DOPPLER'S PRINCIPLE, a name given to the physical law (first enunciated in 1842 by Christian Doppler of Prague), that the appar- ent wave-length of sound or light depends upon the velocities of the observer and of the source from which the radiation proceeds. For the sake of illustration, let the source of the tion be stationary with respect to the medium that transmits the waves, and let the velocity of the waves in this medium be V. If N is the number of waves of a certain definite length that the source emits every second, then the observer will also receive N of these waves every' second, provided he remains stationary. If the observer is moving, however, the case is different. For example, suppose that he is receding from the source of the radiation with a uniform velocity v, and consider what pens in the course of a single second. During this second N waves reach his initial position, just as before; but at the end of the second he is v units of distance beyond that initial position, and hence it is impossible that all of these N waves can have reached him. The deficit will evidently be equal to the number of waves whose combined lengths would just measure v. But the source sends out N waves every second, and when the last of these N is just leaving the source, the first one of the series has proceded to a distance V. Hence V we know that the length of one wave is —; and to find the number of waves that would be required to fill the distance v, we have onry to divide v by the length of a single wave; that V is, we have to divide it by—. Hence the ob i server's motion will diminish the number of Nv waves that reach him every second by —, V and, therefore, when he is receding from the source with the velocity v, he will receive only Nv N(V—v) N — or , waves per second.
V V The result will be, that the wave-length of the sound (or light) will appear to him to be longer than it really is. The same line of reasoning will show that if the observer is stationary and the source is receding with a velocity v, the number of waves that the observer will receive NV per second will be . If the motion is such
V -1- v as to diminish the distance instead of increasing it, the algebraic sign of v must be reversed in the foregoing formula.
The most familiar example of Doppler's principle is afforded by the sudden change in the apparent pitch of a sounding bell or whistle on an express train moving at high speed. If the observer stands close to the track, the pitch falls suddenly and very markedly, as the loco motive passes him. The most important appli cations of the principle, however, are in astronomy, in connection with the measure ment of the velocities of the celestial bodies, by observing the displacement that their motion produces in the positions of the lines of their spectra. (See SPECTROSCOPE). If the earth is approaching a heavenly body, the lines in the spectrum of that body are all shifted slightly toward the violet end, owing to the apparent shortening of each wave length by the motion. If the earth and the heavenly body are receding from each other, there is a similar displace ment of the lines toward the red end. The rotation of Saturn's rings has been experi mentally demonstrated in this way, and the velocities of approach and recession of many of the brighter fixed stars have also been de termined. Certain stars have been demon strated to be double, by the discovery that the lines of their spectra are periodically double and single; the lines appearing single when the relative motion of the two components is perpendicular to the line of sight, and double when the positions of the component stars are such that one star is approaching the earth while the other is receding from it. The orbits of certain of these stars have been determined by such measurements, even when the compo nents of the systems are so close together that no telescope can show them separately, nor make them appear otherwise than as a single point of light. See Dousix STARS.