We can now easily perceive that the shorter and thinner the string is, and the tighter it is, the number of vibrations will be greater and greater. The density of it is also to be considered, and when these conditions are in the smallest proportion then the tone will be highest. The depth will naturally increase with the thickness, density, and length, and with a decreasing tension. But we have strings of same thickness stretched to different degrees of tension, and thus producing different notes. Some strings are covered with wire to increase their gravity, and thus to produce low notes.
When a number of separate sounds succeed each other in very rapid course they produce a sound, but to appear as one sound to the ear they must amount to fifteen or sixteen vibrations every second. The particles of matter in the air form a connected system, and till they are disturbed they remain in equilibrium; but the moment they are in any way thrown out of this state they vibrate as the pendulum vibrates. The particles thus strike each other, and impart a motion to the elastic medium air, so a sound comes to us.
The intensity of sounds gets less the farther it goes from us, or the loudness of sound is less the greater its distance. The law is, that in an unvarying medium the loudness varies inversely as the square of the distance. But Poisson has shown that when air-strata, differing in density, are existing between the ear and the source of the sound, the intensity or loudness with which it is heard depends only on the density of the air at the place the sound originated. This fact has been substantiated by balloonists who heard a railway whistle quite distinctly when they were nearly 20,000 feet above the ground. It therefore follows that sound can be heard in a balloon equally well as on the earth at certain given distances. But as the density of the air diminishes the sound becomes fainter, as has been proved by the bell rung in the receiver of an air-pump. The velocity of sound, to a certain extent, depends upon its intensity, as Earnshaw sought to prove; for he instanced a fact that in the Arctic regions, where sound can be heard for an immense distance, in consequence of the still and homogeneous air, the report of a cannon two miles and a half away was heard before the loud command to “fire,” which must have preceded the discharge. Another instance showing the difference in hearing through mixed and homogeneous media may be referred to. In the war with America, when the English and their foes were on opposite sides of a stream, an American was seen to beat his drum, but no sound came across. “A coating of soft snow and a thick atmosphere absorbed the noise.” Glazed, or hard snow, would have a contrary effect. Reynault also experimentally verified his theory, that sound when passing through a space of nearly 8,000 feet lost velocity as its intensity diminished, and in that distance between its arrival at 4,000 feet and at 7,500 feet, the sound velocity diminished by 2·2 feet per second. He also tried to demonstrate that sound velocity depended upon its pitch, and that lower notes travelled with the greater speed.
The reflection and refraction of sound follows the same fundamental laws as the reflection and refraction of light. The reflection of sound is termed an Echo, which is familiar to all tourists in Switzerland and Ireland particularly. There are several very remarkable echoes in the world: at Woodstock, and at the Sicilian cathedral of Gergenti, where the confessions poured forth near the door to priestly ears were heard by a man concealed behind the high altar at the opposite end. It is curious that such a spot should have been accidentally chosen for the Confessional. The whispering gallery in St. Paul’s is another instance of the echo.
Echoes are produced by the reflection of sound waves from a plane or even surface. A wall, or even a cloud, will produce echoes. Thunder is echoed from the clouds. (The celebrated echo of “Paddy Blake,” at Killarney, which, when you say “How do you do,” is reported to reply, “Very well, thank you,” can scarcely be quoted as a scientific illustration.) And the hills of Killarney contain an echo, and the bugle sounds are beautifully repeated. In the cases of ordinary echo, when the speaker waits for the answer, he must place himself opposite the rock. If he stand at the side the echo will reply to another person in a corresponding place on the farther side, for the voice then strikes the rock at an angle, and the angle of reflection is the same, as in the case of light.
But if it should happen that there are a number of reflecting surfaces the echo will be repeated over and over again, as at the Lakes of Killarney. The Woodstock Echo, already referred to, and mentioned by several writers, repeats seventeen syllables by day, and twenty by night. In Shipley there is even a greater repetition. Of course the echo is fainter, because the waves are weaker if the reflecting surface be flat. But, as in the case of the mirrors reflecting light, a circular or concave surface will increase the intensity. A watch placed in one mirror will be heard ticking in the other focus. Whispering galleries carry sound by means of the curved surface. Sir John Herschel mentions an echo in the Menai Suspension Bridge. The blow of a hammer on one of the main piers will produce the sound from each of the crossbeams supporting the roadway, and from the opposite pier 576 feet distant, as well as many other repetitions.
Refraction of sound is caused by a wave of sound meeting another medium of different density, just as a beam of light is refracted from water. One sound wave imparts its motion to the new medium, and the new wave travels in a different direction. This change is refraction. The sound waves are refracted in different directions, according to the velocity it can acquire in the medium. If a sound pass from water into air it will be bent towards the perpendicular, because sound can travel faster in water than in air. If it pass from air into water its force will cause it to assume a less perpendicular direction, there being greater velocity in water. The velocity in air is only 1,100 feet in a second in our atmosphere. In water sound travels 4,700 feet in the same time. When the wave of sound falls upon a medium parallel to the refracting surface there is, however, no refraction—only a change of velocity, not direction.
When sound waves are prevented from dispersing the voice can be carried a great distance. Speaking tubes and trumpets, as well as ear trumpets, are examples of this principle, and of the reflection of sound.
There are many very interesting experiments in connection with Acoustics, some of which we will now impart to our readers. We shall then find many ingenious inventions to examine—the Audiphone, Telephone, Megaphone, and Phonograph, which will occupy a separate chapter. We now resume.
Amongst the experiments usually included in the course of professors and lecturers who have a complete apparatus at their command, and which at first appear very complicated and difficult, there are some which can be performed with every-day articles at hand. There is no experiment in acoustics more interesting than that of M. Lissajons, which consists, as is well known to our scientists, of projecting upon a table or other surface, with the aid of oxy-hydrogen light, the vibratory curves traced by one of the prongs of a tuning-fork. We can perform without difficulty a very similar experiment with the humble assistance of the common knitting-needle.
Fix the flexible steel needle firmly in a cork, which will give it sufficient support; fasten then at the upper extremity a small ball of sealing wax, or a piece of paper about the size of a large pea. If the cork in which the needle is fixed be held firmly in one hand, and you cause the needle to vibrate by striking it, and then letting it sway of itself, or with a pretty strong blow with a piece of wood, you will perceive the little pellet of wax or paper describe an ellipse more or less elongated, or even a circle will be described if the vibrations be frequent. The effect is much enhanced if the experiment be performed beneath a lamp, so that plenty of light may fall upon the vibrating needle. In this case, the persistence of impressions upon the retina admits of one seeing the vibrating circle in successive positions, and we may almost fancy when the needle is struck with sufficient force, that an elongated conical glass, like the old form of champagne glass, is rising from the cork, as shown in the illustration annexed (fig. 173).
Fig. 173.—Experiment showing vibration of sound waves.
Acoustics may be studied in the same way as other branches of physical science. We will describe an interesting experiment, which gives a very good idea of the transmission of sounds through solid bodies. A silver spoon is fastened to a thread, the ends of which