11/02/2014 -- What makes a passing siren sound strange?

posted Nov 16, 2014, 6:30 PM by Patrick Poole   [ updated Nov 16, 2014, 7:49 PM ]
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Most people have heard an ambulance or firetruck pass them by at high speed, and have been told at one point or another that the odd sound you might hear as it passes comes from something called the Doppler effect. I’ll explain this effect below if you haven’t heard of it, but even if you have it’s easy to get confused about what exactly is going on with this sound modulation. It’s usually best to jump back to the very beginning of an idea rather than try to pluck out just the part of your understanding that isn’t quite right, so here I’ll explain what sound is and how the Doppler effect works, as what you can use it for in meteorology and even astronomy!

Sound is vibration in the air, traveling as a wave

Imagine you’re standing inside a closed, empty room. If there is no furniture or other people in the room we would call it empty, but in reality it’s full of air molecules—you are just like a fish in a fishtank, except you’re surrounded by air instead of water. Air and water are both considered “fluids” because of their tendency to conform to the boundaries of their containers.

When you make a disturbance in the air, say by clapping your hands, the air just between your hands is pushed out of the way quickly right as you clap. Those air molecules knock into the ones just beside them, which knock into the ones just farther on—in this way the disturbance expands outward from the origin (your clap, in this case). Your ears can pick up these sorts of vibrations and send signals to your brain that you comprehend as a clap.

Wave notation

When you speak your vocal chords are vibrating, causing the air in your throat and mouth to vibrate, sending a sound wave traveling through the air. It’s true what they say: in space no one can hear you scream, because there is no air to transmit the vibrations of your vocal chords to anyone else. (Actually, strictly speaking you would still hear yourself scream because those vibrations can still travel through the bone structure in your head to get to your ear drum. This is why a recording of your voice sounds so much different than how you sound to yourself normally—because a lot of what you think of as the sound of your voice comes from this internal bone vibration through your head!)

The frequency (or equivalently, wavelength) of the wave determines the pitch (or musical note) of the sound

Scientists have a lot of mathematical machinery to talk about waves because they occur in important ways so often in nature. One of the most basic wave properties is the frequency of the wave, or how many of the air vibrations occur during a set amount of time. A related idea is the wavelength of the wave, which is how much distance there is between vibrations. When you pluck a guitar string it vibrates, and it turns out that the length of the guitar string determines the frequency of the vibration, or how often it wiggles back and forth. Our brains interpret different frequencies of vibration as different notes, musically, or just as higher or lower pitch in the case of two different people speaking. When you sing different notes you’re changing how fast your vocal chords vibrate, which changes the frequency with which the nearby air vibrates.


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The Doppler effect is a change in the frequency (pitch) of a sound because its source or listener is moving

Sound is vibrations traveling through the air, but what if the source of the sound is also moving? If the source of a sound is moving towards you then the vibrations will seem a bit closer together than they really are because the source moved a bit closer to you between vibrations—the vibrations gets closer together, which means the frequency is higher. A sound source moving away from you adds distance between vibrations as it moves away, so when the vibrations reach you they seem farther apart than they really are, lowering the frequency of the sound. You only really notice this effect when the sound source is moving fast compared to the speed of sound (343 meters/second in normal air), because otherwise the vibrations are moving too fast for the little bit of source speed to bring the next vibration much closer. So you won’t notice it if your friend is walking toward you while playing a note on their trumpet, but you can notice if say an ambulance is speeding towards you down the road.


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Sounds also increase in intensity (loudness) as they approach, but this isn't due to the Doppler effect

A firetruck or ambulance is the most commonly cited example of the Doppler shift, but it’s a bit tricky. For one thing an ambulance siren is not one constant note, as you can hear in the links in the last sentence—it changes frequency up and down on its own, so many people wrongly think that this is due to the Doppler shift.

Ok so think about a fast car going by instead—if the car is going at a constant speed then the engine should be making the same noise the entire time it’s traveling (in other words, the driver always hears the same frequency). The sound waves from the engine are expanding out from the engine, and they do so just like the ripples in a pond move outward from a thrown rock—the difference here is that the sound ripples move out as a sphere (in three dimensions) instead of a circle (like the two dimensional pond surface). That means that the vibration gets weaker as it travels outward, because it’s getting spread out over a larger and larger area—just like ripples on a pond eventually disappear far enough away from where the rock hit the surface, the sound ripples from your clapped hands dissipate as they spread out in three dimensions and at some distance they become too faint to hear.

So the strength of the vibration (or in mathematical terms the amplitude or height of the wave) determines how loud it is, and as the car races towards you it definitely gets a lot louder. Some people associate this loudness increase with the Doppler shift, but remember that the Doppler effect only changes the frequency of the sound.

Bonus physics—Doppler shifts in meteorology and astronomy

Light is also a wave, so it can undergo Doppler shifts as well. In the case of light the frequency determines the type of radiation: x-rays have higher frequencies than radio waves. The same is true of visible light: blue light has higher frequency than red light. (If you didn’t know that x-rays, radio waves, and sunlight were just different versions of the same thing, then stay tuned for an upcoming post on the electromagnetic spectrum!)

Doppler radar sweep

Since the Doppler shift is a frequency change, it modifies the color of visible light—you can emit a known wavelength of light at a moving object and see what signal bounces back to you to determine the speed. This is how meteorologists can determine what storms are doing—by sending a known frequency of light into a storm and seeing what frequency it is when it returns. If the light hits something moving towards you that reflected light will be a little bit higher frequency, and if the clouds were moving away the light will be a little bit lower frequency. That’s why it’s called Doppler radar.

This is also how astronomers know how fast things are moving in the universe: we know what frequencies of light stars are supposed to emit because we know something about the physical processes going on inside them. We never see the exact spectrum of light (all the frequencies that come from a source) that we expect because the star is moving towards or away from us, Doppler shifting its emitted light. By comparing the theoretical spectrum with what we actually detect from a star we can determine how fast it is moving with respect to us (and in what direction). If a star is moving away from us its light will be a little bit lower frequency that it should be (lower frequency means longer wavelength, and the longest visible wavelength is red, so the light from these stars is called “red-shifted”). In fact nearly every star in the night sky is moving away from us, which is evidence that the universe as a whole is expanding (but that’s another post).



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