Doppler affects you and me, quite frequently

It’s making the news in oceans both Indian and Saturnian, tracking the movements of space probes and missing Malaysian airliners. And yet you encounter it every day, when you hear a car passing you on the road change from high to low pitch. So what exactly is the Doppler effect, and how does it work?

(Q: What sound does a cat make when it goes past at high speed? A: Meeeeeeeeeeeeeeeowwwww.)

As you might expect, the Doppler effect was named after the Christian Doppler, an Austrian physicist—although he only became a physicist because he was too frail to enter his father’s stonemason business—who proposed it in Prague in 1842.

It happens whenever there is movement relative to a source that’s emitting waves, whether they’re light, sound, water or something else. In the case of the moving car, think of its soundwaves as a series of peaks and troughs. The car emits one wave, i.e. one peak, and then another about 1 millisecond later.

But in that millisecond the car has moved closer to you, so the second peak has less distance to travel. It therefore reaches you less than 1 millisecond after the first peak does. This means that for you each peak is separated by less than a millisecond, so you hear the sound at a higher frequency.

OK, that maybe a little hard to picture, so try it visually instead. Imagine the waves as concentric rings being emitted by the source, they bunch up at the front and stretch out behind it. Or don’t imagine it: look at the picture below.

Doppler effect showing circular wave fronts emitted from a source moving to the right
Doppler effect from a source moving at 0.7 the speed of wave propagation (Image by Lookang with many thanks to Fu-Kwun Hwang and author of Easy Java Simulation Francisco Esquembre, via Wikimedia Commons)

However you imagine it, the frequency change due to the Doppler effect makes a very convenient way to measure velocity, so it has many applications. Talking about moving cars, well it’s the Doppler effect that the police radar uses to tell whether you’re speeding (see the NSW Police Radar Manual [PDF 4.3 MB]).

It’s also famously what we use to measure the expansion of the universe. When a light source like a star or a galaxy is moving away from us, the electromagnetic waves it emits go to the low frequency or red end of the spectrum, so we say it’s red-shifted. If it’s coming towards us, it’s blue-shifted. By measuring the redshift of galaxies depending on how far away they are from us, we can calculate how fast the universe is expanding (due to the expansion of the universe, the further something is, the faster it is moving away).

But if understanding the history of the universe isn’t enough, the Doppler effect still makes the news; specifically, in the hunt for missing Malaysian Airlines flight MH370.

Using what the BBC called “cutting-edge methods”, the British satellite firm Inmarsat received radio pings from the missing plane, and by comparing how the frequency of the signal differed from what it’s supposed to be when it’s transmitted, they could work out how the plane was moving. That’s how they determined it flew to  the Southern Indian Ocean, where the search is currently focussed.

Diagram showing how by triangulating the pings from the MH 370 with a calculation of its speed as determined by the Doppler effect, it was possible to calculate the aircraft's path

The other bit of recent Doppler effect news was the discovery of an ocean under the icy surface of Enceladus, a moon of Saturn. Again, the scientists used changes in the frequency of radio signals, this time from the spacecraft Cassini, which was flying past it (Iess L, Stevenson DJ, Parisi M, Hemingway D, Jacobson RA, Lunine JI, Nimmo F, Armstrong JW, Asmar SW, Ducci M & Tortora P 2014, “The gravity field and interior structure of Enceladus”, Science, vol. 344, no. 6179, pp. 78–80, DOI: 10.1126/science.1250551).

By looking at how Cassini’s speed changed as it flew past Enceladus, they could determine the forces of gravity acting on it, which in turn allowed them to calculate the distribution of mass inside the moon. These were changes in speed of mere millimetres per second, but allowed them to figure out there was liquid water—which is denser than ice—and a relatively light rocky core.

Cross-section image of Saturn's moon Enceladus, showing its rocky core and liquid ocean at the southern pole, emitting geysers through the icy crust
Diagram of the theorised interior of Saturn’s moon Enceladus, based on measurements by NASA’s Cassini spacecraft and NASA’s Deep Space Network. The gravity measurements suggest an ice outer shell and a low density, rocky core with a liquid water ocean sandwiched in between. This is also responsible for the plumes of water vapour shown at the moon’s South Pole (Image by NASA/JPL-Caltech)

So it may be commonplace, everyday science, but it’s good to see the Doppler effect is still making waves after all these years.

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3 thoughts on “Doppler affects you and me, quite frequently

  1. Hi, amazing technology but having the CHANGE in speed in ” in mere millimetres per second as against around 2km per hour would have made it easier to visualise. However, as normal orbit speed was not given it would have been meaningless anyway to the non-expert medical scientist like me but having a strong interest in areas of science I know very little about but love to learn about

    : all it need to add was “by @@@ % of its normal speed”.

    HOWEVER: I still find it staggering that Galilao actual FOUND these moons with optical equipment any young school child today would put straight in the bin with contempt if given one as present and told to FIND AND DRAW THE MOONS OF SATURN,

    1. That’s an excellent point – it is easier to visualise if you have something to compare it to. However the change in frequency caused by the Doppler effect is proportional to the magnitude of the velocity difference, and not its percentage of the total velocity. That’s why all the published reports of this measurement give only that difference of millimetres per second (actually between 0.2 and 0.09 millimetres per second) and not the orbital speed.

      But although I can’t quickly find the actual speed of the Cassini spacecraft, it’s likely to be of the order of magnitude of the escape velocity of Enceladus, which is 239 metres per second (this is because it’s in orbit around Saturn, not the moon). So that’s a measurement with an accuracy of around 0.0001% – much better than a police radar gun!

      And even though it was actually Christiaan Huygens who first saw Saturn’s largest moon Titan in 1655 (Galileo, who died in 1642, famously observed the moons of Jupiter, which was still enough to overturn the notion of a geocentric cosmos), you’re right that his telescope was pathetic by today’s standards, with only about 50x magnification. Huygens was also the first to identify Saturn’s rings – Galileo saw something funny was going on, but he couldn’t quite make out what it was and thought that Saturn looked like it was actually three planets lined up.

      1. Dear Chris,

        Thanks for that. I have been involved in teaching “adult general science” as a side line and its so difficult at times for an expert to actually understand that even intelligent people might know virtually nothing about what we all take for granted. Did I read some where that one third of US adults still think the sun goes round the earth!

        Try this one out: just ask people where blow flies come from in rotting meat and you will never eat in their house again! (I worked once with a medical engineer with a PhD who was warming up a previously frozen major human organ (legally obtained) in the hand-basin to do some tests on it. He countered my look of concern with the statement “Its OK and safe as its been frozen”, guess what I am glad I have not eaten round his house!

        My Fellowship thesis (33 years ago) was in pregnancy hormones where we were for the first time detecting and QUANTIFYING FLUTUATIONS in “baby derived hormones” during labour in the mothers blood. Here we used coefficient of variation as it showed it best and others and non-experts in particular could understand our results (as against pico grams per litre)!

        Did not understand all your maths but sure they were right and yes I got my planets wrong but wow those early observers sure were amazing at what they really did see (if you are ever at Oxford go and see lots of original stuff in the Museum of the History of Science) .

        Perhaps if the article was at least in part INTENDED for the likes of me some thing like “to show this it was like a police speed gun being able to measure the speed of a car so acccurate it could be “booked” if it exceeeded the legal limit by no more than that of snails pace”

        My grandson of four years asked a good question last week “Grandpa how does the sun fly without a propeller”?. Absolutely logical. CONCERN based on what all toy planes have.

        His father at a similar age told a physics PhD student at a University open day. “Magnatism is easy it makes metals sticky”. His reply was “Oh dear there goes my PhD thesis.”

        My other son at a very slightly older age when he observed people fishing in what I said was a “drinking water lake” asked with concern “where do the fish go to the toilet”? Then insisted on lemonade for the rest of the day!

        Keep up the good work and so glad to have found such an exciting web-site.

        Best regaards

        Philip do keep in touch

        monrobh12@google.com

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