How fast? The Doppler effect bumper sticker

There is a running joke amongst phys­i­cists about a bumper sticker than turns blue.

This is a joke about the Doppler effect. When a source of waves are moving towards a detector (e.g. your ears or eyes) the fre­quency of the wave changes. For a source moving towards you the waves are “com­pressed”, creating a higher fre­quency; for a source moving away the waves are “stretched out”, creating a lower frequency.

The Doppler effect is only really notice­able to humans in the case of sound waves; the Doppler effect is respons­ible for the changing engine note of a vehicle as it passes you. But the effect applies at all fre­quen­cies, including visible light. The joke arises because one would have to be trav­el­ling very fast for the Doppler effect in visible light to be noticeable.

How fast?

Red light has a wavelength of about 700 nano­metres and blue light about 400 nm. If we plug these figures into the Wolfram|Alpha “com­pu­ta­tional know­ledge engine” we get a result of −152 kilo­metres a second, meaning that if the sticker had turned blue someone would be coming towards you at about 340 million miles per hour or about 51% the speed of light.