Part 48

The next step was the psaltery, which was produced in the Middle Ages. It was a box with strings stretched across it and represented the first crude attempt at using a sounding board. A larger instrument which came about the same time and was very like the psaltery, was the dulcimer. Both were played by picking the strings with the finger or a small piece of bone or other substance.

Then came the keyboard, first used on stringed instruments in what is called the _clavicytherium_. This consisted of a box with cat-gut strings ranged in a semitriangle. On the end of each key was a quill, which picked the string when the key was operated.

After this came the clavichord. It was built like a small square piano without legs. The strings were made of brass and on the end of each key was a wedge-shaped piece of brass which picked the strings. The elder Bach composed his music on the clavichord, his favorite instrument, and that is why the music written by Bach is full of soft and melancholy notes. The clavichord produced only such notes.

The next steps brought the virginal, spinet and harpsichord. The strings on all three were of brass with quills at the key ends for picking the strings. The virginal and spinet were very much alike. The harpsichord was larger and sometimes was made with two keyboards. These instruments had notes covering four octaves only.

The arrangement of the strings in the harpsichord provided one step nearer to our piano. It had five octaves of notes and there were at least two strings to each note instead of only one, as in previous instruments.

Why Do We Have Only Seven Octaves On a Piano? Why Not Twelve or More Octaves?

Ordinarily the longest key-board of the piano has seven octaves and three notes in addition, or 52 notes, not counting the sharps and flats. An octave you, of course, know consists of the seven notes C D E F G A B. Every eighth note is a repetition of the one seven notes below or above. The reason that there are no more notes or octaves on the piano is that if we extended the key-board either way one or two octaves more, we should not be able to hear the notes struck on the keys. There would be sound produced, or course, but the vibrations would be too fine for the human ear to hear. It is said that the range of the human ear does not go beyond somewhere between eleven and twelve octaves.

How Sounds Are Produced.

If you look closely at a tuning fork, or a piano string, while it is sounding, you can see that it is swinging rapidly to and fro, or vibrating. Touch it with your finger and thus stop its vibration and it no longer produces sound. The only difference that you can discover in the fork or string when sounding and when silent is that when you stop the motion it is silent and when it vibrates it makes a sound. From this we learn that the sounds are due to the vibrations of sounding bodies. This has been proven by the examination of so many sounding bodies that we believe that all sounds are produced by vibrations.

The question that next presents itself is, how the vibrations affect our ears, so as to produce the sensation of hearing. This may be made clear by a very simple, but striking, experiment. If a bell which has been arranged to be rung by clock-work is suspended under the receiver of an air pump, and the air pumped out, the sound of the bell will grow faint as the quantity of air in the receiver decreases, and finally will stop completely. By looking through the glass of the receiver, however, the bell may be seen ringing as vigorously as at first. We learn thus that the air around a sounding body plays an important part in the transmission of the vibrations to our ears. The way in which the air acts in transmitting the vibrations is as follows. At each vibration of the sounding body, it compresses, to a certain degree, a layer of air in front of it. This layer, however, does not remain compressed, for air is very elastic, and the compressed air soon expands, and in doing so compresses a layer of air just beyond it. This layer expands in its turn, and compresses another layer still further from the body. In this way waves of compression are sent through the air, at each vibration, in all directions from the vibrating body.

It must not be thought that particles of air travel all the way from the vibrating body to the ear when a sound is heard. Each particle of air travels a very short distance, never any further than the vibrating body moves in making a vibration, and the movement of the air particles is a vibratory one, like that of the sounding body. But the particles of air near the sounding body communicate their vibrations to other particles, further from that body, and these, in turn, to others still further away, so, while the particles of air themselves move very short distances, the waves produced by their vibrations may be made to travel a considerable distance.

The size of a sound wave ordinarily is very small, but sound waves are sometimes made of such size and strength as to strike our ears with a force sufficient to rupture the ear drum. Such large and forceful waves come during explosions, such as the discharges of cannon or the explosions of large quantities of gunpowder under any conditions.

What Is Sound?

From what has already been said, you will probably answer that sounds are waves in the air, which produce the sensation of hearing. This is correct, but sound is not limited to vibrations of the air. Other elastic substances can be made to vibrate in the same way, and the waves so produced when conveyed to our ears, produce the sensation of hearing. If you put your ear under water and then strike two stones together in the water you will hear a sound as readily as you would in air. Sound waves may be transmitted by solid bodies also, and some of these are better for this purpose than air or liquids. Perhaps you have tried the experiment of placing your ear against one of the steel rails on a railroad track to listen for the coming of a distant train. If you have tried this, you know that a sound that is too faint, or is made too far away, to be heard through the air, can easily be heard through the rail.

In view of the fact that other substances than air can be thrown into waves that will affect the sense of hearing, we may define sound as vibrations in any elastic object, that produces the sensation of hearing.

The definition is sometimes called the physical definition of sound, in contradistinction to the physiological definition of sound which is given as the sensation produced when vibrations in elastic substances are conveyed to our ears. You will see then that sound when referring to the physical definition is what makes sound known in the physiological definition. The term sound alone, without qualifications, may have either meaning, and therefore statements concerning sound may be misleading, unless we are exact in explaining the sense in which the word is used.

How Fast Does Sound Travel?

When a sound is made close to us, it reaches our ears so quickly that it seems as though it took no time to travel; but when a gun is fired by a person at a distance, you will notice that after you see the flash of the gun, a little time elapses before the sound reaches your ear. It takes a little time for the light from the flash to get to your eyes, but a very short time, which you cannot appreciate. Sound travels much more slowly and the time it takes to travel a few hundred yards is noticeable. Accurate measurements of the speed of sound have been made, and it has been found that sound usually travels in air at a speed of about eleven hundred feet a second. The speed is not always the same, however, for a number of circumstances may cause it to vary. In air which is heated, the speed at which sound travels in it is increased because hot air expands. At the freezing point, sound travels through the air at the rate of 1,091 feet a second, and for every increase in temperature of one degree of heat, the speed is increased about thirteen inches a second. Accordingly at 68° F. the speed would be approximately 1,130 feet a second. Sounds also travel faster in moist air than in dry.

In other gases the speed of sound transmission may be greater or less than in air. For example, in hydrogen gas, which is much lighter than air, sound travels nearly four times as fast as it does in air. On the other hand, in carbonic acid gas, which is heavier than air, sound is transmitted more slowly.

In liquids, which are always heavier than air, you would naturally think that sound would travel more slowly than in air, but this is not true. Liquids are less compressible than gases and this causes the speed with which sound is transmitted in them to be increased. In water sound travels about four times as fast as in air.

What Are the Properties of Sound?

Sounds differ from each other by the extent to which they possess three qualities, namely; intensity, pitch and quality.

The intensity of any sound that we hear depends upon the size of the waves that reach our ears. The size of a sound wave gradually decreases, as the wave travels from its starting point, consequently the intensity of a sound depends upon the distance from the point at which the sound was produced. We know this from experience and if we think of the matter for a moment we will see why it is so. At the start of a sound wave, only a small quantity of air is affected, but for every inch it travels the quantity of air to which the wave is conveyed becomes larger, and the intensity of the waves must grow correspondingly smaller, just as when a pebble is dropped into water, the ripples produced by it are highest at the point where the pebble struck the water, and grows lower and lower as their circle widens.

It has been found possible to measure the intensity of a sound wave, at different distances from the point from which it started, and from these measurements it has been learned that the decrease in the open air, follows a fixed rule that is stated thus: the intensity of a sound wave at any point is inversely proportional to the square of its distance from its starting point. This rule is called “the law of inverse square,” and it means that if the intensity of a wave be measured at two points, distant say one hundred, and two hundred yards, respectively, from the starting point of the sound, the intensity of the sound at the first point will be found to be four times as great as at the second point.

Why Can You Hear More Easily Through a Speaking Tube?

We have seen that the decrease in intensity of a sound wave as it travels through the air, is due to the fact that the quantity of air set in motion by it is constantly increasing. But, if a wave is conveyed through a tube containing air, the quantity of air to which the vibrations are communicated does not increase as the wave travels forward, and theoretically there is no decrease in intensity. When a wave is actually transmitted in this way, however, it is found that there is some decrease in intensity on account of the friction of the particles of air against the sides of the tube; but the decrease from this cause is much slower than that which occurs in the open air, and consequently sounds can be heard at much greater distances through tubes than through the open air. Tubes for speaking purposes are frequently used to connect different parts of the same building, and if the tubes are not too crooked they serve their purpose very well.

Pitch is that property of sounds that determines whether they are high or low. The pitch of a sound depends upon the number of vibrations a second which the body that produces it makes. The sound of an explosion has no pitch because it makes but one wave in the air. The sound made by a wagon on a pavement has no definite pitch, for it is a mixture of sounds, in which the number of vibrations per second is not the same. Pitch is a property of continuous sounds only, and it is apparent chiefly in musical sounds, by which we mean sounds in which the vibrations are continuous and regular. In music, however, pitch is very important. In a musical instrument, the parts are so arranged that the sounds produced can be given any desired pitch, and it is by controlling the pitch that the pleasing effect of musical sounds in large measure is produced. Sounds of low pitch are produced by bodies making but a few vibrations a second while high-pitched sounds are made by bodies that vibrate rapidly.

Quality, may be defined as that property of sounds which enable us to distinguish the notes produced by different instruments. Two notes, one of which is produced upon a piano, and the other upon a violin, may have the same pitch and be equally loud, yet they are easily distinguishable. The difference in them is due to the presence of what are called overtones.

What Is Meant By the Length of Sound Waves?

The length of a sound wave embraces the distance from the point of greatest compression in one wave to the same point in the next. This depends upon the pitch for if a sounding body is making one hundred vibrations a second, by the time the one hundredth vibration is made, the wave from the first vibration will have travelled about eleven hundred feet from the starting point, and the remaining ninety-eight waves will lie between the first and the one hundredth. In consequence of this, the wave length for that particular sound will be about eleven feet. If the sounding body had made eleven hundred vibrations a second by the time the first wave had travelled eleven hundred feet, there would have been eleven hundred waves produced, and the wave length for that sound would be one foot. The wave lengths of sounds produced by the human voice usually lay between one and eight feet, though some singers have produced notes having wave lengths as great as eighteen feet, and others have reached notes so high that the wave length was only about nine inches.

When a tuning fork is struck, it produces a sound so faint that it can scarcely be heard unless the fork is held near the ear; but if the end of the fork is held on a box or table, the sound rings out loudly and seems to come from the table. The explanation of this is very simple. When only the fork vibrates, it produces very small sound waves, because its prongs are small and cut through the air. But when it is set on a box or table, its vibrations are communicated to the support, and the broader surface of the box or table sets a larger mass of air in vibration, and so amplifies the sound of the fork. When a surface is used in this way to reinforce the vibrations of a small body, and thus produce sound waves of greater volume, it is called a sounding board. Many musical instruments, like the violin and the piano, owe the intensity of their sounds to sounding boards, which reinforce the vibrations of their strings.

~WHAT A SOUNDING BOARD DOES~

Columns of air, like sounding boards, serve to reinforce sound waves. Unlike sounding boards, however, they do not respond equally well to a large number of different sounds. They respond to one sound only, or to several widely different ones. This may be shown as follows: Take a glass tube about sixteen inches long, and two inches in diameter, and after thrusting one end of it into a vessel of water, hold a vibrating tuning fork over the other end. By gradually lowering the tube into the water a point will be reached at which the sound becomes very loud, and as this point is passed the sound gradually dies away again. By raising the tube again the sound is again made loud when the tube reaches a certain point. This shows that to reinforce sound waves of a certain vibration frequency, the column of air in the tube must be of certain length.

Let us now see why the waves produced by the tuning fork are reinforced only by a column of air of a certain length. When the prongs of the fork make a vibration, a wave of air is produced which enters the tube, goes down to the water, is reflected, and comes back toward the fork. Now, if the reflected wave reaches the fork at the precise moment when it has completed one-half of its vibration and is about to begin upon the second half, it will strengthen the wave produced by the second half of the vibration; but if the reflected wave reaches the fork before or after the beginning of the second half of the vibration, it will not reinforce it. At the downward movement of the lower prong of the tuning fork, a wave of compression is sent down into the tube, and is reflected at the surface of the water. In order to reinforce the wave produced by the prong when it moves upward, the reflected wave must reach the fork just at the time that the prong reaches its normal position and before it starts upon the second half of its vibration.

Not only do columns of air tend to reinforce notes having a certain rate of vibration, but all elastic bodies have a certain rate at which they tend to vibrate, and when sounds having the same rate of vibration are produced near them, these bodies will vibrate in sympathy with them. If the sounds be kept up long enough, the sympathetic vibrations in objects near them sometimes become so great that they can easily be seen. Goblets and tumblers made of thin glass show this property very strikingly. When the proper notes are sounded the glasses take up the vibrations, and give a sound of the same pitch. If the note is loud, and is continued for some time, the vibrations of a glass sometimes become so great that the glass breaks. Large buildings, and bridges also, have rates at which they tend to vibrate, and this fact is the foundation for the old saying, that a man may fiddle a bridge down, if he fiddles long enough.

Musical Instruments.

By musical sounds, are meant sounds that are pleasant to hear, and their combination in such a way that their effect is agreeable produces music. Any instrument, therefore, that is capable of producing pleasing sounds may be called a musical instrument, and music is sometimes produced by very odd devices; but by musical instruments we ordinarily mean instruments that are especially designed to produce musical sounds. The number of such instruments that have been invented is enormous, but all of them may be divided into comparatively few classes, only two of which are of much importance. The two classes, only two of which are of much importance. The two classes referred to are stringed instruments and wind instruments.

~WHAT PITCH IS IN MUSIC~

Stringed musical instruments are those in which the sounds are produced by the vibration of a number of strings, and are generally reinforced by a sounding board. The strings are arranged in the instruments in such a way that the pitch of the sound produced by each string shall bear relation to the pitch of those obtained from the other strings. As long as this relation exists, the instrument is said to be in tune, and when the relation is destroyed, the instrument is out of tune, and the music produced by it is apt to contain what we call discords.

The conditions that determine the pitch of sounds produced by strings can be very easily discovered by experiment. Thus, by taking two pieces of the same wire, one twice as long as the other, and stretching them equally, you will observe on striking them that the shorter one yields the higher note. If their vibration frequencies are measured it will be found that the shorter string has a vibration frequency just twice as great as that of the longer string. From this we conclude that when two strings of the same size (and material) are stretched equally taut, their vibration frequencies are inversely proportional to their lengths.

By now taking two pieces of wire, of the same size and length, and stretching them so that the tension of one is four times as great as that of the other, we shall find that the vibration frequency of the tighter string is just twice as great as that of the looser. Thus, we see that the vibration frequency depends upon the tension applied to a string, and, that in strings of the same size and length, the vibration frequencies are proportional to the square roots of their tensions.

Now taking two strings of the same length, but with the diameter of one twice as great as that of the other, and stretching them equally, we shall find that the vibration frequency of the smaller string is twice that of the larger; which shows that when the lengths and tensions of two strings are equal, their vibration frequencies are inversely proportional to their diameters.

In constructing stringed instruments, advantage is taken of each of these conditions that affect the vibration of strings, and the requisite pitch is secured in a string by choosing one of convenient length and diameter, and by stretching it to just the right tension.