How Going Fast Taught Us New Physics

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Another explainer. Yes. Oh, yeah. Yes.
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We might have done this long ago, but I'm old
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and I don't remember. Well, now that's the blind leading
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the blind. This is the Doppler effect.
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Oh, sweet.
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Let's go back to the 15th century, 16th century, 17th century,
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18th century. That's a pretty long time. Long period of time.
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Nothing moved fast enough for anyone to even think there's
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such a thing as a Doppler effect.
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Consider that. That's really cool. Okay. Because you don't get
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a Doppler from a horse. No, you don't.
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Yay.
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Yeah, it's just not happening. Right.
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Good thing curious people live among us because when a
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new phenomenon happens.
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It's like, why did that happen? Why did that happen?
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How did that? Why? Let me get into that.
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Yeah.
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Okay, so. When railroads started being built, okay? Early 1800s. Okay.
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People noticed that the train whistle, when it was coming
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towards you, had a different pitch than when the train
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whistle was receding from you.
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Okay. Okay? Mm-hmm. It was a higher pitch. It's the
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same whistle. Same whistle.
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The conductor didn't switch whistles just because it passed in
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front of you.
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Right. Okay? Because that could have happened. That could. If
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you're a scientist, you have to check all possibility.
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Yeah.
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And by the way, that's a pretty fancy train. So
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that was unlikely and, of course, was not actually happening.
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Right. So there's a fellow named Christian Doppler. Christian Doppler. Doppler. Austrian.
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mathematician, physicist, early to mid-1800s, and he noticed this. He said,
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this needs some explaining. So he studies it, and we
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knew that sound propagated in waves, and so if you
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have a train whistle, there's a wave coming out. If
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a wave has wavelength, and that's the distance between what
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and what?
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Top and bottom. No. There'd be half a wavelength. I'm sorry, peak, trough, peak.
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Peak to peak. Right. There you go. It's got to repeat.
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The whole thing's got to repeat. That's the way of life. Peak, trough, peak.
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And there you go.
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So if the train is sitting there and the sound
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is emanating, then whatever is that frequency, an exact identical
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word to frequency is pitch.
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Okay? Right.
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The musician might say pitch. The physicist says frequency. We're
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talking about the same thing.
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Same thing. Okay. Okay?
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Cool.
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A frequency.
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is a little more descriptive because if you're standing there
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timing it, you can ask how many of these go
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by you per second. So the higher the frequency, the
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more of these go by per second. And the only
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way that can happen is if the wavelength is shorter.
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We agree?
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Yes.
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I mean, that's the only way it can work. It
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can't work any other way.
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The only way you can get more of these per second,
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you've got a higher frequency, higher pitch.
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Combine the idea.
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That the sound has a frequency with the fact that
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the train is moving. So I'm squeezing the wavelengths as
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they come out in front of me.
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Exactly. And the opposite of that is happening on the
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other side. Right. I'm stretching it out. Stretching it out. Exactly. Right.
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So the train whistle coming towards you should then have
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a higher frequency than is native for that whistle. And
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as it recedes from you, the frequency should be lower.
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But that's precisely what is observed, what is heard in
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a train whistle. And what would the frequency be when
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it's right in front of you? Directly in front of you? Yeah,
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because it's moving past you. Now it's right in front
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of you.
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Um.
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Hold on. I'm trying to think here because the waves
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are being pushed. Don't overthink it. Okay, don't. If the
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frequency is higher than normal. Oh, because you're pushing it.
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And lower than normal over here. Well, then it's neutral there.
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Thank you. It's just neutral. At some point, it's got
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to go through the actual frequency. And when's that going
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to happen? Right there in front of you.
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Because when it's right in front of you, it's neither
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moving towards you or away from you.
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This sound is moving. At what speed? Well, it's the
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speed of sound.
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Thank you!
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See? Chuck, I ask easy questions. Don't overthink my situation.
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Don't overthink. There you go. Okay?
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Right.
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It's moving the speed of sound. Of course. And that's
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true no matter where. Okay?
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Yes, the speed of sound in a medium can be different,
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but for this experiment, the speed of sound has one value.
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Okay? That's great. It's simple.
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Yeah.
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Okay, so he wrote a formula to calculate this. That
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is not simple. It's the Doppler formula.
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Okay, what he discovered is that the ratio of the
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speed of the train to the speed of sound equals
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the ratio of the new frequency of the sound to
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the native frequency of the sound.
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Okay. The speed of sound is the same.
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Yes.
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But the train is moving. It's pushing the sound. Squeezing it.
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Squeezing it. Squeezing the wavelength. The wavelength itself.
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But notice it's not making the sound go faster. No,
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it can't make the sound go faster. But that was
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not obvious.
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No, it's not. That's what I'm saying. Yeah.
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If I've got a fast-moving train, am I pushing my
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sound forward?
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No, you're not. And this, by the way, is his observation. Yeah.
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Because he's like, if you intuit this, you're like, oh,
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it's pushing the sound, so the sound just gets pushed.
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And the speed of the sound, you think would be
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the speed of the sound plus the speed of the train.
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Plus the speed of the train.
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But it's not. But it's not. It's not. And I'm
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still amazed. We could have figured this out centuries before.
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With no problem. We had no occasion to even. But
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no reason. No reason to. No reason to do it.
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No reason to do it.
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Right.
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Okay.
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So built into the formula is the fact that as
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the train moves faster, Right. there's an even higher shift
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in the frequency.
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Right, yeah, that makes sense.
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That makes complete sense, both coming towards you and going away.
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So it's gotta relate the original frequency to the frequency
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you hear, to the speed of the train, and the
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speed of sound.
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And the speed of sound.
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And whatever is the medium, air at a given temperature,
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it'll be some number.
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That's gonna change depending.
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If it's water, if it's air, if it's the vacuum
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of space, there's no sound at all.
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No sound at all, right, right, right. Unless you're in
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Star Wars.
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Now here's something cool. Let's make the train go faster
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and faster and faster. The pitch up front is gonna
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get higher and higher and higher.
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Okay.
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Right, because it's getting squeezed and squeezed and squeezed.
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Okay. There's a point. Come on! What? What? Let me.
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Okay. There's a point where the train is moving so fast.
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Yes!
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That The end of the wave lands on top of
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the beginning of the wave.
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Yes. And it never.
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Moves forward from the train itself, or the thing. Whatever
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is pushing it. Whatever is pushing it, okay? Dude, that's amazing.
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That's when the train, we don't have trains that do this, but. Well,
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they do in China. When the plane.
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Hits the speed of sound, then the sound never gets
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ahead of the plane. Because all crests are piled on
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top of each other.
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Instead of this, they're like this. Every single crest. It's
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a sandwich. It's a sound sandwich.
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Everything's right at the front of the thing, okay? And
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all that sound is now magnified. We have a term
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for this.
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Say it. Say it. Boom! A sonic boom. Dude!
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That's how you get a sonic boom. That's how you
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get it. That's how you get it. It's a Doppler
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shift equation gone rogue.
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Gone wild. Off the chain. That's on steroids. I love it.
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Off the chain. That's crazy. Yeah. That is amazing. And
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like I said, in front of the plane, you don't
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hear it at all. Right. Well, you got to be moving.
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you know, it'll catch up with you, but if the
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plane is coming towards you and it's going the speed
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of sound or faster, it is silent movie until it
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passes you.
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That's really cool.
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That is why when these meteorites are big enough and
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they come through the atmosphere and they're going so fast,
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You see them go, streak of light, and then all
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the windows go.
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Yeah, it's a time delay. Definitely a time delay.
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Yes.
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Yes.
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What?
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So, consider.
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If you are at an angle to the train as
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it comes towards you, you're not getting the full brunt
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of the Doppler shift from it. You're getting a diminished
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fraction of the Doppler shift.
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Okay.
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Because the train... is moving sideways to you, not directly
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at you.
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Right, okay.
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Okay, so the formula works if you're standing on the track.
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If you're standing off the track, then there's an angle
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that you make with the train, and there's a cosine
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in there, remember your trigonometry, which will diminish the effect
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of the whistle for you.
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Okay. Okay?
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In a way, I'm picturing it as, I'm trying to
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picture the sound wave, and it's almost like, it's a
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glancing blow as opposed to a head on.
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Yeah, head on that you get the full effect. Right. Okay?
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The more you come off the angle, off that axis,
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then the train is not coming straight at you. The
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rate at which it's coming towards you is not as
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fast as the rate at which it's coming towards you
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if you're on.
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The track itself. There you go. Okay. That's all. It's
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just a geometry thing. Okay.
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And so what that means is if you get a
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speeding ticket because the radar gun is bouncing waves off
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of you, and inside the radar gun, the software is
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calculating the Doppler shift of the light waves, it's microwaves.
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The microwaves, because it's just waves, Doppler shift applies to-
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Don't make a difference. Wave is a wave. Wave is
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a wave. Don't make a wave. Okay? The Doppler shift.
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On your moving car, the only way they can know
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your actual speed is that they are standing right in
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front of your car as you drive towards them.
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But they're never right in front of you. They're in
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the bushes. They're always off somewhere. Off somewhere. Your Honor,
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I'm going to need to see the calibration of that
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radar gun. Well, listen to me. So what it means
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is they will never read, unless they're on a turn,
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and they get you, you know. Right.
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Because you're coming around, but that puts them directly in
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front of you. Directly in front of you as you
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come around, okay?
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Okay. But in a normal straightaway. Okay.
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They'd have to be in the middle of the road
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standing right in front of your speeding ass car to
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get the proper speed. If they're off axis, they will
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never get the proper speed. They will get less than
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your proper speed. This is my point. That's my point.
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That's why I always lose in court. Because they're getting
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you on the glancing blow. They're getting you on the lesser.
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And if that broke the speed limit.
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Yeah, you definitely would have broken the speed limit.
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If they say I clocked you at 114, what they
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really meant was you need to go to prison.
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Now, they are relying on a reflected signal. Right. Because
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the signal they send out will be a certain frequency.
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And then it bounces back.
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Bounces back with the speed of the object. And so
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you can do that in the software. If you have
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a car that absorbs microwaves, they'll turn on the radar gun,
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and they get no signal back. And they can't know
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how fast you were traveling.
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I want that car.
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But it also means, because the full-up Doppler formula has
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the speed of the observer built into it, A police
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car can get your speed even though it is moving.
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That's... Pretty dope. Okay. No, the obvious one is it's
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just trailing you. Right. It matches your speed. It matches
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your speed. That's easy. But if he's coming towards you. Right.
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And he can pop you while he's. Pop you. And like, gotcha. Gotcha. Gotcha.
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Coming straight at you. And it's going to get the
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right number. Wow. Because of Christian Doppler. Wow. In 1842.
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F you, Christian Doppler. F you, buddy.
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And of course, we use the Doppler shift in a
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slightly different way, getting the speed of stars that come
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towards us or away from us.
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In our galaxy. And the light shifts.
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Yeah, the light shifts. So we know what the frequency
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of light would be in a laboratory. So it's usually
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spectral features that only exist in one place in the spectrum.
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And you see it shifted. Then you say, oh, I
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know exactly how fast you're going. Look at that. Okay.
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And if it shifts one way or the other, you
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come towards me, you go away. But if it's going
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sideways to me, it's hard. I've got to wait around
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for it to show up in a different place. That
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takes a long time. But forward or away from us,
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we got it. By the way, you could sit there
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at the side of the freeway. And the cars will
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just make these sounds. We are so accustomed to that,
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you're not even thinking. You're not even thinking, why is that?
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You've got to be curious about that. And not everyone is,
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and fortunately, Doppler was. It's so common, though, nobody is curious.
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Nobody's curious anymore.
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Yeah, I mean, even like NASCAR and Formula One, it's like,
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that's how they come by you.
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Okay, so we're done here. This was great. A little
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bit Doppler.
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No, that was fun. That was really fun. This has
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been another explainer, Neil deGrasse Tyson.
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Thanks, Chuck. Always a pleasure. Keep looking up.