When a tuning-fork is struck, and held out in the air, the vibrations
can be felt for a time by the fingers; but the sound is hardly audible
unless the fork be placed close to the ear. Let the stem of the fork
rest upon the table, a chair, or any solid body of considerable size,
and the sound is so much increased in loudness as to be heard in every
part of a large room. The reason appears to be, that in the first case
the vibrations are so slight that the air is not much affected. Most of
the force of the vibration is absorbed by the hand that holds it; but
when the stem rests upon a hard body of considerable extent, the
vibrations are given up to it, and every part of its surface is giving
off the vibrations to the air. In other words, it is a much larger body
that is now vibrating, and consequently the air is receiving the
amplified sound-waves.
If the stem of the fork had been made to rest upon a bit of rubber, the
sound would not only not have been re-enforced in such a way, but the
fork would very soon have been brought to rest; for India rubber
_absorbs_ sound vibrations, and converts them into heat vibrations, as
is proved by placing such a combination upon the face of a thermo-pile.
If one will but put his hand upon a table or a chair-back in any room
where a piano or an organ is being played, or where voices are singing,
especially in church, he cannot fail to feel the sound; and if he
notices carefully he will perceive that some sounds make such table or
seat to shake much more vigorously than others,--a genuine case of
sympathetic vibrations.
It is for this reason that special materials and shapes are given to
parts of musical instruments, so that they may respond to the various
vibrations of the strings or reeds. For instance, the piano has an
extensive thin board of spruce underneath all the strings, which is
called the sounding-board. This board takes up the vibrations of the
strings; but, unlike the rubber, gives them all out to the air, greatly
re-enforcing their strength, and changing somewhat their quality. But
the air itself may act in like manner. In almost any room or hall not
more than fifteen or twenty feet long, a person can find some tone of
the voice that will seem to meet some response from the room. Some short
tunnels will from certain positions yield very powerful, responsive,
resonant tones. There is certainly one such in Central Park, New York.
It is forty or fifty feet long. To a person standing in the middle of
this, and speaking or making any kind of a noise on a certain pitch, the
resonance is almost deafening. It is easy to understand. When a column
of air enclosed in a tube is made to vibrate by any sound whose
wave-length is twice the length of the tube, we have such column of air
now filled with the condensed part of the wave, and now with the
rarefied part; and as these motions cannot be conducted laterally, but
must move in the direction of the length of the tube, the air has a
very great amplitude of motion, and the sound is very loud. If one end
of the tube be closed, then the length must be but one-fourth of the
wave-length of the sound. Take a tuning-fork of any convenient pitch,
say a C of 512 vibrations per second: hold it while vibrating over a
vertical test-tube about eight inches long. No response will be heard;
but, if a little water be carefully poured into the tube to the depth of
about two inches, the tube will respond loudly, so that it might be
heard over a large hall. In this case the length of the air-column that
was responding, being one-fourth the wave-length, would give twenty-four
inches as the wave-length of that fork.
It is easy in this way to measure approximately the number of vibrations
made by a fork.
Letting _l_ = depth of tube,
_d_ = diameter of tube,
_v_ = velocity of sound reduced for temperature,
_N_ = number of vibrations,
Then _N_ = _v_
------------
(4(_l_+_d_)).
When a vibrating tuning-fork is placed opposite the embouchure of an
organ-pipe of the same pitch, the pipe will resound to it, giving quite
a volume of sound. In 1872 it occurred to me, that the action of an
organ-pipe might be quite like that of a vibrating reed in front of the
embouchure. As the air is driven past it from the bellows, the form of
the escaping air will evidently be like a thin, elastic strip; and,
having considerable velocity, it will carry off by friction a little of
the air in the tube: this will of course rarefy the air in the tube
somewhat, and a wave of condensation will travel down the tube. At the
bottom, being suddenly stopped, its re-action will be partly outwards,
and so will drive the strip of air away from the tube. After this will
follow, for a like reason, the other phase of the wave, the rarefaction,
which will swing the strip of air towards the tube. This theory I
verified by filling the bellows with smoke, and watching the motion of
the escaping air and smoke with a stroboscope. This view is now
advocated by an organ-builder in England, Herman Smith; but whether he
discovered it before or after me, I do not know.
When a membrane vibrates, its motion is generally perceptible to the
eye; and it may have a very great amplitude of motion, as in the case of
the drum; and various instruments have been devised for the study of
vibrations, using membranes like rubber, gold-beater's skin, or even
tissue paper, to receive the vibrations. One of the musical instruments
of a former generation of boys was the comb. A strip of paper was placed
in front of it, and placed at the mouth, and sung through, the paper
responding to the pitch with a loose nasal sound. Koeenig fixed a
membrane across a small capsule, one side of which was connected by a
tube to any source of sound, and the other side to a gas-pipe and a
small burner. A sound made in the tube would shake the flame, and a
mirror moving in front of the flame would show a zigzag outline
corresponding to the sound vibrations.
In like manner if a thin rubber be stretched over the end of a tube one
or two inches in diameter and four or five inches long, and a bit of
looking-glass one-fourth of an inch square be made fast to the middle of
the membrane, the motions of the latter can be seen by letting a beam
of sunlight fall upon the mirror so as to be reflected upon a white wall
or screen a few feet away. (Fig. 8.)
[Illustration: FIG. 8.]
When a sound is made in this tube, the spot of light will at once assume
some peculiar form,--either a straight line with some knots of light in
it, or some curve simple or compound, and such as are known as Lissajous
curves. If, while some of these forms are upon the screen, the
instrument be moved sideways, the forms will change to undulating lines
with or without loops, varying with the pitch and intensity, but being
alike for the same pitch and intensity. (Fig. 9)
This instrument I called the opeidoscope.
[Illustration: FIG. 9.]
The vibration of a membrane and that of a solid differ chiefly in the
amplitude of such vibration. The scratch of a pin at one end of a long
log can be heard by an ear applied to the other end of the log; but
every molecule in the log must move slightly; and there are all degrees
of movement between that visible to the eye, which we call mass motion,
and that called molecular simply because we cannot measure the amplitude
of the motion. We may, then, roughly divide all bodies into two classes,
as to their relations to sound,--such as re-enforce it, and such as
distribute it: the first depending upon the form of the body, as related
to a particular sound; the second independent of form, and responding to
all orders of vibrations. Air, wood, and metals belong in this latter
class. The common toy-string telegraph, or _lovers' telegraph_, is an
example of this class. Two tin boxes are connected by a string passing
through the middle of the bottom of each. When the string is stretched,
and a person speaks in one box, what is said can be heard by an ear
applied at the other. If the speaking-tubes be made about four inches in
diameter, and about four inches deep, they are capable of doing much
more service than is generally supposed to be possible. I know of two
lines, one of five hundred feet and the other of a thousand feet in
length, over which one can talk, and be heard with distinctness. In the
line of a thousand feet, the end of the tube is made of sheepskin
tightly stretched, and the line is made of No. 8 cotton thread. The
greater the tension, the better is the sound transmitted. The thread is
supported at intervals by running through a loop on the ends of cords
not less than three feet long, attached to supports. The thread pierces
the membrane, and is attached to a small button which is in contact with
the membrane. Wind and rain affect this line disadvantageously. The
other line of five hundred feet, between a passenger and a freight
depot, has the tube end covered with stretched calfskin. Instead of
thread, a copper-relay wire is employed (any small uninsulated wire will
do as well). This permits a good tension, and is unaffected by the
weather. One may stand in front of it about three feet, and converse
with ease, and in an ordinary tone. The wire is supported in loops of
string, as in the other.
Musicians have in all times employed various instruments for the
production of musical effects. Whistles made of bone were used by
pre-historic men, some of them having finger-holes so that different
tones could be produced. A stag-horn that was blown like a flageolet,
and having three finger-holes, has also been found; while on the old
monuments of Egypt are pictured harps, pipes with seven finger-holes, a
kind of flute, drums, tambourines, cymbals, and trumpets. In later times
these primeval forms have been modified into the various instruments in
use in the modern orchestra. It seems as if no musician had ever been
interested in the question as to why one instrument should give out a
sound so different from another one, even though it was sounding upon
the same pitch. No one can ever mistake the sound of a violin, or a
horn, or a piano, for any other instrument; and no two persons have
voices alike. This difference in tone, which enables us to identify an
instrument by its sound or a friend by his voice, is called quality of
tone, or _timbre_.
About twenty years ago, that great German physicist Helmholtz undertook
the investigation of this subject, and succeeded in unravelling the
whole mystery of the qualities of sound.
He discovered first, that a musical sound is very rarely a simple tone,
but is made up of several tones, sometimes as many as ten or fifteen,
having different degrees of intensity and pitch. The lowest sound, which
is also the strongest, is called the _fundamental_; and it is this tone
we mean when we speak of the pitch of a sound, as the pitch of middle C
upon a piano, or the pitch of the _A_ string on a violin. The higher
sounds that accompany the fundamental are called sometimes harmonics,
sometimes upper partial tones, but generally _overtones_. The character
or quality of a sound depends altogether upon the number and intensity
of these overtones associated with the fundamental. If a sound can be
made upon a pipe and a violin, that consists wholly of the fundamental
with no overtones, the two instruments sound absolutely alike. It is
exceedingly difficult to do this; and such sound when produced is
smooth, but without character, and unpleasing.
Second, Helmholtz discovered that the overtones always stand in the
simplest mathematical relation to the fundamental tone,--in fact, are
simple multiples of that tone, being two, three, four, and so on, times
the number of vibrations of it.
This will be readily understood by considering the position of such
related sounds when they are written upon the staff.
[Illustration]
If we start with C in the bass as indicated in the staff, calling that
the fundamental, then the notes that will represent the above ratios
are those indicated by smaller notes, which are the overtones up to the
ninth. The first overtone, being produced by twice the number of
vibrations, must be the octave; the second, the fifth of the second
octave; the third will be two octaves from the first, and so on: the
number of vibrations of each of these notes being the number of the
fundamental multiplied by its order in the series.