ACOUSTICS.
THE EAR, AND HEARING—PHYSIOLOGY OF HEARING AND SOUND—SOUND AS COMPARED
WITH LIGHT—WHAT IS SOUND?—VELOCITY OF SOUND—CONDUCTIBILITY—THE
HARMONOGRAPH.
Before entering upon the science of ACOUSTICS, a short
description of the ear, and the mode in which sound is conveyed to our
brain, will be no doubt acceptable to our readers. The study of the
organs of hearing is not an easy one; although we can see the exterior
portion, the interior and delicate membranes are hidden from us in the
very hardest bone of the body—the _petrous_ bone, the temporal and
rock-like bone of the head.
[Illustration:
Fig. 170.—1. Temple bone. 2. Outer surface of temple. 3. Upper wall
of bony part of hearing canal. 4. Ligature holding “hammer” bone to
roof of drum cavity. 5. Roof to drum cavity. 6. Semicircular canals.
7. Anvil bone. 8. Hammer bone. 9. Stirrup bone. 10. Cochlea. 11.
Drum-head cut across. 12. Isthmus of Eustachian tube. 13. Mouth of
tube in the throat. 14. Auditory canal. 15. Lower wall of canal.
16. Lower wall of cartilaginous part of canal. 17. Wax glands. 18.
Lobule. 19. Upper wall of cartilaginous portion of canal. 20. Mouth of
auditory canal. 21. Anti-tragus.]
The ear (external) is composed of the auricle, the visible ear, the
auditory canal, and the drum-head, or _membra tympani_. The tympanum,
or “drum,” is situated between the external and the internal portions
of the ear. This part is the “middle ear,” and is an air cavity, and
through it pass two nerves, one to the face, and the other to the
tongue. The internal ear is called the “labyrinth,” from its intricate
structure. We give an illustration of the auditory apparatus of man
(fig. 170).
The auricle, or exterior ear, is also represented, but we need not go
into any minute description of the parts. We will just name them (fig.
171).
Sound is the motion imparted to the auditory nerve, and we shall see
in a moment how sound is produced. The undulations enter the auditory
canal, having been taken up by the auricle; the waves or vibrations
move at the rate of 1,100 feet a second, and reach the drum-head,
which has motion imparted to it. This motion or oscillation is
imparted to other portions, and through the liquid in the labyrinth.
The impressions of the sound wave are conveyed to the nerve, and this
perception of the movement in the water of the labyrinth by the nerve
threads and the brain causes what we term “hearing.”
[Illustration: Fig. 171.—1. Pit of anti-helix. 2, 6, 10. Curved edge
of the auricle. 3. Mouth of auditory canal. 4. Tragus. 5. Lobe. 7.
Anti-helix. 8. Concha. 9. Anti-tragus.]
Let us now endeavour to explain what sound is, and how it arises. There
are some curious parallels between sound and light. When speaking of
light we mentioned some of the analogies between sound and light, and
as we proceed to consider sound, we will not lose sight of the light we
have just passed by.
Sound is the influence of air in motion upon the hearing or auditory
nerves. Light, as we have seen, is the ether in motion, the vibrations
striking the nerves of the eye.
There are musical and unmusical sounds. The former are audible when the
vibrations of the air reach our nerves at regular intervals. Unmusical
sounds, or irregular vibrations, create _noise_. Now, musical tones
bear the same relation to the ear as colours do to the eye. We must
have a certain number of vibrations of ether to give us a certain
colour (_vide_ table). “About four hundred and fifty billion impulses
in a second” give red light. The violet rays require nearly double. So
we obtain colours by the different rate of the impingement of impulses
on the retina. The eyes, as we have already learned, cannot receive
any more rapidly-recurring impressions than those producing violet,
although as proved, the spectrum is by no means exhausted, even if they
are invisible. In the consideration of Calorescence we pointed this
out. These invisible rays work great chemical changes when they get
beyond violet, and are shown to be heat. So the rays which do not reach
the velocity of red rays are also heat, which is the effect of motion.
Thus we have HEAT, LIGHT, and SOUND, all
the ascertained results of vibratory motion. The stillness of the
ether around us is known as “Darkness”; the stillness of the air is
“Silence”; the comparative absence of heat, or molecular motion of
bodies is “Cold”!
In the first part we showed how coins impart motion to each other.
VELOCITY OF LIGHT WAVES.
_According to_ SIR J. HERSCHEL.
Colour of the No. of Undulations No. of Undulations
Spectrum. in an inch. in a second.
Extreme Red 37,640 458,000,000,000,000
Red 39,180 477,000,000,000,000
Intermediate 40,720 495,000,000,000,000
Orange 41,610 506,000,000,000,000
Intermediate 42,510 517,000,000,000,000
Yellow 44,000 535,000,000,000,000
Intermediate 45,600 555,000,000,000,000
Green 47,460 577,000,000,000,000
Intermediate 49,320 600,000,000,000,000
Blue 51,110 622,000,000,000,000
Intermediate 52,910 644,000,000,000,000
Indigo 54,070 658,000,000,000,000
Intermediate 55,240 672,000,000,000,000
Violet 57,490 699,000,000,000,000
Extreme Violet 59,750 727,000,000,000,000
When an impulse was given the motion was carried from coin to coin,
and at length the last one in the row flew out. This is the case with
sound. The air molecules strike one upon another, and the wave of
“sound” reaches the tympanum, and thus the impression is conveyed to
the brain. We say we hear—but why we hear, in what manner the movement
of certain particles affects our consciousness, we cannot determine.
That the air is absolutely necessary to enable us to hear can readily
be proved. The experiment has frequently been made; place a bell under
the receiver of an air-pump, and we can hear it ring. But if we exhaust
the air the sound will get fainter and fainter. Similarly, as many
of us have experienced upon high mountains, sounds are less marked.
Sound diminishes in its intensity, just as heat and light do. Sound is
reflected and refracted, as are light and radiant heat. We have already
shown the effect of reflectors upon heat. Sound is caught and reflected
in the same way as light from mirrors, or as the heat waves in the
reflectors. We have what we term “sounding boards” in pulpits, and
speaking tubes will carry sound for us without loss of power. Echoes
are merely reflected sounds.
The velocity of sound is accepted as 1,100 feet in a second, which
is far inferior to the velocity of light. Fogs will retard sound,
while water will carry it. Those who have ever rowed upon a lake will
remember how easily the sound of their voices reached from boat to
boat, and Dr. Hutton says that at Chelsea, on the Thames, he heard
a person reading from a distance of a hundred and forty feet. Some
extraordinary instances could be deduced of the enormous distances
sound is said to have travelled. Guns have been heard at eighty miles
distant, and the noise of a battle between the English and Dutch, in
1672, was heard even in Wales, a distance of two hundred miles from the
scene of action.
Sound always travels with uniform velocity in the air in the same
temperature. But sound! What is the cause of it? How does it arise?
These questions can now be fully answered with reference to the
foregoing observations. Phenomena of vibration render themselves
visible by light, heat, and sound, and to arrive at some definite
ideas of sound vibrations we may compare them to waves, such as may be
produced by throwing a stone into a pond.
There are, so to speak, “standing” waves and “progressive” waves. The
former can be produced (for instance) by thrumming a fiddle-string,
and when the equilibrium of the cord is disturbed, the position of the
equilibrium is passed simultaneously by the string-waves. In water
the waves or vibrating points pass the position of equilibrium in
succession.
Waves consist of elevations and depressions alternately, and when we
obtain two “systems” of waves by throwing two stones into water, we
can observe some curious effects. It can be seen how one series of
depressions will come in contact with the other series of depressions,
and the elevations will likewise unite with the result of longer
depressions and elevations respectively; or it may very well be that
elevation will meet depression, and then the so-called “interference”
of waves will produce _points of repose_. These points are termed
_nodes_. The waves of the string proceed in the plane of its axis;
water waves extend in circles which increase in circumference.
The progression or propagation of sound may be said to begin when some
tiny globule of matter expands in the air. The air particles strike one
against the other, and so the motion is communicated to the air waves,
which in time reach the ear. But the velocity of the sound is not equal
in all substances. Air will convey it around our earth at the rate of
765 miles an hour, or 1,090 feet in a second. That is, we may accept
such rate as correct at a temperature of 32° Fahr., and at a pressure
of thirty inches, and the velocity increases almost exactly one foot
per second for each degree of temperature above 32°. Therefore on an
average, and speaking in “round numbers,” the estimate of 1,100 feet in
a second may be accepted as correct. In hydrogen gas the rate is much
higher. Through water again it is different, and still faster through
iron, glass, and wood, as will be seen in the following table:—
TAKING AIR AS 1.
Whalebone 6⅔
Tin 7½
Silver 9
Walnut 10⅔
Brass 10⅔
Oak 10⅔
Earthen pipes 11
Copper 12
Pear-wood 12½
Ebony 14⅔
Cherry 15
Willow 16
Glass 16⅔
Iron or Steel 16⅔
Deal 18
So there is a considerable difference in the velocities of sound
through the solid substances quoted, but these figures cannot be taken
as exact, as different samples may give different results. In wires
and bells the bodies themselves produce the sounds we hear. In wind
instruments and the voice the air is the cause of the sound.
The very deepest notes are produced by the fewest vibrations. Fourteen
or fifteen vibrations will give us a very low note, if not the very
lowest. The pipe of sixteen feet, closed at its upper end, will
produce sound waves of thirty-two feet. High notes can be formed from
vibrations up to 48,000 in a second. Beyond these limits the ear cannot
accept a musical sound.
[Illustration: Fig. 172.—The vibration of strings.]
We will explain the phenomenon of the vibration of strings by means of
the illustration. In the cut we find a string or wire, which can be
lengthened or shortened at pleasure by a movable bridge, and stretched
by weights attached to the end (fig. 172).
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).
[Illustration: 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 are thrust
into both ears, as shown in fig. 174; we then slightly swing the
spoon until we make it touch the edge of the table; the transmission
of sound is in consequence so intense that we are ready to believe
we are listening to the double diapason of an organ. This experiment
explains perfectly the transmission of spoken words by means of the
string of a telephone, another contrivance which any one may make for
himself without any trouble whatever. Two round pieces of cardboard are
fitted to two cylinders of tin-plate, as large round as a lamp-glass,
and four-and-a-half inches in length. If the two rounds of cardboard
are connected by a long string of sixteen to eighteen yards, we can
transmit sounds from one end to the other of this long cord; the
speaker pronouncing the words into the first cylinder, and the listener
placing his ear against the other. It is easy to demonstrate that sound
takes a certain time to pass from one point to another. When one sees
in the distance a carpenter driving in a stake, we find that the sound
produced by the blow of the hammer against the wood only reaches the
ear a few seconds after the contact of the two objects. We see the
flash at the firing of a gun, before hearing the sound of the report—of
course on the condition that we are at a fairly considerable distance,
as already remarked upon.
[Illustration: Fig. 174.—Conductibility of sound by solid bodies.]
[Illustration: Fig. 175.—Musical glasses.]
We can show the production of the Gamut by cutting little pieces of
wood of different sizes, which one throws on to a table; the sounds
produced vary according to the size of the different pieces. The same
effect may be obtained much better by means of goblets more or less
filled with water; they are struck with a short rod, and emit a sound
which can be modified by pouring in a greater or less quantity of
water; if the performer is gifted with a musical ear, he can obtain,
by a little arrangement, a perfect Gamut by means of seven glasses
which each give a note (fig. 175). A piece of music may be fairly
rendered in this manner, for the musical glasses frequently produce a
very pure silvery sound. We will complete the elementary principles
of acoustics by describing a very curious apparatus invented by
M. Tisley, the HARMONOGRAPH. This instrument, which we can easily
describe, is a most interesting object of study. The Harmonograph
belongs to mechanics in principle, and to the science of acoustics
in application. We will first examine the apparatus itself. It is
composed of two pendulums, A and B (fig. 176), fixed to suspensions.
Pendulum B supports a circular plate, P, on which we may place a small
sheet of paper, as shown in the illustration. This paper is fixed by
means of small brass clips. Pendulum A supports a horizontal bar, at
the extremity of which is a glass tube, T, terminating at its lower
extremity with a capillary opening; this tube is filled with aniline
ink, and just rests on the sheet of paper; the support and the tube are
balanced by a counterpoise on the right. The two pendulums, A and B,
are weighted with round pieces of lead, which can be moved at pleasure,
so that various oscillations may be obtained. The ratio between the
oscillations of the two pendulums may be exactly regulated by means of
pendulum A carrying a small additional weight, the height of which may
be regulated by means of a screw and a small windlass. If we give to
pendulum A a slight movement of oscillation, the point of tube T traces
a straight line on the paper placed in P; but if we move pendulum B,
the paper also is displaced, and the point of tube T will trace curves,
the shape of which varies with the nature of the movement of pendulum
B, the relation between the oscillations of the two pendulums, etc. If
the pendulums oscillate without any friction the curve will be clear,
and the point will pass indefinitely over the same track, but when
the oscillations diminish, the curve also diminishes in size, still
preserving its form, and tending to a point corresponding with the
position of repose of the two pendulums. The result is therefore that
the curves traced by the apparatus, of which we produce three specimens
(figs. 177, 178, 179), are traced in a continuous stroke, commencing
with the part of the greatest amplitude.
[Illustration: Fig. 176.—M. Tisley’s Harmonograph.]
By changing the relation and phases of the oscillations we obtain
curves of infinitely varied aspect. M. Tisley has a collection of more
than three thousand curves, which we have had occasion to glance over,
in which we failed to meet with two corresponding figures. The ratio
between these curves corresponds with some special class, of which
the analyst may define the general characters, but which is outside
our present subject. By giving the plate P a rotatory movement, we
obtain spiral curves of a very curious effect, but the apparatus is
more complicated. Considered from this point of view it constitutes
an interesting mechanical apparatus, showing the combination of
oscillations, and resolving certain questions of pure mechanics. From
the point of view of acoustics it constitutes a less curious object of
study. The experiments of M. Lissajons have proved that the vibrations
of diapasons are oscillations similar to, though much more rapid than
those of the pendulum. We can therefore with this apparatus reproduce
all the experiments of M. Lissajons, with this difference, that the
movements being slower are easier to study. When the ratio between the
_number of vibrations_—we purposely use the term vibration instead of
the term oscillation—is a whole number, we obtain figs. 177 and 178. If
the ratio is not exact, we obtain fig. 179, which is rather irregular
in appearance, corresponding to the distortions noticeable in M.
Lissajon’s experiments. Fig. 178 has been traced in the exact ratio
2:3; fig. 177 in the ratio 1:2; and fig. 179 corresponds to the ratio
1:2 and a small fraction, which causes the irregularity of the figure.
[Illustration: Fig. 177.—Ratio 1:2. Fig. 178.—Ratio 2:3.]
[Illustration: Fig. 179.—Ratio 1:2 and a fraction.]
[Illustration: Fig. 180. Construction of the Harmonograph. Fig. 181.]
[Illustration: Fig. 182.—Method of constructing an Harmonograph.]
[Illustration: Fig. 183.—The apparatus completed.]
In considering the harmony of figs. 177 and 178,—the first of which
corresponds to the octave, the second to the fifth, whilst fig.
179 corresponds to the disagreeable interval of the ninth,—one is
almost tempted to put a certain faith in the fundamental law of
_simple ratios_ as the basis of harmony. At first sight this appears
beyond doubt, but perhaps musicians would be hardly content with the
explanation. M. Tisley’s Harmonograph, it will be seen, is a rather
complicated apparatus; and I will now explain how it may be constructed
by means of a few pieces of wood. I endeavoured to construct as simple
an apparatus as possible, and with the commonest materials, feeling
that it is the best means of showing how it is possible for everybody
to reproduce these charming curves of musical intervals. Also I
completely excluded the employment of metals, and I constructed my
apparatus entirely with pieces of wooden rulers, and old cigar boxes.
I set to work in the following manner: on the two consecutive sides
of a drawing board I fixed four small pieces of wood (fig. 180), side
by side in twos, having at the end a small piece of tin-plate forming
a groove (fig. 181). In these grooves nails are placed which support
the pendulums. The piece of wood is placed on the corner of the table,
so that the pendulums which oscillate in two planes at right angles,
are in two planes that are sensibly parallel to the sides of the table.
The pendulums are made of a thin lath, with two small pieces of wood
fixed to them containing some very pointed nails, on which the pendulum
oscillates. Fig. 182 gives an illustration. The pendulums have a pin
fixed in vertically, which passes through a piece of wood, and by
means of a hinge connects the upper ends of the two pendulums. This
contrivance of the pin is very useful, and if care is taken to make the
hole through the hinge in the form of a double cone, as shown in fig.
182, _c_, it makes a perfect joint, which allows the piece of wood to
be freely moved.
[Illustration: Fig. 184.—Details of mechanism.]
To complete the apparatus, the heads of the two pendulums are united by
the hinge, at the bend of which a slender glass tube is fixed, which
traces the curves. The hinge is given in fig. 184, and to its two
extremities are adjusted the two pins of the pendulum (fig. 183). The
pendulums are encircled with round pieces of lead, which can be fixed
at any height by means of a screw.