Interference
Next, we may test what happens when we have two sources side by side                         several wavelengths apart (Fig. 28–3). The law is that the                         two sources should add their effects at point $1$ when both of the                         sources are connected to the same generator and are both moving up and                         down the same way, so that the total electric field is the sum of the                         two and is twice as strong as it was before. Now comes an interesting possibility. Suppose we make the charges in                         $S_1$ and $S_2$ both accelerate up and down, but delay the timing                         of $S_2$ so that they are $180^\circ$ out of phase. Then the field                         produced by $S_1$ will be in one direction and the field produced                         by $S_2$ will be in the opposite direction at any instant, and therefore                         we should get no effect at point $1$. The phase of oscillation                         is neatly adjustable by means of a pipe which is carrying the signal                         to $S_2$. By changing the length of this pipe we change the time it                         takes the signal to arrive at $S_2$ and thus we change the phase of                         that oscillation. By adjusting this length, we can indeed find a place                         where there is no more signal left, in spite of the fact that both                         $S_1$ and $S_2$ are moving! The fact that they are both moving can be                         checked, because if we cut one out, we can see the motion of the                         other. So the two of them together can produce zero if                         everything is adjusted correctly.                          Now, it is very interesting to show that the addition of the two                         fields is in fact a vector addition. We have just checked it                         for up and down motion, but let us check two nonparallel                         directions. First, we restore $S_1$ and $S_2$ to the same phase; that                         is, they are again moving together. But now we turn $S_1$ through                         $90^\circ$, as shown in Fig. 28–4. Now we should have at                         point $1$ the sum of two effects, one of which is vertical and the                         other horizontal. The electric field is the vector sum of these two                         in-phase signals—they are both strong at the same time and go                         through zero together; the total field should be a signal $R$                         at $45^\circ$. If we turn $D$ to get the maximum noise, it should be at                         about $45^\circ$, and not vertical. And if we turn it at right angles                         to that direction, we should get zero, which is easy to                         measure. Indeed, we observe just such behavior! Now, how about the retardation? How can we demonstrate that the signal                         is retarded? We could, with a great deal of equipment, measure the                         time at which it arrives, but there is another, very simple                         way. Referring again to Fig. 28–3, suppose that $S_1$                         and $S_2$ are in phase. They are both shaking together, and they                         produce equal electric fields at point $1$. But suppose we go to a                         certain place $2$ which is closer to $S_2$ and farther                         from $S_1$. Then, in accordance with the principle that the acceleration                         should be retarded by an amount equal to $r/c$, if the retardations                         are not equal, the signals are no longer in phase. Thus it should be                         possible to find a position at which the distances of $D$ from $S_1$                         and $S_2$ differ by some amount $\Delta$, in such a manner that there                         is no net signal. That is, the distance $\Delta$ is to be the distance                         light goes in one-half an oscillation of the generator. We may go                         still further, and find a point where the difference is greater by a                         whole cycle; that is to say, the signal from the first antenna reaches                         point $3$ with a delay in time that is greater than that of the second                         antenna by just the length of time it takes for the electric current                         to oscillate once, and therefore the two electric fields produced                         at $3$ are in phase again. At point $3$ the signal is strong again. This completes our discussion of the experimental verification of some                         of the important features of Eq. (28.6). Of course we                         have not really checked the $1/r$ variation of the electric field                         strength, or the fact that there is also a magnetic field that goes                         along with the electric field. To do so would require rather                         sophisticated techniques and would hardly add to our understanding at                         this point. In any case, we have checked those features that are of                         the greatest importance for our later applications, and we shall come                         back to study some of the other properties of electromagnetic waves                         next year.