Doppler effect

The perceived frequency of a wave depends on the relative speed of its source.

You, for sure, at least once in your life happened to stand by the road along which a car rushes with a special signal and a siren on. As the siren howl approaches, its tone is higher, then when the car is level with you, it goes down, and finally, when the car starts to move away, it goes down even more, and you get the familiar: yyyiiiieeeeeeEAAAAOoooooouummmm – about such a scale. Themselves, perhaps unconsciously, you are observing the most fundamental (and most useful) property of waves.

Waves are generally a strange thing. Imagine an empty bottle dangling near the shore. She walks up and down, not approaching the shore, while the water seemingly rushes on the shore in waves. But no – the water (and the bottle in it) – remain in place, fluctuating only in a plane perpendicular to the surface of the reservoir. In other words, the movement of the medium in which the waves propagate does not correspond to the movement of the waves themselves. At least, football fans have learned this well and learned to use it in practice: by sending a “wave” through the stadium, they themselves do not run anywhere, they just get up and sit down in their turn, and the “wave” (in Great Britain this phenomenon is usually called the “Mexican wave “) Runs around the stands.

Waves are used to describe them frequency (the number of wave peaks per second at the observation point) or the length (distance between two adjacent ridges or depressions). These two characteristics are interconnected through the speed of wave propagation in the medium, therefore, knowing the speed of wave propagation and one of the main wave characteristics, one can easily calculate the other.

As soon as the wave has gone, the speed of its propagation is determined only by the properties of the medium in which it propagates, while the source of the wave no longer plays any role. On the surface of the water, for example, waves, being excited, then propagate only due to the interaction of forces of pressure, surface tension and gravity. Acoustic waves propagate in air (and other sound-conducting media) due to the directional transfer of the pressure difference. And none of the wave propagation mechanisms depends on the wave source. Hence the Doppler effect.

Let’s think again about the howling siren example. Let’s assume, for a start, that the special vehicle is stationary. The sound from the siren reaches us because the elastic membrane inside it periodically affects the air, creating compression in it – areas of increased pressure – alternating with rarefaction. The peaks of compression – the “crests” of the acoustic wave – propagate in the medium (air) until they reach our ears and act on the eardrums, from which a signal will come to our brain (this is how hearing works). The frequency of the sound vibrations we perceive, we traditionally call the tone or pitch: for example, the vibration frequency of 440 hertz per second corresponds to the “A” note of the first octave. So, while the special vehicle is standing, we will still hear the unchanged tone of its signal.

But as soon as the special vehicle moves from its place in your direction, a new effect will be added. During the time from the moment of emission of one peak of the wave to the next, the car will travel a certain distance towards you. Because of this, the source of each next peak of the wave will be closer. As a result, the waves will reach your ears more often than they did while the car was stationary, and the pitch of the sound you perceive will increase. Conversely, if the vehicle moves in the opposite direction, the peaks of acoustic waves will reach your ears less often, and the perceived frequency of the sound will decrease. Here is an explanation of why when a car with special signals drives past you, the siren tone goes down.

We have examined the Doppler effect in relation to sound waves, but it applies equally to any other. If a source of visible light approaches us, the wavelength we see is shortened, and we observe the so-called purple offset (Of all the visible colors of the spectrum of the light spectrum, violet corresponds to the shortest wavelengths). If the source is removed, there is an apparent shift towards the red part of the spectrum (lengthening of the waves).

This effect is named after Christian Johann Doppler, who first predicted it theoretically. The Doppler effect interested me for the rest of my life because of the way in which it was first tested experimentally. Dutch scientist Christian Buys Ballot (1817-1870) put the brass band in an open railway carriage, and on the platform gathered a group of musicians with perfect pitch. (Ideal hearing is the ability, after hearing a note, to name it exactly.) Whenever a train with a musical carriage passed the platform, the brass band would play a note, and the observers (listeners) recorded the musical score they heard. As expected, the apparent pitch was in direct proportion to the speed of the train, which, in fact, was predicted by Doppler’s law.

The Doppler effect is widely used both in science and in everyday life. It is used all over the world in police radars to catch and fine traffic offenders who exceed the speed limit. The radar gun emits a radio wave signal (usually in the VHF or microwave range) that is reflected off the metal body of your car. The signal comes back to the radar with a Doppler frequency shift, the value of which depends on the speed of the car. By comparing the frequencies of the incoming and outgoing signals, the device automatically calculates the speed of your car and displays it on the screen.

A somewhat more esoteric application of the Doppler effect was found in astrophysics: in particular, Edwin Hubble, for the first time measuring the distance to the nearest galaxies with the latest telescope, simultaneously discovered a red Doppler shift in the spectrum of their atomic radiation, from which it was concluded that galaxies are moving away from us (cm. Hubble’s law). In fact, it was as unambiguous a conclusion as if you, closing your eyes, suddenly heard that the sound of the engine of a car of a model you know was lower than necessary, and concluded that the car was moving away from you. When Hubble discovered, moreover, that the farther the galaxy, the stronger the redshift (and the faster it flies away from us), it realized that the universe was expanding. This was the first step towards the Big Bang theory – and this is a much more serious thing than a train with a brass band.

Christian Johann DOPLER
Christian Johann Doppler, 1803–53

Austrian physicist. Born in Salzburg in the family of a bricklayer. He graduated from the Polytechnic Institute in Vienna, remained in it in junior teaching positions until 1835, when he received an offer to head the department of mathematics at the University of Prague, which at the last moment forced him to abandon the overdue decision to emigrate to America, desperate to achieve recognition in academic circles at home. Finished his career as a professor at the Royal Imperial University of Vienna.