What is Doppler shift and how does it affect the world around us and how using it as an excuse for running that red light may not be such a great idea

If you go and sit out on a not to busy road on a reasonably quiet day, you may notice, that as cars drive past, that the noise they produce seems to differ in pitch depending on whether they’re travelling away or towards you. It seems as if, when approaching you, that the car emits a higher pitched sound, and as it travels away, a lower pitched sound. This strange phenomenon is known as Doppler shift, or the Doppler Effect. It’s caused by waves becoming squashed up in front of a moving object, as the emitted waves struggle to pull away, and becoming spaced out behind the moving object, as the waves struggle to keep up, in both cases changing the pitch of the sound, or frequency of the light, as the wavelengths become shorter and longer.

The basic equation of low speed Doppler shift is:

Where c is the speed of the wave, vr is the speed of the observer, vs is the speed of the emitter and f0 is the frequency of the emitted wave.

This idea was first proposed by the Austrian physicist Christian Doppler in 1842, his paper “”Über das farbige Licht der Doppelsterne und einiger anderer Gestirne des Himmels” (On the coloured light of the binary stars and some other stars of the heavens) it details the effects of heavenly movement of the frequency of light received from observable stars. Basically, how the movement of stars in relation to earth affected the colour of the observed light. This technique of observing the difference between the expected frequency and actual frequency of light emitted by stars and galaxy’s has very useful applications. It allows astronomers and cosmologists to determine the rate of expansion in the universe by measuring the “red shift” of galaxy’s, how much the their observed light has been shifted towards the red end of the spectrum due to their movement away from us.

Now this is all well and good, but what does this all mean for us, average Joe, not Johnny the astronomer, and how can we use it to our advantage? Well the thought occurred to me recently, how fast would you have to be going to see a red traffic light as green? It’s an interesting thought. Imagine you’ve just been pulled over for running a red light on a busy box junction, nobody was hurt, but the police still saw you. How fast would you have to be traveling for the light to have appeared green to you, and thus, to get away with the minor traffic offense on a technicality? Well, we can’t use the equation we saw earlier as there are several inherent problems with it. Firstly, it only works for slow speeds, and as is plainly obvious, we’re going to have to be travelling at some speed before things start changing colour, and secondly, it only works accurately for sound waves, or waves that have to travel through a medium, unlike light which can travel though a vacuum. So, we have to use another equation, this time the Relativistic Doppler effect equation, which takes into account the speed of light so it doesn’t affect our calculations as much.

And with some fancy rearranging, this becomes

Now add in some numbers

And we come out with a speed of around the third the speed of light, which is speeding by anyone’s standards. So, you may get away with one traffic offence on a technicality, but there wouldn’t be much hope of getting off on this one.

N.B. see https://journalclubscienceblog.wordpress.com/2012/07/17/what-would-happen-if-we-travelled-near-the-speed-of-light/ for another reason why this isnt a good idea

By Alex Davis





Advancing Physics AS text book

A calculator