Francis Lieber.

Library of universal knowledge. A reprint of the last (1880) Edinburgh and London edition of Chambers' encyclopaedia, with copious additions by American editors (Volume 13) online

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from its source, let us consider a series of spherical waves diverging from a point. The
length of a wave, as we know from the theory, does not alter as it proceeds. (Indeed, as
we shall presently see, the pitch of a note depends on the length of the wave; and we
know that the pitch is not altered by distance.) Hence, if we consider any one spherical
wave, it will increase in radius with the velocity of -sound, but its thickness will remain
unaltered. The same disturbance is thus constantly transferred to masses of air greater
and greater in proportion to the surface of the spherical wave, and therefore the amount
in a given bulk (say a cubic inch) of air will be inversely proportional to this surface. But
the surfaces of spheres (q.v.) are as the squares of their radii hence the disturbance in a
given mass of air, i.e., the loudness of the sound, is inversely as the square of the dis-
tance from the source. This follows at once from the law of conservation of energy (see
FORCE), if we neglect the portion which is constantly being frittered down into heat by
fluid friction. All sounds, even in the open air, much more rapidly in rooms, are ex-
tinguished ultimately b}' conversion into an equivalent of heat. Hence sounds really
diminish in intensity at a greater rate than that of the inverse square of the distance;
though there are cases on record in which sounds havbeen heard at distances of nearly
200 miles. But if, as in speaking-tubes and speaking-trumpets, sound be prevented from
t diverging in spherical waves, the intensity is diminished only by fluid friction, and thus
the sound is audible at a much greater distance, but of course it is confined mainly to a
particular direction.

As already remarked, the purest sounds are those given by a tuning-fork, which (by
the laws of the vibration of elastic solids) vibrates according to the same law as a pendu-
lum, and communicates exactly the same mode of vibration to the air. If two precisely
similar tuning-forks be vibrating with equal energy beside each other, we may have
either a sound of double the intensity, or anything less, to perfect silence, according to
their relative phases. If the branches of both be at their greatest elongations simulta
neously, we have a doubled intensity if one be at its widest, and the other at its nar-
rowest, simultaneously, we have silence, for the condensation produced by one is exactly
annihilated by the rarefaction produced by the other, and rice versa. But if the branches
of one be loaded with a little wax, so as to make its oscillations slightly slower, it will
gradually fall behind the other in its motion, and we shall have in succession every grade
of intensity from the double of either sound to silence! The effect will be a periodic
swelling and dying away of the sound, and this period will be longer the more nearly
the two forks vibrate in the same time. This phenomenon is called a beat, and we see at
once from what precedes, that it affords an admirable criterion of a perfect unison, that
is, of two notes whose pitch is the same. It is easy to see, by the same kind of reasoning,
that if two forks have their times of vibration nearly as 1:2, 2: 3, etc. i.e., any simple
numerical ratio there will be greater intervals between the beats according as the exact
ratio is more nearly arrived at.

We must now consider, so far as can be done by elementary reasoning, the various
simple modes of vibration of a stretched string, such as the cord of a violin Holding
one end of a rope in the Land, the other being fixed to a wall, it is easy (after a little

653

Sound.

practice) to throw it into any of the following forms, the whole preserving its shape,
but rotating round the horizontal line.
If the tension of the rope be the same
in all these cases, it is easy to see that
the times of rotation must be inversely
as the number of equal segments into
which the rope is divided; for the va-
rious parts will obviously have the
same form; and the masses and dis-
tances from the axis of rotation being

proportional to their lengths, the cen- *^~ """t^,^ ^^*~~ "*">. j^ g< &

trifugal forces (q.v.) will be as the
squares of the lengths, and inversely
as the squares of the times of rotation.
But these centrifugal forces are bal-
anced by the components of the ten-
sions at the extremities, in directions
perpendicular to the horizontal line;
which are, by hypothesis, the same for
all the figures. Hence the time of ro-
tation is directly as the length of each segment. Now (see PENDULUM) any such rota-
tion is equivalent to two mutually perpendicular and independent pendulum vibrations
of the cord from side to side of the horizontal line. Thus, a violin string may vibrate,
according to the pendulum law, in one plane, either as a whole (fig. 1), as two halves (fig. 2),
as three thirds (fig. 3), etc. ; and the times of vibration are respectively as 1, |, J, . . . Nay,
more, any two or more of these may coexist in the same string, and thus, by different
modes of bowing, we may obtain very different combinations of simple sounds: a simple
sound being defined as that produced by a single pendulum motion, such as that of a
tuning-fork, or one of the uncomplicated modes of vibration of a string.

The various simple sounds which can be obtained from a string are called harmonics
of the fundamental note; the latter being the sound given by the string when vibrating
as a whole (fig. 1). For each vibration of the fundamental note, the harmonics have two,
three, four, &c. Of these, the first is the octave of the fundamental note; the second
the twelfth, or the fifth of the octave; the third the double octave; and so on. ^ Thus, if
we have a string whose fundamental note is C, the series of simple sounds it is capable
of yielding is:

C, Ci, Gi, Ca, E a , G 2 (Bt> s ), C 3 , D 3 , E 3 , &c.

Of those written, all belong to the ordinary musical scale except the seventh, which is
too flat to be used in music. This slight remark shows us at once how purely artificial
is the theory of music, founded as it is, not upon a physical, but on a sensuous basis.

To produce any one of these harmonics with ease from a violin string, we have only
to touch it lightly at -J, ^, , &c. of its length from either end and bow as usual. This
process is often employed by musicians, and gives a very curious and pleasing effect
with the violoncello or the double-bass. The effect of the finger is to reduce to rest the
point of the string touched; and thus to make it a point of no vibration, or, as it is tech-
nically called, a node.

In the case of a pianoforte wire, a blow is given near one end. producing a displnoe-%
ment which runs back and forward along the wire in the time in which the wire would
vibrate as a whole. The successive impacts of this wave on the ends of the wire (which
are screwed to the sounding-board), are the principal cause of the sound. But more of
this case later.

The theory of other musical instruments is quite as simple. Thus, in a flute, or
unstopped organ pipe, the sound is produced by a current of air passing across an orifice
at the closed end. This produces a wave which runs along Ihe tube, is reflected at the
open end, runs back, and partially intercepts the stream of air for an instant, and so on.
Thus the stream of air is intercepted at regular intervals of time, and we have the same
result as in the sirene (q. v.). In this case, there is one node only, viz., at the middle of
the pipe. If we blow more sharply, we create two nodes, each distant from an end by
J of the length of the tube. The interruptions are now twice as frequent, and we have
the first harmonic of the fundamental note. And so on, the series of harmonics being
the same as for a string. We may easily pass from this to the case of an organ-pipe
closed at the upper end. For if, while the open pipe is sounding its fundamental note,
a diaphragm be placed at the node, it will not interfere with the motion, since the, air ix
at rest at a node. That is, the fundamental note of a closed pipe is the same as that of
an open pipe of double the length. By examining the other cases in the same way, we
find that the numbers of vibrations in the various notes of a closed pipe are in the pro-
portions 1:3:5:7: &c., the even harmonics being wholly absent.

There is another kind of organ pipe, called a reed pipe, in which a stream of air sets
a little spring in vibration so as to open and close, alternately, an opening in the pipe.
If the spring naturally vibrates in the time corresponding to any harmonic of the pipe,

Sound.
Sounding.

that note comes out with singular distinctness from the combination just as the scund
of a tuning-fork is strongly re-enforced by holding it over the mouth-hole of a flute which
is fingered for the note of the fork. If the spring and the tube have no vibration in
common, the noise produced is intolerably discordant. The oboe, bassoon, and clari-
onet are mere modifications of the reed-pipe; and so are horns in general, but in them
the reed is supplied by the lip of the performer. Thus, a cornet, a trumpet, or a
French horn, gives precisely the same series of harmonics as an open pipe.

The statements just made as to the position of the nodes in a vibrating column of air
are not strictly accurate, for the note is always found to be somewhat lower than that
which is calculated from the length of the tube and the velocity of sound. Hopkiui
showed experimentally that the distance between two nodes is always greater than twice
the distance from the open end to the nearest node. The mathematical difficulties
involved in a complete investigation of the problem were first overcome by Helmholtz
in 1859, in an admirable paper published in Crette's Journal. The results are found to
be in satisfactory accordance with those previously derived from experiment.

We have now to consider the subject of the quality of musical sounds; and one of
its most important branches, what constitutes the distinction between the various vowel-
sounds. It had long been recognized that the only possible cause of this distinction
between sounds musically identical must lie in the nature of the fundamental noise, or, to
express it differently, the nature of the periodic motion of each particle of air. But it
appears that Helmholtz was the first to enter upon a complete examination of the point,
both mathematically and experimentally, and the results he has arrived at form by no
means the least remarkable of the contents of his excellent work, Die Lehre wn den
Tonempfindungen, recently published.

It was established by Fourier that any periodic expression whatever may be resolved
into the sum of a number of simple harmonic terms, whose periods are, respectively, that
of the original expression, its half, its third part, etc. Hence any periodic motion of air
(i.e., any musical sound) may be resolved into a series of simple pendulum vibrations
(i.e., pure musical sounds, such as those of turning-forks), the first vibrating once in the

given period, the second twice, and so on. These notes are, as we have seen, the several
armonics of the lowest. Hence the quality of a musical sound depends upon the num-
ber and loudness of the harmonics by which it is accompanied.

Two experimental methods were employed by Helmholtz, one analytical, the other
synthetical. In the first he made use of resonance-cavities fitted to the ear, and giving
scarcely any indication of external sounds until one is produced which exactly corre-
sponds in pitch with the note which the cavity itself would yield. With a series of such
cavities, tuned to the several harmonics of some definite note, the note was examined
when played on various instruments, and when sung to different vowel-sounds. It was
thus ascertained which harmonics were in each case present, and to what extent, pro-
ducing the particular quality of the sound analyzed. The second method was founded
on the fact, already noticed, that a tuning-fork gives an almost pure musical sound (i.e.,
free from harmonics). A series of tuning-forks, giving a note and its harmonics, were
so arranged as to be kept constantly in vibration by an electro-magnetic apparatus.
Opposite to each was fixed a resonance-cavity exactly tuned to it, and capable of being
opened more or less at pleasure. When nil the cavities were shut, the sound was scarcely
audible; so that by opening them in various ways, any combination of harmonics might
be made to accompany the fundamental note. These combinations were varied by trial,
tmtil the quality of the resultant sound was brought to represent as nearly as possible
that of some vowel. The results of this second series of experiments coincided with
those of the first. It appears from these investigations that the German U is the quality
of a simple sound, though it is improved by adding faintly the two lowest harmonics;
that O depends mainly on the presence of the third harmonic; and so on with the other
sounds. It also appears, and it is well known by experience, that different vowel-
sounds, to be sung with accuracy, require to be sung to different notes, the proper note
being that for which the cavity of the mouth is adapted for the production of the accom-
panying harmonics which determine the quality of the particular vowel.

In strings and pipes, as we have seen, the higher notes are strictly harmonics of the
fundamental note, and therefore the sounds of instruments which depend on these sim-
ple elements are peculiarly adapted for music. On the other hand, when, as in masses
of metal, etc., the higher notes are not harmonics of the fundamental note, the mixed
sound is always more or less jarring and discordant. Such is the case with bells, trum-
pets, cymbals, triangles, etc.; and, in fact, these sounds are commonly characterized ag
"metallic." To produce from such instruments a sound as pleasing as possible, they
must be so struck that as few as possible of the higher notes are produced, and these as
feebly as possible. Thus, for instance, to get the most pleasing sound from a piano forte
wire, it should not be struck at the middle, as in such a case the first, third, fifth, etc.,
harmonics of the fundamental note will be wanting. If, however, it be struck at about
4 of its length from one end, the harmonics produced will be mainly the first five; and
these all belong to the chord of the fundamental note. A valuable recent work is lord
Rayleigh's Theory of &jund (2 vols. 1878).

SOUND (A.S. and Ger. sund; according to Grimm, for suund, from the root of swim),
a word signifying generally a strait or narrow sea-way, but applied specially to the

655

Sound.
Sounding.

strait which leads from the Cattegat into the Baltic sea, between Sweden on the e.
and the Danish island of Seelaud on the west. It forms the usual passage from the
n. to the Baltic Sea, is 40 m. long, and nearly 3 HI. broad at its narrowest part, between
the towns of Helsingborg and Elsinore. Its entrance is defended by the strong castle
and fortress of Kronborg. See ELSINORE.

SOUND DUTIES, certain dues formerly payable to the Danish government by all
vessels passing the sound or strait separating Sweden from Seeland. These duties
originated in an agreement between the king of Denmark and the Hanse Towns in
1348, by which the former undertook to maintain the light-houses in the Cattegat, and
the latter to pay duty for them. England became bound to pay duty by a treaty of
date 1450, and other countries followed. The Sound duties were abolished on Mar. 14,
1857, by a treaty between Denmark and other powers. A pecuniary compensation of
3, 386,528 (the share contributed by Great Britain being 1,125,206) was stipulated to
be paid to Denmark, which was to be held bound to maintain the light-houses and super-
intend the pilotage of the Sound.

SOUNDING is the act of ascertaining the depth of the water. This is done either for
purposes of navigation in piloting a ship among shoals or rocks, for ascertaining her
position where the depth and nature of the bottom is previously known, or construct-
ing a chart, etc. It is generally effected by means of a marked line, to which is
attached a tapered lead, the bottom or foot of the lead being hollowed to receive some
grease or tallow to which a portion of the soil at the bottom of the sea will adhere.
Other methods have been devised for ascertaining depth, such as by a rotating fan-
wheel, etc., but ihe first method is that still most generatU' used for ordinary depths.

SOUNDING. DEEP SEA. Until within a few years past, the term deep sounding was
understood to be that in which a ship sounded to ascertain her position, and where the
depth exceeded that which could be obtained with the lead Uirown by the hand, or hand-
lead; but the necessities of telegraphic communication across the ocean, by means of
cables containing insulated wires, have caused the ocean to be measured at depths which
were never before considered necessary, or even practicable.

The act of obtaining a deep-sea sounding may be said to consist of two parts 1. To
get the sinkers to the bottom as quickly as possible with the line straight up and down;
and 2. To bring a portion of the soil of the bottom, as a proof, to the surface; this
necessitates the use of a small but strong line, with heavy sinkers and a detaching appa-
ratus for freeing the sinkers when they reach the bottom, as from the smallness of the
line and the great friction of all passing through the water, the strain of bringing the
sinkers up would be too great for its strength. It may be stated that there is no diffi-
culty whatever in obtaining a sounding, and regaining the sinker with bottom specimen,
up to a depth of 1000 to 1200 fathoms (1 m.), by means of a heavy lead fitted with a
valved tube (fig. 1); but when the depth exceeds 2,000 fathoms the difficulties in obtain-
ing a correct sounding increase in a compound ratio with the depth.

The first detaching apparatus (fig. 2) was devised by Mr. Brooke, a midshipman
of the United States navy: it is extremely simple and efficient. It consists of a rod
with a movable hook at the upper end, .

and a tube at the lower end. The sinker
is a perforated shot, through which the
tube passes, and by means of a ring below
the shot the weight is suspended to the
hook by wire, the hook being^ kept up by
the sounding-line: the tube is filled with
cut quills. When the weight touches the
ground, the line is slackened, the hook
Falls, and the suspending wire beingfreed,
the shot slides off, while the quills being
thrust into the soil, secure a small portion,
which is brought up with the rod.

Many different kinds of detaching ap-
paratus have been invented since, but that

1

made use of on board H.M.S. Challenger,
in her deep-sea exploration voyage, is but
a modification of the original Brooke's
machine. The Hydra machine (fig. 3)
consists of a tube of iron, 24 in. in diame-
ter and 4i ft. in length, a; the lower 12
in., b, is tsparate from, but screws to the
upper part at c; it is fitted with a butter-
fly valve at the lower end, to retain the
bottom specimen. At the upper end of the tube is a piston-rod d, which mores freely
in the tube. To the upper part of this rod is fixed a steel spring, bent in a bow e; a slit
in the spring is adapted to the hook/, which protrudes beyond the spring when the lat-
ter is forced back. The sinkers (rig. 4) are cast-iron disks" of half a cwt. each, the hol
through the center, a, being sufficiently large for the sounding-tube to pass through.

Sound.
Sour.

They are made to fit each other bymeansof small conical protuberances on the one side,
and corresponding hollows on the other, b, so that when placed one on another, the
groove c in the one' weight corresponds, to that on the other. The upper and lower
sinkers differ a little in form.

When a sounding is to be taken the machine is prepared as in Fig. 5, a wooden stand
being used for the purpose. The sinkers a, a, are piled to the required weight, say 4 c\vt. ;
the tube is then passed through them, and an iron ring (with a bight of iron wire
attached) bb, is passed on the lower end of the tube, and the wire led along the contin-
uous grooves on each side of the sinkers c, and the bight passed over the hook d, the
spring being pressed back. When the weight of the sinkers rests on the ring, and is
supported by the wire, the weight keeps the spring pressed in ; but as soon as the sinkers
touch the ground and the weight is relieved from the wire, the spring throws it off the
hook, and the tube is drawn clear through the sinkers.

When the tube, with sinkers complete is ready, it is carefully hoisted over the side,
lowered gently into the sea, and eased down one or two hundred fathoms before being
let go. It is then let go, and the passing of each 100-fathoms mark is timed and recorded
in a printed form made to contain all the particulars of the sounding.

BIT William Thomson, F.R.S., has invented a mode of deep-sea sounding by using
piano wire instead of hempen lines, which promises to obviate much of the present diffi-
culty in deep-sea sounding.

Many very deep soundings are on record, but the two deepest well-authenticated
soundings are among those obtained by H.M.S. Challenger. The first was about 80 m.
to the northward of the Virgin islands, the depth being 3,875 fathoms, or nearly 4
miles. Unfortunately, not thinking that so near the islands so great a depth would be
found, only 3 cwts. of sinkers were used (the usual quantity for such extreme depths
being 4 cwts.); this weight, with a one-inch line, took an hour and twelve minutes to
reach the bottom. As the ascertainment of the sinkers reaching ,the bottom depends on
the time intervals, it may be stated that the line let free to run with this weight would
take about 43 seconds running out the first 100 fathoms, and the time increases as nearly
as possible three seconds for each successive 100 fathoms; so that when the interval is
prolonged beyond this rate, the sinker has reached the bottom. On this occasion the
last 50 "fathoms ran out at the rate of 2 minutes 36 seconds per 100 fathoms. The other
was to the n. of New Guinea, where the depth was 4,475 fathoms, or more than 5 miles.

An idea of the average depth of the n. Atlantic ocean may be had from the fact that
of 108 soundings obtained by the Challenger, 48 were between 1000 and 2,000 fathoms,
56 between 2,000 and 3,000, while only the other 4 exceeded 3,000. See DREG'GE;
DREDGING.

SOUND, REFRACTION OF. Sound moves in straight lines, in spherical-fronted
waves; and any small beam thereof, if unequally retarded or accelerated on either side,
bends toward the side of retardation so that the acoustic impulses, always directly radial
from the face of the sound wave, vary in their point of available impact, as the "ait
mirror" of sound turns distorted by disturbance. 1. Sound passing from airinto water, or
water into air, provides the only example really available, of acoustic refraction by dif-
ference of elasticity. Sound, encountering a strong opposition in the density of fluids,
and a still greater in solids, yet avails itself of the enormously disproportioned intensity
of resilience or elasticity. 1 he waves of sound arising from an explosion underwater
are conveyed by the water long distances; but when cast off into the air above the
explosion, the few and retarded vibrations diverge so enormously at such a height, by
reason of the flat reflector of the water at the surface, and the hollow arc of force beneath
generated by the explosion, as to become nearly inaudible, with their low velocity. Guns
at sea, fired on a horizontal with an energy far stronger than the inertia of the air, reverse
this; and with sound waves compressed between the force of the cannon and reflection
from the water, transmit their force to a great distance. 2. The refraction of sound
through differences of density has been shown by a convex lens of carbonic acid inclosed
in a collodion film, transferring the ticking of a watch to a focus, where it was heard
only on the interposition of the lens. The wave front received a concave form on its
entrance, accelerated on its exit at the rim, its lagging center became more concave, th.3
normals converging to a focus. 3. Prof. Stokes in 1857 first suggested the refraction of
sound by varying velocities of wind. Of two winds at different'levels, the upper, if the
faster, will retard an opposing sound wave most, and so elevate the sound focus; if the
sound advanced with the wind, the focus would lower, on account of the " drag" of