wind was eliminated. A second commission repeated these experiments in 1832, using a distance of 18.6 kilometers, or a little more than 11.5 miles. The value found was 331.2 meters per second at 0° C. The accepted value is now 331.3 meters. The speed in water is about 1400 meters per second, and in iron 5100 meters.

The speed of sound in air is found to increase with an increase in temperature. The amount of this increase is about 60 centimeters per second per degree centigrade, or about 2 feet per second per degree centigrade. Hence the speed at 20° C. is about 343.3 meters per second. It is sufficiently accurate to remember 1090 feet per second at 0° C. (= 32° F.), or 1130 feet per second at 20° C. (= 68° F.).

381. Mechanism of transmission. When a firecracker or toy cap explodes, the powder is suddenly changed to a gas, the volume of which is enormously greater than the volume of the powder. The air is therefore suddenly pushed back in all directions from the center of the explosion. This means that the air particles which lie about this center are given violent outward velocities.* When these outwardly impelled air particles collide with other particles, they give up their outward motion to these second particles, and these in turn pass it on to others, etc. It is clear, therefore, that the motion started by the explosion must travel on from particle to particle to an indefinite distance from the center of the explosion. (See opposite pages 362 and 419.) Furthermore, it is also clear that, although the motion travels on to great distances, the individual particles do not move far from their original positions; for it is easy to show experimentally that whenever an elastic body in motion collides with another similar body at rest, the colliding body simply transfers its motion to the body at rest and comes itself to rest.

*These outward velocities are simply superposed upon the velocities of agitation which the molecules already have on account of their temperature. For our present purpose we may ignore entirely the existence of these latter velocities and treat the particles as though they were at rest, save for the velocities imparted by the explosion.

Let six or eight equal steel balls be hung from cords in the manner shown in Fig. 348. First let all the balls but two adjacent ones be held to one side, and let one of these two be raised and allowed to fall against the other. The first ball will be found to lose its motion in the collision, and the second will be found to rise to practically the same height as that from which the first fell. Next let all the balls be placed in line and the end one raised and allowed to fall as before. The motion will be transmitted from ball to ball, each giving up the whole of its motion practically as soon as it receives it, and the last ball will move on alone with the velocity which the first ball originally had.

FIG. 348. Illustrating the

particle to particle

The preceding experiment furnishes a very nice mechanical illustration of the manner in which the air particles which receive motions from an exploding firecracker or a vibrating propagation of sound from tuning fork transmit these motions in all directions to neighboring layers of air, these in turn to the next adjoining layers, etc., until the motion has traveled to very great distances, although the individual particles themselves move only very minute distances. When a motion of this sort, transmitted by air particles, reaches the drum of the ear, it produces the sensation which we call sound. In physics, however, the word "sound" means not the sensation but rather the wave motion capable of producing it.

382. A train of waves; wave length. In the preceding paragraphs we have confined attention to a single pulse traveling out from a center of explosion. A very simple and beautiful way of showing the sort of disturbance which is set up in the air by a continuously vibrating body is furnished by the socalled manometric flames (see opposite page 349).

First let the mirror be rotated when no note is sounded before the mouthpiece. There will be no fluctuations in the flame, and its image, as seen in the moving mirror, will be a straight band, as shown in 2. Next let a mounted C fork be sounded, or some other

HERMANN LUDWIG FERDINAND VON HELMHOLTZ (1821-1894) Noted German physicist and physiologist; professor of physiology and anatomy at Bonn and at Heidelberg from 1855 to 1871; professor of physics at Berlin from 1871 to 1894; published in 1847 a famous paper on the conservation of energy, which was most influential in establishing that doctrine; invented the ophthalmoscope; discovered the physical significance of tone quality and made other contributions to acoustics and optics; was preeminent also as a mathematical physicist

This device consists of the following parts: a chamber in the block B, through which gas is led by way of the tubes C and D to the flame F; a second chamber in the block A, separated from the first chamber by an elastic diaphragm made of very thin sheet rubber or paper and communicating with the source of sound through the tube E and trumpet G; and a rotating mirror M by which the flame is observed. With constant speed of rotation the number of teeth per inch gives the pitch of the sound. Quality is also analyzed by the manometric flame, as shown on page 373

simple tone produced in front of G. The image in the mirror will be that shown in 3. Then let another fork having twice as many vibrations per second be sounded in place of the C. The image will be that shown in 4. The images of the flame are now twice as close together as before, since the blows strike the diaphragm twice as often.*

When the note was produced before the mouthpiece G, the up-and-down motions of the flame observed in the revolving mirror were due to variations in the pressure of the gas coming to the flame through the chamber B. These variations in pressure were the direct result of vibrations of the diaphragm which could have been caused in no other way than by a regular succession of air pulses striking upon it.

ABC

Wave length

Consider the pulses produced by the prong of Fig. 349. Each time that this prong moves to the right it sends out a pulse which travels through the air at the rate of 1100 feet per second, in exactly the manner described in the preceding paragraphs. Hence, if the prong is vibrating uniformly, we shall have a continuous succession of pulses following each other through the air at exactly equal intervals. Suppose, for example, that the prong makes 110 complete vibrations per second. Then at the end of one second the first pulse sent out will have reached a distance of 1100 feet. Between this point and the prong there will be 110 pulses distributed at equal intervals; that is, each two adjacent pulses will be just 10 feet apart. If the prong made 220 vibrations per second, the distance between adjacent pulses would be 5 feet, etc. The distance between two adjacent pulses in such a train of waves is called a wave length.

FIG. 349. Vibrating reed sending out a train of equidistant pulses

*If a rotating mirror is not to be had, a piece of ordinary mirror glass held in the hand and oscillated back and forth about a vertical axis will be found to give satisfactory results.