SOUND.
248. =What Sound is.=--Sound is such a vibration of substances
as can, on being transmitted to the ear, act upon the sense of
hearing. I say _such_ a vibration, because there may be vibrations
which will not produce the sensation of sound, Vibrations which are
either very slow or very quick will not do it. Thus if a plate of
metal or a string make less than 15 or more than 48,000 vibrations
in a second, no effect is produced upon the ear. The capacity of
hearing differs, however, in different persons, so that although
few can hear vibrations which are beyond the range which I have
mentioned, there are many whose capacity falls much within it
either at one end or both ends of the scale. The range for animals
is not the same as that for man. Thus the lion and the elephant can
hear a sound when the vibrations are too infrequent to make any
impression upon our ears; while small animals have a susceptibility
in the organ of hearing for vibrations so quick that we can not
hear them, and at the same time are not susceptible to the slower
vibrations. How far the range varies in different animals has not
been ascertained to any extent.
[Illustration: Fig. 182.]
249. =The Vibration of Sounding Bodies Manifest to the Senses.=--If
we place the hand upon a large bell that has been struck we can
feel the vibration. If we strike one of the ends of a tuning-fork
upon some hard body we can see the vibration, as represented in
Fig. 182 by the dotted lines. If we look in upon the strings of a
piano as it is played, the vibration of the larger strings is very
observable to the eye. If we rub the edge of a drinking-glass so as
to produce a musical sound, the water which is in it will be thrown
into waves from the vibration of the glass.
[Illustration: Fig. 183.]
250. =Wind Instruments.=--In wind instruments, as the flute, horn,
etc., it is the vibration of the body of air in the instrument
which causes the sound. In the common tin whistle or bird-call,
Fig. 183, the sound is produced by the vibration imparted to the
contained air by the impulse of the breath through the orifice, B.
[Illustration: Fig. 184.]
251. =An Analogy.=--The vibration of a sounding body is much like
that of a pendulum. The end of the tuning-fork, Fig. 182, on being
struck passes to _b_, and in returning passes by the point of rest,
A, as the pendulum does, and reaches _a_. So, also, if a string,
A B, Fig. 184, be drawn aside to D, as it flies back to C it will
by its inertia pass on to E, and so will continue to vibrate back
and forth for some time. The same rule also applies to the extent
of the vibrations here as in the case of the pendulum, § 209. The
quickness of the vibration is not at all affected by its width.
The farther the string, A B, is drawn to one side the greater will
be the force with which it will return, and hence it will arrive
at its position on the other side of the middle line as soon when
drawn far away from this line as it would if drawn but little away.
The same thing is true of the vibrations or waves of air, though it
can not so easily be made plain to you.
252. =How the Sensation of Sound is Produced.=--The vibration of a
sounding body is transmitted to the ear ordinarily through the air,
and there strikes upon a little drum, a membrane at the bottom of
the external cavity of the ear just like a common drum-head. Here
the vibration of the air is communicated to this drum, and from
this to a chain of very small bones. From the last of these bones
it is transmitted to another very small drum, and from this to a
fluid in some very complicated passages in the most solid bone
in the body. These may be called the _halls of audience_. In the
fluid contained in them are spread out the branches of the nerve
of hearing, which receive the impression of the vibration, and
transmit it to the brain, where the mind takes knowledge of it.
Observe that the vibration, transmitted first through the air, then
through the drum, then the chain of bones, then another drum to a
fluid, stops at the fluid. What is transmitted from this to the
brain by the nerve we know not, and so we call it an impression.
253. =Sound Transmitted through Various Substances.=--In ordinary
hearing sound, as you have seen, is transmitted through various
substances before the vibration arrives at the liquid in the halls
of audience. But sound need not take this course in all cases to
arrive at the nerve of hearing. If, for example, you place a watch
between your teeth, the sound will go through the solid teeth and
the bones of the jaw directly to the halls of audience by a short
cut, instead of going round through the outer ear-passage to the
drum, and so through the chain of bones. Fishes in hearing receive
the vibration through water. If you place your ear at the end of a
timber, while some one scratches with a pin at the other end, you
hear the sound distinctly, for the vibration is transmitted through
the timber; as in the case of the watch between the teeth, it goes
through the solid bone.
[Illustration: Fig. 185.]
254. =Sound not Transmitted through a Vacuum.=--As sound is a
vibration of some substance it can not be transmitted through
absolute space. This can be proved by an experiment with the
air-pump, as represented in Fig. 185. The apparatus in the receiver
is so arranged that the bell, _a_, can be struck by pressing down
a sliding rod, _h_. If it be struck before the air is exhausted
the sound is heard through the glass. But the more you exhaust the
air the fainter will be the sound; and at length, if you keep on
pumping, it can not be heard at all. The same experiment can be
tried with a music-box. It is from the thinness of the air on high
mountains, and at the great heights reached by balloons, that all
sounds are so faint. The report of a pistol fired off on top of
Mont Blanc is a mere crack compared with its report when fired in
the valley below.
255. =Motion of the Heavenly Bodies without Noise.=--Sound is
often heard at a very great distance on the earth. The sound of an
eruption of a volcano has been heard in one case at the distance
of 970 miles. But suppose that the same sound should occur at the
same distance from the earth, that is, over 900 miles beyond the
atmosphere that enrobes the earth, no inhabitant of our world could
hear it, for the same reason that you do not hear the bell ringing
in an exhausted receiver. If, therefore, any sound, however loud,
should be given forth by any of the heavenly bodies we could not
hear it. The course of these bodies in their orbits is noiseless,
because they meet with no resistance from any substance. Bodies
passing rapidly through our atmosphere cause sound, from the
resistance which the air gives to their passage. The whizzing of
a ball is an example of this. It is the passage of the electric
fluid through the air which produces the thunder. But the heavenly
bodies, having no such resistance, make no sound in their course,
though their velocity be so immense. In the expressive language of
the Bible, "their voice is not heard."
256. =Velocity of Sound.=--The velocity of sound varies in
different media. Thus it passes through water four times as rapidly
as it does through air. Dr. Franklin, with his head under water,
heard distinctly the sound of two stones struck together in the
water at the distance of more than half a mile. Sound passes
through solids much more easily, and therefore more rapidly, than
through liquids. Thus its velocity through copper is twelve times
and through glass seventeen times greater than through air. If you
place your ear against a long brick wall at one end, and let some
one strike upon the other end, you will hear two reports, the first
through the wall and the second through the air. Indians are in the
habit of ascertaining the approach of their enemies by putting the
ear to the ground. When the eruption of a volcano is heard at a
great distance the sound comes through the solid earth rather than
through the air. The ready transmission of sound through solids
furnishes us with a very valuable means of examining diseases of
the lungs and heart. The sounds occasioned by the movement of the
air in the lungs and by the action of the heart are very distinctly
heard through the solid walls of the chest.
257. =Measurement of Distances by Sound.=--It makes no difference
with the velocity of sound whether it be loud or not. Thus the
sounds of a band of music at a distance all reach your ear at the
same time, the sounds of the instruments that can scarcely be heard
keeping exact pace in the air with the sounds of the loudest. So,
also, the velocity of sound is uniform throughout its whole course,
being just as rapid when it is about to die away as it was when it
began. It is from this uniformity in the velocity of sound that we
can estimate the distance of the object by which any sound is made.
We do it by a comparison between light and sound. Sound moves at
the rate of 1120 feet in a second. Now light moves 192,000 miles a
second, and therefore, for all ordinary distances on the earth, we
need make no allowance of time for light in comparison with sound.
If we see, then, the operation by which a sound is produced we can
estimate its distance from us by the length of time which elapses
between what we see and what we hear. In this way we can estimate
very accurately the distance of a cannon that we see fired, or the
distance of a flash of lightning.
258. =Loudness of Sound.=--The loudness of sound depends upon the
width of the vibrations producing it. The harder you strike the
end of the tuning-fork, Fig. 182, the farther will it vibrate the
one way and the other, and the louder will be the sound. The same
thing is true of the strings of a piano. A round bell, when it
is struck, tends in its vibration to take an oval form, and the
extent of its vibration back and forth as it does this governs the
loudness of the sound. As sound passes from the sounding body the
vibration gradually lessens, and at length dies away. It is like
the successive vibrations or waves of water produced by dropping
a stone in it. The louder the sound is the larger are the first
vibrations, and the farther will the vibrations extend, as in water
a large stone dropped into it will produce larger waves than a
small one, and the waves will extend over a greater space.
259. =Diffusion of Sound.=--When there is no hindrance sound
spreads equally in all directions. It is in this respect with the
vibrations or waves of air as it is with the waves of water when
a stone is dropped into it. Light is also diffused in the same
manner, as you will see in another chapter.
[Illustration: Fig. 186.]
260. =Reflection of Sound.=--As waves of water striking against
any object bound off, so it is with the vibrations or waves of
sound. And the same is true of this as of all motion, as stated
in § 206, that the angle of incidence is equal to the angle of
reflection. The reflection of sound is the cause of _echoes_. In
order that an echo be perfect the sound must be reflected back
to the ear from some plane surface of some size. Sometimes when
there are successive plane surfaces of rocks along a river there
are successive echoes. Thus in Fig. 186 (p. 200) is represented
a locality on the Rhine where a sound is reflected at successive
places, 1, 2, 3, 4. The rolling of thunder, though sometimes
caused by the different distances of parts of the same flash of
lightning, is commonly owing to reflections of the sound among
the clouds. From this cause the report of a cannon is more apt
to be a rolling sound when there are clouds above than when the
sky is clear. Sound is continually reflected in every variety of
direction from obstacles with which it meets. Thus in a room it is
reflected from the walls and from all the objects in the room;
and the more varied are the surfaces the more varied and confused
are the reflections. You know that a voice has a very different
sound in a room when it is empty from what it has when the room
is filled with an audience. Indeed, a blind speaker can estimate
very nearly the size of his audience by the sound of his own voice.
The explanation is, that with a full audience the surfaces for
reflection are vastly multiplied, and so deprive the sound of the
sharp and ringing character which is given to it by reflection from
comparatively few surfaces which are plane and firm. The effect
produced by an audience upon the voice of the speaker is quite
analogous to that of muffling upon the sound of a drum.
[Illustration: Fig. 187.]
261. =Whispering Galleries.=--The reflection of sound from curved
surfaces gives us some interesting phenomena. The waves of sound
in being reflected from a concave surface are gathered together
to some point. If the surface be a perfectly spherical one, and
the sound issue from the centre, the reflection will be from all
points to the centre. But suppose the concave surface have the
curve of an ellipse, as represented in Fig. 187. This, instead
of having a centre, has two foci, _c_ and _g_. Now if a sound
proceed from one focus, _c_, the waves of sound, as represented by
the lines _c d_, _c e_, _c f_, _c h_, will all be reflected to the
other focus, _g_; so that if a person speak in a very low tone or
even whisper at _c_, he may be heard distinctly by another at _g_,
though persons at other points may hear nothing. We may have this
result with a curved wall extending even several hundred feet; and
such structures are called whispering galleries. If in one of these
galleries a person standing in one focus speak loudly he will be
heard by others at any point by the _direct_ waves of sound; but
the reflected sound will be added to the direct in the case of one
standing at the other focus.
[Illustration: Fig. 188.]
[Illustration: Fig. 189.]
262. =Concentration of Sound.=--It is by the reflection of sound
that it can be concentrated in various ways. Thus in using a
speaking-trumpet the waves of sound, instead of moving in all
directions as soon as they escape from the mouth, are reflected by
the sides of the instrument toward a central line as represented
in Fig. 188. The waves or vibrations, being thus concentrated have
more intensity and are thrown to a greater distance than if they
issued directly from the mouth. So a speaking-tube, confining the
vibrations, carries the voice to distant parts of a building. For
the same reason the voice can be heard much farther through a
narrow street than in an open space. So, also, a speaker can be
heard more distinctly in a hall than when addressing an audience
of the same size in the open air. The "sounding-board," once
so fashionable in churches, was really of considerable service
in preventing the escape of the vibrations of the voice of the
preacher upward, and directing them downward upon the audience. In
the hearing-trumpet, Fig. 189, the vibrations are collected in
the broad open end of the instrument, and by reflection are thrown
together into a narrow compass before they enter the ear to strike
upon the drum. We often instinctively make the palm of the hand act
as an ear-trumpet when we do not hear distinctly. Many animals have
the external ears movable, so that they can direct their concave
surface toward the point from which they wish to hear. Such ears
are movable ear-trumpets.
263. =Difference Between a Musical Sound and a Noise.=--The
difference between a musical sound and a noise is very analogous to
the difference between a crystal and the same substance destitute
of the crystalline arrangement. In both there are vibrations, but
in the musical sound they have perfect regularity, while in a noise
the vibrations are irregular, and there is confusion. Indeed so
regular are the vibrations of musical sounds that the rules and
principles of music have all the rigid exactness of mathematics.
264. =How Different Notes are Produced.=--The quicker is the
vibration the higher is the note. Thus a short and small string on
a violin or in a piano gives a higher note than a long and large
string, because its vibrations are quicker. The tension of the
string also has an influence, the note being raised by increasing
the tension. In tuning a violin the right pitch is given to each
string by lessening or increasing the tension by means of the
screws to which the strings are attached. In playing upon it
various notes are made upon each string by shortening the vibrating
portion more or less by pressure of the finger.
[Illustration: Fig. 190.]
In wind instruments the note depends on the length and size of the
column of air contained in them. This may be illustrated by an
organ-pipe, Fig. 190 (p. 203). It is one of the pipes of what is
called the flute-stop. It is constructed very much like a boy's
willow whistle. The air from the bellows of the organ enters at P,
and causes a vibration of the whole column of air in the pipe, the
sound issuing at _t_. In the upper end is a movable plug, _s_, by
which, in tuning, the note of the pipe is regulated. If the note be
too grave this plug is pushed downward, so as to shorten the column
of air.
It is from difference in rapidity of vibration that a large bell
gives a graver note than a small one. So, too, when musical sounds
are produced by passing the moistened fingers over the edges of
glass vessels, the larger the vessel the graver is its note. A
tumbler will give a graver note than a wine-glass.
265. =Human Voice.=--The principles which I have developed in
relation to musical instruments apply to the voice. The musical
instrument of man, by which the voice is produced, is contained
in a very small compass. It is that box at the top of the throat
commonly called Adam's apple. Across this, from front to rear,
stretch two sheets of membrane, leaving a space between their
edges. In our ordinary breathing these membranes are relaxed, and
the space between their edges is considerable, to allow the air to
pass in and out freely. But when we speak or sing these membranes,
or vocal chords, as they are termed, are put into a tense state
by muscles pulling upon them, and the opening between them is
lessened. The voice is produced by the air that is forced out from
the lungs, which, striking on the chords, causes them to vibrate.
The nearer their edges are together, and the more tense they are,
the higher is the note. The sounds are produced precisely as those
of the Æolian harp are, the air causing in the one case a vibration
of strings, and in the other of edges of membranes.
266. =Harmony.=--When notes, on being sounded at the same time,
are agreeable to the ear, they are said to harmonize. Now this
harmony depends on a certain relation between the vibrations.
The more simple is the relation the greater is the harmony. For
example, if we take the first note, termed the fundamental note, of
what is called the scale in music, it harmonizes better with the
octave than with any other of the eight notes, because for every
vibration in it there are just two in the octave. Take in contrast
with the octave the second note. Here to every eight vibrations of
the first note we have nine of the second, and the consequence is
a discord when they are sounded together. The difference between
the two cases is this: In the first case the commencement of every
vibration in the fundamental note coincides with the commencement
of every second vibration in the octave. But in the other case
there is a coincidence at only every eighth vibration of the first
note with every ninth of the second. Next to the octave, the most
agreeable harmony with the fundamental note is that of the fifth
note of the scale. Here we have three vibrations to every two of
the first note, and so every second vibration in the first note
coincides with every third vibration of the fifth. Next comes the
harmony of the fourth, there being here a coincidence at every
third vibration of the fundamental note. The more frequent, you
see, are the coincidences between the vibrations the greater is the
harmony. In the three cases just stated the coincidence is in the
first at the commencement of _every_ vibration of the fundamental
note, in the second case at the commencement of every _second_
vibration, and in the third at the commencement of every _third_
vibration.
267. =The Diatonic Scale.=--In order that you may see the relative
numbers of the vibrations for each of the notes I will give them
for the whole scale. They are as follows:
1 9/8 5/4 4/3 3/2 5/3 15/8 2
C D E F G A B C.
According to this the note D has nine vibrations to every eight
vibrations of C, E has five to every four of C, etc., the octave
C having just twice the number of vibrations that the fundamental
note C has. You have here expressed the _proportion_ between the
numbers of vibrations in the different notes. Suppose, then,
that you know the number of vibrations in a second that C, the
fundamental note, has, you can readily calculate the number of
vibrations of each of the other notes. It is done by multiplying
the number which C has by the fractions over the other notes. Thus
if the number of vibrations in a second in the fundamental note be
128, by this process we make the vibrations of all the notes to be
thus:
C D E F G A B C
128 144 160 170 192 213 240 256.
There are really but seven notes in what is called the diatonic
scale, the eighth note, C, being truly the first of seven other
notes above, having relations to each other similar to those of
the notes below, and constituting another octave. So we may have
several octaves, one above another.
It is interesting to observe that the proportionate lengths of
strings required to produce the eight notes of the scale have an
exact numerical relation, but the _reverse_ of that of the numbers
of the vibrations. Thus if you have eight strings of the same size,
their vibrating lengths required for the notes are as follows:
C D E F G A B C
1 8/9 4/5 3/4 2/3 3/5 8/15 1/2.
For the notes of the octave above the lengths are thus:
C D E F G A B C
1/2 4/9 2/5 3/8 1/3 3/10 4/15 1/4.
268. =Unison.=--In tuning instruments so as to make them harmonize
the result is obtained when the corresponding parts of the
instruments have the same number of vibrations. Thus the string in
one violin that gives any particular note must vibrate just the
same number of times in a second that the strings giving the same
note in other violins do, or it will not be in perfect unison with
them. The same is true of other strings for other notes, and also
of the corresponding parts of all kinds of instruments which are
to be played together. When, in tuning instruments together, it is
said that a string of a violin, for example, is too _flat_, the
difficulty is that it does not vibrate with sufficient rapidity,
and it is therefore screwed up to make its note _sharp_ enough, as
it is expressed, to be in unison with the note of the corresponding
strings or parts of other instruments.
269. =Mysteries of Sound and Hearing.=--There are many things of a
mysterious character in relation both to sound and the manner in
which it causes the sensation of hearing. I will barely notice but
two of these. The effect, or rather the chain of effects, resulting
in hearing is wholly mechanical, until we come to the nerve of
hearing, which branches out with minute fibrils in the halls of
audience of the internal ear. It is merely a series of vibrations.
Now how it is that the mere agitation of a fluid inclosed in hard
bone can communicate through fine white fibres to the brain,
and through that to the mind, the idea that we have of all the
various sounds that are produced, is a great mystery. All that we
know is that the nerve is the medium of the communication, but
of the manner in which it performs its office we know absolutely
nothing. Again, while it is sufficiently mysterious that this
information can thus be given to the mind when one sound after
another communicates its vibration to the liquid in the ear, the
mystery is greatly enhanced when various sounds come to the ear
at one and the same time. To get a distinct idea of the very
compound and wonderful character of the process of hearing in such
a case we will suppose that a full band of music is playing, and
at the same time mingled with its sounds there are various other
sounds heard, some of them perhaps discordant. What a diversity of
vibrations we have here! We have the slow vibrations produced in
the grave notes, and the quick vibrations of the higher ones, all
traveling together through the air to the ear, and each preserving
its distinctive character. And more than this, after they arrive
at the ear they are communicated unaltered through the drum, the
chain of bones, the second drum, and the liquid where the nerve is,
so that a correct report of each of all the notes is given through
the nerve to the mind. Then, too, if there be any discord its
vibration travels along with the rest, and so do the vibrations of
other sounds, as the roaring of the wind, the report of cannon, and
the noise of the people. And besides all this, in the multiplicity
of the vibrations thus transmitted through so many different
substances the mind gets a true report of the comparative loudness
of the sounds, and even of their character, so that the sounds of
drum, fife, trumpet, etc., are all accurately distinguished. In
view of such wonders how significant is the question, "He that
planted the ear, shall he not hear?"