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Doppler effect

Swing a ringing phone inside a long sturdy sock and you will hear the strangely familiar Doppler effect.

Doppler effect

Swing a ringing phone inside a long sturdy sock and your audience will here the strangely familiar Doppler effect. (Source: Ruben Meerman/ABC Science)

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Smart phones are expensive so please take care not to swing yours too close to a wall or a person or inside a sock that's almost worn right through. Other than that, this is a very safe demonstration.

You'll need a smart phone with internet access and a long sturdy sock.

For safety, measure the sock fully stretched and keep at least that distance away from walls and audience members during your demonstration.

On your smart phone, navigate to a free online tone generator such as this one. You can set most online tone generators to any audible frequency you like and you can adjust the volume using the speaker settings on your phone.

Put the phone with the tone playing inside the sock and slide it all the way to the toes.

Hold the sock firmly and swing the phone around your head. The audience will hear a warbling sound. Stop whirling the sock and the sound is steady. If you are performing the demonstration indoors, you will hear the warble too because the sound is reflected from the surrounding walls.


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What's going on?

When a sound source starts moving, the frequency you hear changes. You notice this when a car zooms past or an aeroplane flies overhead. Cars, police sirens and jet engines all produce a consistent sound, but the pitch you hear is higher on approach and lower on retreat. This famous effect is named after Christian Johan Doppler but he first noticed it in starlight, not sound.

Light and sound both travel as waves. When a sound source moves, you hear a change in pitch. When a light source such as a star moves, you see a change in colour. The light from a star that is moving away from you is shifted toward the red end of the visible spectrum. A star moving toward you is blue-shifted. The red-shift we observe in the light from nearly every star in the sky is how we know that the universe is expanding in every direction. The fact that light from the further stars is more red-shifted is how we know that the expansion of the universe is accelerating.

The proportion by which the frequency of waves is Doppler-shifted depends only on the relative speeds of the source and the observer and for sound, there is a further psychological twist in this tale.

To appreciate the 'psychoacoustic' side of this trick, you need to know that the Doppler shift for any given speed is always the same fraction of the emitted sound frequency. You also need to remember that the fraction of a large quantity is always bigger than the same fraction of a smaller quantity (for example, one third of nine is three, but one third of ninety is thirty). So, the higher the frequency, the bigger the Doppler shift will be in absolute terms. Amazingly, however, the human brain perceives the Doppler shift as being equal no matter what the frequency of the emitted sound is. If all this talk of fractions sounds a bit confusing or ethereal, perhaps some solid numbers will help.

For a phone swinging at about one revolution per second in a sock that's roughly one metre long, the maths is relatively simple. The phone is travelling at 6.28 metres per second (the circumference of a circle is 2 times pi times the radius, remember?) Half the time, the phone is moving toward a stationary observer's ears, and half the time it's moving away.

Sound travels at around 340 metres per second (just over 1200 kilometres per hour) in air at room temperature and atmospheric pressure. If you plug these numbers into Doppler's marvellous equations, you'll see that a 1000 Hertz tone warbles about 37 Hertz from 982 Hertz (about a B5 on a piano keyboard) up to 1018 Hertz (just below the C6). Now wind the tone up to 2000 Hertz, recalculate, and you get a 74 Hertz warble. That's twice the frequency range as before and it warbles from 1963 Hertz (about a B6 on the piano) to 2037 Hertz (just below a C7).

The musically minded reader will immediately notice that, in terms of musical notes on a piano, the 'distance' between the lower and higher pitch of both these warbles is the same in both cases. Twice the frequency difference but they are separated by the same distance (or number of keys) on a piano's keyboard. The mathematically AND musically minded reader probably saw (or heard) this surprising result coming several paragraphs ago but the fascinating fact remains. The human perception of sound and universal enjoyment of music are a psycho-mathematical instinct and you can prove it by simply swinging a phone in a sock and crunching some numbers. Kezam!


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Published 10 April 2013

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