is used, not so much to make high-energy electrons(actually if we could get them out of the machine more conveniently we would not say this)as to make very energetic photons--gamma rays--by passing the energetic electrons through a solid tungsten"target, "and letting them radiate photons from this bremsstrahlung effect 34-6 The Doppler effect Now we go on to consider some other examples of the effects of moving sources Let us suppose that the source is a stationary atom which is oscillating at one of its natural frequencies, wo. Then we know that the frequency of the light we would observe is wo. But now let us take another example, in which we have a similar oscillator oscillating with a frequency wl, and at the same time the whole atom the whole oscillator, is moving along in a direction toward the observer at velocity v. Then the actual motion in space, of course, is as shown in Fig. 34-10(a). Now we play our usual game, we add cT; that is to say, we translate the whole curve backward and we find then that it oscillates as in Fig. 34-10(b). In a given amount of timeT, when the oscillator would have gone a distance ur, on the xvs. ct diagram it goes a distance(c-v)r So all the oscillations of frequency wI in the time Ar are for d in the interval AT=(1-u/c)AT; they are squashed together, (bI as this curve comes by us at speed c, we will see light of a higher frequency higher by just the compression factor(1-y/c). Thus we observe (34.10) curves of a moving oscilloto. and x'-t Fig. 34-10. The x We can, of course, analyze this situation in various other ways. Suppose that the atom were emitting, instead of sine waves, a series of pulses, pip, pip, pip, pip, at a certain frequency w1. At what frequency would they be received by us? The first one that arrives has a certain delay but the next one is delayed less because in the meantime the atom moves closer to the receiver. Therefore the time between the"pips "is decreased by the motion. If we analyze the geometry of the situation we find that the frequency of the pips is increased by the factor 1/(1 -v/c) Is w=wo/(1-U/c), then, the frequency that would be observed if we took an ordinary atom, which had a natural frequency wo, and moved it toward the receiver at speed v? No; as we well know, the natural frequency w 1 of a moving atom is not the same as that measured when it is standing still, because of the relativistic dilation in the rate of passage of time. Thus if wo were the true natural frequency, then the modified natural frequency w1 would be Therefore the observed frequency w is (3412) 1-v/c The shift in frequency observed in the above situation is called the Doppler effect: if something moves toward us the light it emits appears more violet, and if it moves away it appears more red We shall now give two more derivations of this same interesting and important result. Suppose, now, that the source is standing still and is emitting waves at frequency wo, while the observer is moving with speed v toward the source. After a certain period of time t the observer will have moved to a new position, a distance at from where he was at [=0. How many radians of phase will he have seen go by? A certain number, wof, went past any fixed point, and in addition the observer has swept past some more by his own motion, namely a number utko(the number of radians per meter times the distance). So the total number of radians in the time I, or the observed frequency, would be w1=w0 kol. We have made this analysis from the point of view of a man at rest; we would like to know hor it would look to the have to worry again about the difference in clock rate for the two observers and this time that means that have to divide by V1-u2/c2. So if ko is the wave number, the number of radians