that sound requires a certain time to pass from one place to another. Thus, if we pay attention to a woodman felling trees at a distance, we see the axe fall in silence, and only hear the sound a moment afterwards. In like manner, when a gun is fired, the report is heard after the flash of light. Thunder, too, is only heard some time after lightning, although in the cloud both thunder and lightning are heard simultaneously.

The velocity of sound was determined experimentally by the members of the Bureau of Longitude of Paris in June 1822, during the night. A cannon was placed on a hill at Montlhéry near Paris, and another on a plateau near Villejuif. The distance of the two places was carefully measured, and was found to be 61,045 feet, and a gun was fired at each station twelve successive times at intervals of 10 minutes (fig. 139). Observers placed near the pieces noted

by means of accurate and delicate watches, the time which elapsed between the appearance of the flash and the hearing the sound at the opposite station; and the mean of the observations gave the number 54.6 seconds. This was just the time which the sound required to travel from one station to the other; for we shall afterwards see that the velocity of light is such that the time it requires to traverse the above distance is inappreciable. Hence by a simple calculation we find that sound travels 1,118 feet in a second.

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The above observations were made when the air was at a tem

perature of 16o. At a lower temperature the velocity of sound

is less.

From some accurate experiments made by the above method near Amsterdam, the velocity of sound is taken at 1,093 feet per second in dry air at zero. Its velocity increases about 2 feet per second for every degree centigrade. So that at 15° C., which is the ordinary temperature, the velocity of sound is 1,120 feet per second.

A knowledge of the velocity of sound enables us to measure distances. Thus, suppose we want to know the distance at which a gun is fired, of which we only hear the report 15 seconds after seeing the flash. As sound travels at 1,120 feet in a second, it must traverse 16,800 feet in the time mentioned, and this would be the distance at which the gun was fired. In the same manner we may calculate the depth of a well from the number of seconds which elapses between the moment at which a stone falls into it and that at which the sound is produced. The calculation is, however, a little more complicated, for the time which the body requires in falling has to be taken into account.

The velocity of sound is not the same in different gases; it is greater in those which are less dense. Dulong found the velocity at zero to be 846 feet per second for carbonic acid, 1,040 feet in oxygen, and 1,093 in air, 1,106 in carbonic oxide, and 4,163 feet in hydrogen.

The velocity of sound is the same in air for all sounds, whether strong or weak, grave or acute.

For this reason the tune played by a band is heard at a great distance without alteration, except in intensity, which could not be the case if some sounds travelled more rapidly than others.

159. Velocity of sound in liquids and in solids. We have already seen that liquids conduct sound; they even conduct it better than gases. The velocity of sound in water was investigated in 1827 by Colladon and Sturm. They moored two boats at a known distance in the Lake of Geneva. The first supported a bell immersed in water, and a bent lever provided at one end with a hammer which struck the bell, and at the other with a lighted wick, so arranged that it ignited some powder the moment the hammer struck the bell. To the second boat was affixed an ear-trumpet, the bell of which was in water, while the mouth was applied to the ear of the observer, so that he could measure

the time between the flash of light, and the arrival of sound by the water. By this method the velocity was found to be 4,708 feet in a second at the temperature 8°, or four times as great as in air. That sound travels more rapidly in solids than in air is easily shown. If a person holds his ear against one end of a tolerably long iron bar, while another person gives a hard blow at the other end, two distinct sounds are heard; the first transmitted by the metal, and the other transmitted by the air. The velocity of sound in iron is 16,802 feet in a second; in copper, 11,606; in oak, 10,900; and in fir, 15,218 feet.

160. Reflection of sound.—We have seen that sound is propagated in air by means of spherical waves, alternately condensed and rarefied, and which are developed about it in all directions. So long as these sonorous waves are not obstructed in their motion, they are propagated in the form of concentric spheres; but when they meet with an obstacle, they follow the general law of elastic bodies; that is, they are repelled like an ivory ball which strikes against a wall; they return upon themselves, forming new concentric waves, which seem to emanate from a second centre on the other side of the obstacle. This phenomenon constitutes the reflection of sound.

The reflection of sound, or rather of sound waves, follows the same laws as the reflection of heat and of light, which we shall subsequently have to explain.

161. Echoes and resonances.-An echo is the repetition of a sound in the air, caused by its reflection from some more or less distant obstacle. Thus, if a few words are loudly spoken at a certain distance from a wood, a rock, or a building, it usually happens that, after a brief interval, the same phrase is heard repeated, as if spoken in the distance by another person; these are the sound waves, which are reflected by the obstacle. There must, however, be a certain distance between the place at which the sound is produced and that at which it is heard.

A very sharp quick sound can produce an echo when the reflecting surface is 55 feet distant; but for articulate sounds at least double that distance is necessary, for it may be easily shown that no one can pronounce or hear distinctly more than five syllables in a second. Now, as the velocity of sound at ordinary temperatures may be taken at 1,125 feet in a second, in a fifth of that time sound would travel 225 feet. If the reflecting surface is 112.5 feet distant, sound would travel through 225 feet in going and returning. The

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Echoes.

155

time which elapses between the articulated and the reflected sound would, therefore, be a fifth of a second, the two sounds would not interfere, and the reflected sound would be distinctly heard. A person speaking with a loud voice in front of a reflecting surface at the distance of 1125 feet can only distinguish the last reflected syllable: such an echo is said to be monosyllabic. If the reflector were at a distance of two or three times 112.5 feet, the echo would be dissyllabic, trisyllabic, and so on.

Multiple echoes are those which repeat the same sound several times; this is the case when two opposite surfaces (for example, two parallel walls) successively reflect sound. There are echoes

which repeat the same sound 20 or 30 times. An echo in the château of Simonetta, in Italy, repeats a sound 30 times. At Woodstock there is one which repeats from 17 to 20 syllables. Near Verdun is an echo formed by two parallel towers, at a distance from each other of about 164 feet. A person placing himself between them, and speaking a word with a loud voice, hears it repeated a dozen times. Echoes usually modify sound; some repeat it with noise; others with a mocking, laughing tone, or a plaintive accent.

We have seen that when the distance at which a sound is reflected is 112 feet an echo is produced; and the question may be asked, what happens when the distance is less than this? As the sound has then a smaller distance to traverse, both in going and coming, than 112 feet, it follows that the reflected sound is added to the directly spoken one. They cannot be heard separately, but the sound is strengthened. This is what is called resonance, and its effects are so much the more marked the more elastic are the surfaces from which the sound is reflected. In uninhabited houses, where there is no furniture, the walls, the flooring, and the ceiling readily vibrate, and we all know how the noise of footsteps and the sound of the voice then resound. Tapestry and hangings, which are not elastic, deaden the sound.

As the laws of the reflection of sound are the same as those of light and heat, curved surfaces produce acoustic foci, like the luminous and calorific foci produced by concave reflectors. If a person standing under the arch of a bridge speaks with his face turned towards one of the piers, the sound is reproduced near the other pier with such distinctness that a conversation can be kept up in a low tone, which is not heard by any one standing in the intermediate spaces.

There is a square room with an elliptical ceiling, on the groundfloor of the Conservatoire des Arts et Métiers, in Paris, which presents this phenomenon in a remarkable degree when persons stand in the two foci of the ellipse.

It is not merely by solid surfaces, such as walls, rocks, etc., that sound is reflected. It is also reflected by clouds, and on passing into a layer of air of greater density than its own; it is also further reflected by the vesicles of mist. When the weather is foggy, sounds undergo innumerable partial reflections, and are rapidly destroyed.

Whispering galleries are formed of smooth walls, having a continuous curved form. The mouth of the speaker is presented at one point, and the ear of the hearer at another and distant point. In this case, the sound is successively reflected from one point to the other until it reaches the ear.

Different parts of the earth's surface are unequally heated by the sun, owing to the shadows of trees, evaporation of water, and other causes, so that in the atmosphere there are numerous ascending and descending currents of air of different density. Whenever a sonorous wave passes from a medium of one density into another it undergoes partial reflection, which, though not strong enough to form an echo, distinctly weakens the direct sound. This is doubtless the reason, as Humboldt remarks, why sound travels further at night than at daytime; even in the South American forests, where the animals, which are silent by day, fill the atmosphere in the night with thousands of confused sounds.

162. Causes which influence the intensity of sound.-Many causes modify the force or the intensity of the sound. These are, the distance of the sonorous body, the amplitude of the vibrations, the density of the air at the place where the sound is produced, the direction of the currents of air, and, lastly, the proximity of other sonorous bodies.

i. The intensity of sound is inversely as the square of the distance of the sonorous body from the ear. This law has been deduced by calculation, but it may be also demonstrated experimentally. Let us suppose several sounds of equal intensity, for instance, bells of the same kind, struck by hammers of the same weight, falling from equal heights. If four of these bells are placed at a distance of 20 yards from the ear, and one at a distance of 10 yards, it is found that the single bell produces a sound of the same intensity