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320

Measurement of the Velocity of Sound.

wind in a hurricane, and sixteen times as swift as an express train.

By noting, then, how long the flash of a gun is seen before the report reaches the ear, one may learn the distance of the ship o battery from which the gun is fired. The captain of a ship chasing or chased might thus discover its distance by shots fired from the enemy's vessel. In the same manner the distance of a thundercloud may be ascertained by the interval between the flash and the peal. When this interval is between four and five seconds, the distance of the cloud will be about a mile; and one reason of the long-continued roll of thunder is, that although the lightning darts almost instantly through a whole chain of clouds, even of miles in length, the sounds proceeding from the different points of its path are only heard in succession, as they arrive at the ear from unequal distances. (The pulse at the wrist of a healthy man is a convenient measure of time for ascertaining distances by the motion of sound, -each beat marking nearly a second, and therefore indicating a distance of nearly a quarter of a mile.)

489. The depth of a deep well, such as that at Carisbrooke, in the Isle of Wight, may be determined in a similar way by dropping a stone into it. The number of seconds which elapse between the time at which the stone is dropped and its meeting the surface of the water, if it can be seen, will allow of a rough calculation. In this case, however, we must estimate and allow for the time which the stone occupies in falling, according to the laws described in a former part of this work.

A long line of muskets fired at the same instant cannot appear as a single report to any person who is not in the centre of a circle, of which the line forms a part; and a company of soldiers, in like manner, cannot simultaneously respond to their officer's command to fire unless they form a circle round him.

An extended orchestra of musicians cannot be heard equally well from all situations near them: hence the absurdity of a monster band where good music is intended.

490. The rate at which sound travels has been determined by a variety of experiments. One of the most simple methods was that adopted by Moll and Van Beck at Utrecht in 1823. This consisted in firing cannon at stated intervals from two places, the exact distance between which was known. The time required for the report to be heard from one point to the other was accurately determined by chronometers

Velocity of Sound in Air.

321

All sounds, whether strong or weak, grave or sharp, travel with equal velocity; in fact, were it not so, there would be no power to appreciate harmony in musical sounds. Some facts, however, appear to show that in certain cases a very intense sound travels with greater rapidity than a low sound.

In damp air sound travels more slowly than in dry air. The elasticity of the air is reduced by moisture, and not only the velocity, but the intensity of sound, is reduced under these circumstances. Thus, it has been observed that the sound of the human voice, the ringing of a bell, the blast of a trumpet, and, indeed, all sounds whatever, are more or less deadened by a damp state of the atmosphere, and are not heard as in dry air.

Dry, frosty air is usually considered, by reason of its greater density, to be most favourable to the transmissibility of sound. Church bells, in country places, are heard more distinctly and with greater intensity in dry than in damp weather, and a change of weather is often predicted by a rustic according to the sound produced upon his ear.

Peschel states that when the air is calm and dry, the report of a musket may be heard at 8000 paces; the marching of a company of soldiers may be heard, on a still night, at a distance of from 580 to 830 paces; a squadron of cavalry, at a foot pace, 750 paces; trotting or galloping, at 1080 paces distant; heavy artillery, travelling at a foot pace, is audible at a distance of 660 paces; if at a trot or gallop, at 1000 paces. A powerful human voice, in the open air, at an ordinary temperature, is audible at a distance of 230 paces. The pace here described as the standard of measurement used for military purposes, represents a yard or rather less. The above figures may therefore be taken as indicating yards.

491. Several circumstances affect the velocity of sound in air; and in making experiments for its determination, due account must be taken of these. First, the wind affects it, very much as a current of water affects the motion of a sailing vessel: i.e., it accelerates or retards the velocity, according as it may be moving in the same or in an opposite direction. At equal distances sound is much more intense in calm than in windy weather. Secondly, the temperature of the air has a marked influence on its rate of conveying sound. Increase of temperature (see Art. 413) augments the elasticity of air, and therefore, as may easily be conceived, increases the rapidity with which individual particles will deliver the sound-pulsations. The velocity increases about I'I foot for every degree of the thermometer

322

Velocity of Sound in Liquids.

above 32°. Thus the velocity of sound in air of the same temperature as freezing water, has been found to be only 1089 feet per second, while at the temperature of 60° F. it is 1120, and at 80° F. it is as high as 1140 feet per second. (See Art. 104.) Thirdly, for the same temperature and elasticity, the velocity of sound varies with the degree of density of an aërial or gaseous substance. In hydrogen, which, with the temperature and elasticity of common air, is only one-sixteenth of its density, sound travels four times faster than in air; while in carbonic acid gas, which is heavier than air, sound passes more slowly.

The subjoined figures represent in metres the relative velocity of sound in the different gases at the temperature of 32° F. :-Carbonic acid, 261; oxygen, 317; air, 333; carbonic oxide, 337; hydrogen, 1269. These results are derived from the experiments of Dulong. Sir David Brewster states that in sulphurous acid gas sound moves only at the rate of 751 feet in a second, while in hydrogen it moves at the rate of 3000 feet in the same period of time. (See Art. 539.)

From the known density and elasticity of air, Newton calculated that the velocity of sound in it, at 32° F., should be 916 feet per second; and the difference of nearly one-sixth, by which his theoretical calculation fell short of the ascertained velocity, baffled the ingenuity of the profound philosopher. The true explanation was afterwards given by the French mathematician Laplace. He considered that the sound-pulse, in its passage through the air, produced in its alternate condensations and rarefactions an alternate heating and chilling of the air, effects which combined to increase the difference of elastic force in the two portions of the wave, and so to increase the rapidity of propagation of the pulsation.

492. In liquids and solids, sound travels much faster than in air, not on account of the closer proximity of the particles, but rather by reason of the superior elasticity of liquids and solids. Liquids, as we have seen (Art. 294), are almost incompressible; and the greater the force with which they resist compression, the more rapid will be the rebound after compression, and the more rapid, therefore, will be the passage of sonorous pulses through them.

In water a wave of sound passes four times as rapidly as in air. The velocity has been estimated at about 4708 feet in a second of time. Some experiments made on the Lake of Geneva, in 1827, by Colloden and Sturm, showed that the velocity in water, compared with air, was as 1435 to 333. In saline solutions it is said to travel still more rapidly than in water.

Velocity of Sound in Solids.

323

Sounds are not readily transmitted from air to a denser medium like water. Thus, blows struck on a diving bell thirty feet below water may be distinctly heard at the surface of the water, but a sound immediately above the water will not be heard by persons within the bell.

493. In solids sound travels more rapidly than in liquids. Its velocity in solids has been estimated at 11,280 feet in a second (Art. 104), but the velocity is found to vary according to the nature of the solid. Thus, in the metals it is from 4 to 16 times that in air. If the rate of transmission in air is taken as 1, that in gold is 5; in silver and platinum, 8; in copper, II; in steel wire, 16.

Biot performed a variety of experiments on the velocity of sound in cast-iron, using for this purpose the water pipes of the city of Paris, which were pipes 3000 feet in length. He found it to be 10 times greater than in air. In ice sound travels at about the same rate as in water; and in glass, Chladni found that its velocity was 17 times greater than in air. (For another mode of measurement see Art. 539.) The same observer found that in woods it was from 10 to 17 times quicker than in air. This shows that it is not mere density or closeness of the particles which is the explaining cause. If air = I, beech and pine = 10; ash, alder, fir, and acacia = 15; and aspen = 16. This is the velocity along the fibre, which is in general three or four times greater than that across the fibre; a striking illustration of the difference of physical properties due to mere molecular arrangement.* (See Art. 538.)

The conduction of sound by solids, and especially by wood, is well illustrated in the telegraph posts, between which lines of 180 feet of metallic wire are stretched. Under a gentle wind these long wires vibrate and produce a loud sound, not always heard in the air, but rendered immediately perceptible when the ear is placed against the wooden post. This sound sometimes amounts to a musical murmur rising and falling with the wind, and at others to a roar like the escape of high-pressure steam from a distant locomotive.

It has been shown, however, that the velocity is affected by the strength of the sound; strong sounds travel more quickly than weak ones. The difference of velocity in solids and in air, may be readily heard by applying an ear to a wall or the end of a long iron pipe, while a person strikes the wall or pipe with a hammer

* According to Sir David Brewster sound moves through tin at the rate of 8175 feet, and through iron, glass, and some kinds of wood at the rate of 18,530 feet in a second.

324

Law of Intensity of Sound.

at some distance. Two sounds are heard, the first through the solid, followed by the second through the air, the interval being quite appreciable.

494. Sound, like gravitation, light, heat, or any other uniformly spreading influence, follows the law of the intensity being inversely as the square of the distance (see Art. 19). Thus, at twice the distance, sound has only one fourth of its intensity; so that to make himself heard at this distance, a man must raise his voice not twice only, but to four times the pitch. Hence four bells, or four cannon, would have the same strength in sound as one bell rung or one cannon fired at half the distance. But if, instead of being allowed to spread on all sides, the sound be confined in a long smooth tube, it suffers little diminution of intensity by distance. Thus a watch placed at the end of a long gas-tube, without any sharp bends in it, may be distinctly heard ticking at the other end of the tube, though its beats are altogether inaudible through the air. A continuous plank or metallic rod has the same power of sound-conduction. A conversation has been held in an ordinary tone of voice between two persons through empty water-pipes nearly three-quarters of a mile in length. The use of speaking tubes in manufactories, business establishments, hotels, and even private dwelling-houses, is now quite common. These tubes operate by confining the undulations of sound and spreading or radiating in all directions.

preventing them from The sides of the tube

not only confine the sound, but produce a continued reflection of it.

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495. As a wave of water is turned back by a smooth wall or other such obstacle, so the pulses or waves of sound are regularly reflected from flat surfaces. After reflection, it appears just what it would have been at the same distance beyond (had there been no obstacle), only moving in a different direction. A wave of sound falling perpendicularly on a wall, returns with equal velocity in the same direction until it reaches the spot from which it emanated, and it thus produces what is called an Echo.* Flat

*This reflection, owing to the nature of the medium conveying sound, takes place in spherical or concentric undulations, which spread as if they had emanated from another centre placed at an equal distance on the other side of the obstacle which reflects them.

In order that an echo should be heard by the person making the sound,

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