then what you hear is 400 pulses in twelve thirteenths of a second. That's not 400 Hz any more, that's 433 Hz.
So, the car horn is 400 Hz, but you hear 433 Hz, simply because it's moving toward you.
The opposite effect happens when the car drives away from you: it still generates 400 pulses in one second, but the later pulses take longer to reach you, so your listening experience is prolonged, and you hear fewer pulses per second.
When a car drives past you, you hear the contrast between the artificially higher pitch on one hand, and the artificially low pitch on the other hand. It doesn't take much speed to make this effect noticeable, because the speed of sound is only about 10 times highway speed, and our hearing mechanism can easily detect a one tenth change in pitch.
All types of wave are susceptible to the Doppler effect. It happens to electromagnetic waves, but since the speed of light is about 10 million times highway speed, and our eyes don't detect a one 10 millionth change in hue.
Someone did notice the Doppler effect in waves, and that someone was none other than Edwin Hubble, of Hubble Space Telescope fame. I don't think Edwin was still alive by this point, but I'm sure he would have been amused to hear the story of the space telescope. It used the hugest and most powerful optical lens ever made, but it looked like crap when they turned on the telescope. Apparently they spent so much effort making the lens surface absolutely perfect that they forgot to check that the lens was the right shape in the first place. And it wasn't. But they fixed it, and now it takes incredible pictures of things that are very, very far away.
Edwin Hubble was analyzing the light emitted by various stars. This is one way to guess what the stars are made of, because atoms and molecules generate specific frequencies of light. Hubble was studying stars in distant galaxies, and noticed that there was lots of light at four frequencies that didn't match the characteristics of any known atom. Figuring it was unlikely in the 1920s to find a star made of a mysterious new element, he then noticed that the four new frequencies were very close to the four frequencies generated by hydrogen atoms. To be precise, the four frequencies were 0.0033 percent lower than the four characteristic frequencies of hydrogen.
Edwin Hubble was witnessing the Doppler effect. He was looking at a star that was moving away from Earth at a million metres per second, or 1/300 the speed of light. All the light from the star looked 1/300 more red than it would have if it hadn't been moving away from Earth.
You can use observations like that one to jump to an interesting conclusion. If you look at stars further and further from Earth, you see more and more red shift. Everything is moving away from the Earth. Either Earth is in a special place in the Universe, which would mean that the fundamental assumption of science is wrong... or the universe is expanding. Either way, the reason why we see much more red shift than blue shift is simply that most of the visible things in the Universe that move near the speed of light are very distant stars, and they're moving away from us.
What does all this have to do with sonic boom?
Say a jet flies toward you at Mach 1, the speed of sound, 330 metres per second. Its jet engines generate a rather loud 4000 Hz whine. In the space of one second, it generates 4000 sound pulses and moves 330 metres closer to you. That means the first sound pulse takes one second longer to reach you than the 4000th pulse. And if the 4000th pulse is generated one second later, that means they both reach you at the same time. And so do the rest of the 4000 pulses. You hear nothing while the plane approaches; it just builds up a wall of sound pressure in front of its nose. When the plane passes over you, the wall of sound passes through you, and you get the last 20 seconds worth of jet engine sounds, all in one ear splitting, window shattering, instant.
And that's why they don't fly supersonic jets at Mach 1 over populated areas.