Bumper stickers and the Doppler effect

Question:

What does this sticker mean? It is a red bumper sticker with white writing and reads "If this sticker is blue, you are driving too fast."

Answer:

This sticker refers to the Doppler Effect. This is the effect where objects that recede from us appear redder than they really are and object that approach us look bluer. Admittedly the change is very small for the frequencies involved in visible light, but it is how astronomers work out the speed of recession of the galaxies – the so called Red Shift which gives evidence for the Big Bang and the expansion of the Universe.

You can calculate the speed needed for the sticker to change from red to blue. The speed given is the speed with which you are catching up the car in front.

Using the Doppler formula Dl = l v/c gives v = [300x10^{- 9}x3x10⁸]/750x10^-9 = 120 million metres a second or 40% of the speed of light! If you see it happening you are really likely to be stopped for speeding!!