The piano is now complete except for polishing and tuning. The tuning
is left to the last. The tuner must have a good ear for music. With
his key he tightens or loosens each of the pegs to which the wires are
attached until it is perfectly in tune and all in harmony. The piano is
now ready to play upon.]
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.
When a string is plucked in the middle, it vibrates as a whole, and
its rate of vibration, or vibration frequency, is determined by the
three conditions that have just been discussed; but if a finger is
laid on the string, in the middle, and the string is plucked between
the middle and the end, the string will vibrate in halves, and the
middle point will remain at rest. If the string had been touched at a
point one-fourth of the length from the end it would have vibrated in
fourths, and there would have been three stationary points.
When vibrations are set up in a string, with nothing to prevent the
free vibration of the whole string, it first vibrates as a whole, and
the sound produced is known as the fundamental tone of the string; but
very soon smaller vibrations of segments of the string begin, first
of halves of the string, then of thirds, and then of fourths. These
smaller vibrations produce sound waves that blend with the fundamental
tone and are known as overtones. The combined sound of the fundamental
tone and the overtones is called a note. The overtones present in
notes that have the same fundamental tone are not the same when the
notes are produced by different instruments, and, consequently,
the sound of notes of the same pitch is not the same on different
instruments. This difference in notes of the same pitch has already
been mentioned, but the way in which overtones are produced was not
explained in connection with it.
In wind instruments the sounds are produced by the vibrations of
columns of air in pipes. In the organ, which is probably the best
example of a wind instrument, the vibrations are usually produced by
causing a current of air to strike a sharp edge, just above the opening
of the pipe, as is done in a common whistle. A portion of the air
current is deflected into the organ pipe, and it sets up vibrations in
the air within the pipe.
The pitch of the sound produced by an organ pipe is determined by the
length of the pipe. A pipe that is open at both ends, called an open
pipe, produces a sound that has a wave length twice as great as the
length of the pipe; and if the pipe is open at one end only, a closed
pipe, the sound produced has a wave length twice the length of the open
pipe. Hence it will be seen that a closed pipe produces a sound that
has the same pitch as that produced by an open pipe that is twice as
long.
Talking Machines.
The phonograph, graphophone, gramophone, sonophone, and other talking
machines, furnish one of the best proofs of the wave theory of sound,
because their invention was based upon that theory. The first talking
machine was that invented by Thomas A. Edison and called by him the
phonograph. The others merely show the principle of the phonograph
applied in different ways, and need not be separately described. The
reasoning that led Edison to invent the phonograph was that if the
sound waves produced by the human voice were allowed to strike a thick
disk of hard rubber or metal, they would cause the disk to vibrate in
a certain way, and if the disk were again made to vibrate as it had
done under the influence of the voice, the sounds of the voice would be
reproduced. The difficult part of the task of making a talking machine
was in finding a way to make the disk vibrate again as it did under
the influence of the voice. This, however, was finally accomplished,
providing the disk with a needle, that rests on a cylinder of hard
wax, which turns slowly under the point of the needle while the sound
waves are striking the disk. The vibrations of the disk cause the point
to indent the surface of the wax so as to produce a groove of varying
depth on its surface. After the vibrations of the speaker’s voice have
been recorded in this way on the surface of the wax cylinder the needle
can be made to retrace its path, and will cause the disk to vibrate as
it did under the tones of the speaker’s voice. These last vibrations of
the disk produce sound waves similar to those of the voice, but their
amplitude is less and the sound is not so loud.
Why Does Red Make a Bull Angry?
It is very doubtful if a red flag really makes a bull more excited or
more quickly than a rag of any other color or any other object which
the bull can see plainly but does not understand. Conceding for the
moment that red excites a bull more than any other color, the answer to
the question will be found in the statement that anything unusual which
the bull sees has a tendency to make him angry and the thing which he
can see at a distance more quickly will start him going most quickly.
He can see a red rag better perhaps than almost any other color. There
may be something about the color which excites him just as some notes
on the piano will worry some dogs, but there is no way of studying the
bull’s anatomy to determine why red should excite him more than any
other color, if that is so.
[Illustration: FIG. 1.]
[Illustration: FIG. 2.]
[Illustration: FIG. 3.]