at that part of the wave; while similar lines drawn to the curve OR B, below A B, show the amount of rarefaction at these points of the wave.

The curve A COR B is not a real picture of a sonorous wave; it is merely a good way of showing its length, and the manner in which the air is condensed and rarefied in it; for sonorous waves are not formed of heaps and hollows like the waves you have seen on the sea. They are not heaps and hollows of air, but only condensations and rarefactions of air. In short, Fig. 36 is merely a convenient symbol which stands for a sonorous wave.

0

A

R

B

FIG. 36.

EXPERIMENT 59.-Look at the row of dots seen in the slit when the disk is at rest, and find the two dots which are nearest to each other; this place in the slit corresponds to the point C in Fig. 36. Next find where the dots are farthest apart; this place corresponds to R in Fig. 36. The distance from C to R is one half wave-length; therefore the distance between two adjoining places, where the dots are nearest together, equals the length of one whole

wave.

CHAPTER VIII.

ON THE INTERFERENCE OF SONOROUS VIBRATIONS AND ON THE BEATS OF SOUND.

EXPERIMENT 60.-Cut out two small triangles of copper foil or tinsel, of the same size, and with wax fasten one on the end of each of the prongs of a tuning-fork. Put the fork in the wooden block and set up the guide (as in experiment, Fig. 21). Prepare a strip of smoked glass, and then make the fork vibrate and slide the glass under it, and get two traces, one from each prong.

FIG. 37.

You observe that the draw together. This

Holding the glass up to the light you will see the double trace, as shown in Fig. 37. wavy lines move apart and then shows us that the two prongs, in vibrating, do not move in the same direction at the same time, but always in opposite directions. They swing toward each other, then away from each other.

EXPERIMENT 61.-What is the effect of this movement of the prongs of the fork on the air? A simple experiment will answer this question.

Place three lighted candles on the table at A, B, and C (Fig. 38). Hold the hands upright, with the space between the palms opposite A, while the backs of the hands face the candles B and C. Now move the hands near each other, then separate them, and make these motions steadily and not too quickly. You thus repeat the motions of the prongs of the fork. While vibrating the hands observe attentively the flames of the candles. When the hands are coming nearer each other, the air is forced

out from between them, and a puff of air is driven against the flame A, as is shown by its bending away from the hands. But, during the above movement, the backs of the hands have drawn the flames toward them, as shown in Fig. 38. When the hands are separating, the air rushes in between them, and the flame A is drawn toward the hands by this motion of the air, while at the same time the flames at B and C are driven away from the backs of the hands. From this experiment it is seen that the space

between the prongs and the faces of the prongs of a fork are, at the same instant, always acting oppositely on the air. This will be made clearer by the study of the diagram, Fig. 39.

This figure supposes the student looking down on the tops of the prongs of the fork. Imagine the prongs swinging away from each other in their vibration. Then the action of the faces c and c on the air is to condense it, and this condensation tends to spread all around the fork. But, by the same movement, the space rr between the prongs is enlarged, and hence a rarefaction is made there. This rarefaction also spreads all around the fork. But, as the condensations produced at c and c and the rarefactions at r and r spread with the same velocity, it follows

that they must meet along the dotted lines I, I, I, I, drawn from the edges of the fork outward. The full -circle lines around the fork in Fig. 39 represent the middle of the condensed shells of air, while the broken -circle lines stand for the middle of the rarefied shells of air.

The

Now what must happen along these dotted lines, or, rather, surfaces ? Evidently there is a struggle here between the condensations and the rarefactions. former tend to make the molecules of air go nearer together, the latter try to separate them; but, as these actions are equal, and as the air is pulled in opposite directions at the same time, it remains at rest-does not vibrate. Therefore, along the surfaces I, I, I, I, there is silence. When the prongs vibrate toward each other they make the reverse actions on the air; that is, rarefactions are now sent out from c and c, while condensations are sent from r and r, but the same effect of silence along I, I, I, I is produced.

EXPERIMENT 62.-That this is so, is readily proved by the following simple experiment. Vibrate the fork and hold it upright near the ear. Now slowly turn it round. During one revolution of the fork on its foot, you will perceive that the sound goes through four changes. Four times it was loud, and four times it was almost if not quite gone. Twirl the fork before the ear of a companion; he will tell you when it makes the loudest sound, and when it becomes silent. You will find that when it is loudest the faces c, c of the prongs, or the spaces r, r between them, are facing his ear; and when he tells you that there is silence you will find that the edges of the fork, that is, the planes 7, 1, 1, 1, are toward his ear.