WAVES AND RIPPLES IN THE AIR.
Leaving the consideration of waves and ripples on a water-surface,
we pass on to discuss the subject of waves and ripples in the air.
Nearly every one is aware, in a general way, that sound is due to
a disturbance created in the atmosphere. Few, however, are fully
acquainted with the nature of the movements in the air which excite
our sense of hearing, and to which we owe, not only the pleasures of
conversation and the enjoyment of all the sounds in nature, but those
delights of music which are amongst the purest forms of pleasure we
possess.
In the first place, it is necessary to demonstrate the fact that in
a place where there is no air there can be no sound. Before you on
the table is a brass plate covered with a glass dome. Under the dome
is a piece of clockwork, which, when set in action, strikes a gong.
This clockwork is suspended by silk strings from a frame to keep it
out of contact with the plate. The plate is in connection, by a pipe,
with an air-pump downstairs, and from the space under the dome we can
at pleasure remove the air. Before so doing, however, the clockwork
shall be set in motion, so that you will then see the hammer striking
the gong, and you also hear the sound. If now we exhaust the air,
the sound rapidly dies away, and when a fairly perfect vacuum has
been made, whilst you see the hammer continuing to pound the bell,
you notice that no sound at all reaches your ears. Turning a tap, I
let in the air, and once more the ring of the bell peals forth. The
experiment shows conclusively that sound is conveyed to us through
the air, and that if we isolate a sounding body by removing the air
around it, all transmission of sound is stopped. Even rarefying the air
greatly weakens the sound, for it is noticed that an exploding pistol
or cracker does not create the same intensity of sensation in the ear
at the top of a very high mountain as it does in the valley below.
We have then to show, in the next place, that a substance which
is emitting sound is in a rapid state of vibration, or to-and-fro
movement. Taking a tuning-fork in my hand, I strike its prongs against
the table, and you hear it faintly sounding. Your unassisted vision
will not, however, enable you to see that the prongs are in rapid
motion. If, however, I hold it against a pith-ball suspended by a silk
fibre, you see by the violent bouncing of the ball that the prongs must
be in energetic vibration.
Another experiment of the same kind, which you can yourselves repeat,
is to elicit a sound from a small table-gong by striking it with the
hammer. Then hold near the surface of the metal a small ball of wood or
cork, to which a suspending thread has been tied. The ball will keep
jumping from the gong-surface in a manner which will convince you that
the latter is in a state of violent agitation. The mode and extent of
this movement in a sound-emitting body must next be more thoroughly
examined. Let me explain the means by which I shall make this analysis.
On the prong of a tuning-fork, T (see Fig. 44), is fixed a small
mirror, M, and a ray of light is reflected from an electric lantern on
to this mirror. The ray is then reflected back again on to a sort of
cubical box, C, the sides of which are covered with looking-glass, and
finally it falls upon the screen. The mirrors are so arranged that if
the cubical mirror is at rest and the fork also, a bright spot of light
is seen upon the screen. If the fork is set in vibration, then the spot
of light moves up and down so rapidly that it forms a vertical bar
or line of light upon the screen. The cubical mirror is carried upon
an axis, and can be set in rotation. If the fork is at rest and the
cubical mirror revolves, then the spot of light marches horizontally
across the screen, and when the motion of the mirror is sufficiently
rapid it forms a horizontal and brilliant band of light. If, then,
these two motions are performed at the same time, the tuning-fork being
set in vibration and the cubical mirror in rotation, we find that the
spot of light on the screen executes a wavy motion, and we see in
consequence a sinuous bright line upon the wall.
[Illustration: FIG. 44.]
We have here two principles involved, which it may be better to
explain a little more in detail. An impression made upon the eye lasts
for about the tenth part of a second. Hence, if a luminous point or
bright object moves sufficiently rapidly, we cease to be able to
follow its movement, and we receive on our eyes merely the effect of
a luminous line of light. Every boy sees this when he whirls round a
lighted squib or stick with a flaming end. In the next place, notice
that two independent movements at right angles combine into what is
called a resultant motion. Thus the vertical up-and-down motion of the
spot of light in our experiment, combined with its uniform horizontal
movement, results in the production of a wavy motion. For the sake of
those who wish to repeat the experiment, a few little hints may be
given. The revolving cubical mirror is a somewhat expensive piece of
apparatus, but found in every well-appointed physical laboratory. A
cheap substitute, however, may be made by firmly sticking on to the
sides of a wooden box pieces of thin looking-glass. The box is then to
be suspended by a string. If the string is twisted, the box may be set
spinning like a joint of meat roasting before the fire. An ordinary
magic lantern may be used to provide a parallel beam of light. In
lecture demonstrations it is necessary to employ the electric arc lamp,
and to make use of an arrangement of lenses to create the required
powerful parallel beam of light. Then as regards the fork. We are
employing here a rather elaborate contrivance called an electrically
driven tuning-fork, but for home demonstration it is sufficient to
make use of a single piece of stout steel clock-spring, or any other
flexible and highly tempered piece of steel. This must be fixed to a
block of wood as a support, and to its end must be fastened with care a
small piece of lead, to which is attached a fragment of thin silvered
glass of the kind called a galvanometer mirror, which may be procured
of any scientific instrument maker. The position of this vibrating
spring must be such that, if the spring vibrates alone, it will reflect
the ray of light on to one face of the cubical mirror, and thence on to
a white wall, and create a vertical bar of light, which becomes a spot
of light when the spring is at rest. It is possible to purchase very
small concave mirrors about half an inch in diameter, made of glass
silvered at the back. If one of these can be procured, then there is
no need to employ an optical lantern; with an ordinary table-lamp, or
even a candle as a source of light, it is easy to focus a bright spot
of light upon the screen, which effects the desired purpose of making
evident the motion of the spring.
Before we dismiss the experiment, let me say one or two more words
about it. You notice when it is proceeding that the luminous wavy
line is a regular and symmetrical one. This shows us that the
motion of the prong of the fork is similarly regular. This kind of
backwards-and-forwards motion is called an _harmonic motion_, or a
_simple periodic motion_. It is very similar to the kind of movement
executed by the piston of a steam-engine as it oscillates to and fro.
The exact nature of the wavy line of light you see upon the screen can
be delineated by a line drawn as follows: On a sheet of paper describe
a circle, and divide its circumference into twelve equal parts (see
Fig. 45). Through the centre and through each of these points on the
circumference draw parallel lines. Divide up a length of the line drawn
through the centre into twelve equal parts, and number these divisions
1 to 12. Number also the points on the circumference of the circle.
Through the twelve points on the horizontal line erect perpendiculars.
Make a dot at the intersection of the perpendicular, or ordinate,
as it is called, drawn through point 1 on the horizontal line, and
the horizontal through point 1 on the circumference of the circle.
Do this for all the twelve intersections, and then carefully draw a
smooth curve through all these points. We obtain a wavy curve, which is
called a _sine curve_, or _simple harmonic curve_, and is the same form
of curve as that exhibited on the screen in the experiment with the
tuning-fork and spot of light. The piece of the curve drawn as above is
called _one wave-length_ of the harmonic curve.
[Illustration: FIG. 45.—A simple harmonic curve.]
In our case the tuning-fork is making one hundred complete vibrations
(to _and_ fro) per second. Hence the periodic time, or time occupied by
one complete wave, is the hundredth part of a second. To realize what
this small interval of time means, it is sufficient to remember that
the hundredth part of a second is to one second as the duration of this
lecture (one hour) is to four days and nights.
The prongs of a sounding tuning-fork or the surface of a gong or a
bell, when struck, are therefore in rapid motion. We can then proceed
to an experiment fitted to indicate the difference between those
motions in sounding bodies which create musical tones, and those which
create mere noises or vocal sounds.
I have on the table before me a bent brass tube provided with a
mouthpiece at one end, and the other end of the tube is covered over
with a very thin piece of sheet indiarubber tied on like the cover of
a jam-pot. To the outer surface of this indiarubber is cemented a very
small, light silvered-glass mirror. The same arrangements are made as
in the case of the previous experiment, and the ray of light from a
lantern is reflected from the little mirror on to the revolving cubical
mirror, and thence on to the screen. Setting the cubical mirror in
rotation, we have a line of bright light upon the screen. If, then,
my assistant sings or speaks into the mouthpiece, the motion of the
indiarubber sets in vibration the little attached mirror. This mirror
is not attached to the centre of the membrane, but a little to one
side. Hence you can easily understand that when the indiarubber is
bulged in or out, the attached mirror is more or less tilted, and the
spot of light is displaced up or down on the screen. In this manner the
movements of the spot imitate those of the diaphragm. Hence the form of
the bright line on the screen is an indication of the kind of movement
the diaphragm is making. Let us then, in the first place, sing into the
tube whilst the cubical mirror is uniformly rotated. If my assistant
sounds a full pure note, you will see that the straight line of light
instantly casts itself into a wavy form, which is not, however, quite
of the same shape as in the case of the tuning-fork. Here the zigzag
line resembles the outline of saw-teeth (see Frontispiece).
If he varies the loudness of his sound, you see the height of the teeth
alter, being greater the louder his note. If he changes the tone,
singing a bass or a treble note, you observe that, corresponding to a
high or treble note, the waves are short, and corresponding to a deep
or bass note, the waves are long. Accordingly, the shape of the line
of light upon the screen gives us exact information as to the nature of
the movement of the indiarubber diaphragm, viz. whether it is moving in
and out, slowly or quickly, much or little.
Again, suppose, instead of singing into the tube, my assistant speaks
a few words. If, for instance, he repeats in a loud tone the simple
but familiar narrative of “Old Mother Hubbard,” you will see that,
corresponding to each word of the sentence, the line of light upon the
screen bends itself into a peculiar irregular form, and each particular
word is as it were written in lines of fire upon the wall.
Notice how certain sounds, such as _b_ and _p_ and also _t_ are
represented by very high notches or teeth in this line of light. These
sounds are called _explosive consonants_, and if you examine the manner
in which they are made by your mouth, you will notice that it consists
in closing the mouth by the lips or tongue placed between the teeth,
and then suddenly withdrawing the obstruction so as to allow the air
from the lungs to rush forcibly out. Hence the air outside, and in this
case the diaphragm, receives a sudden blow, which is represented by
this tall tooth or notch in the luminous band. The experiment teaches
us that whereas _musical tones_ are caused by certain very regular and
uniform vibrations of the sounding body, _vocal sounds_ and _noises_
are caused by very irregular movements. Also that loud sounds are
created by large motions, and feeble ones by small motions. Again, that
the difference between tones in music is a difference in the rate of
vibration of the sounding body. We may infer also that the difference
between the quality of sounds is connected with the _form_ of the
wave-motion made by them.
Having established these facts, we must, in the next place, proceed
to notice a little more closely the nature of an _air wave_. It will
be necessary to remind you of certain qualities possessed not only by
the air we breathe, but by all gases as well. Here is a cylinder with a
closely fitting piston, and a tap at the bottom of the tube. If I close
the tap and try to force down the piston, I feel some resistance, which
increases as the piston is pushed forward. If the pressure is removed,
the piston flies back to its old position, as if there were a spring
underneath it. The air in the tube is an elastic substance, and it
resists compression. At constant temperature the volume into which the
air is squeezed is inversely as the pressure applied.
The air, therefore, possesses _elasticity of bulk_, as it is called,
and it resists being made to occupy a smaller volume. Again, the air
possesses _inertia_, and when it is set in motion it continues to
move like any other heavy body, after the moving force is withdrawn.
We have, therefore, present in it the two essential qualities for the
production of a wave-motion, as explained in the first lecture. The air
_resists_ compression in virtue of elasticity, and when it is allowed
to expand again back, it _persists_ in motion in virtue of inertia.
Let us consider next the process of production of a very simple sound,
such as an explosion. Suppose a small quantity of gun-cotton to be
detonated. It causes a sound, and therefore an air wave. The process by
which this wave is made is as follows: The explosion of the gun-cotton
suddenly creates a large quantity of gas, which administers to the air
a very violent outward push or blow. In consequence of the inertia of
the air, it cannot respond everywhere instantly to this force. Hence
a certain spherical layer of air is compressed into a smaller volume.
This layer, however, almost immediately expands again, and in so doing
it compresses the next outer layer of air and rarefies itself. Then,
again, the second layer in expanding compresses a third, and so on.
Accordingly, a state of compression is handed on from layer to layer,
and each state of compression is followed by one of rarefaction. The
individual air-particles are caused to move to and fro in the direction
of the radii of the sphere of which the source of explosion is the
centre. Hence we have what is called a spherical longitudinal wave
produced.
Each air-particle swings backwards and forwards in the line of
propagation of the wave. The actual motion of each air-particle is
exceedingly small.
The speed with which this zone of compression travels outwards, is
called the velocity of the sound wave, and the extent to which each
air-particle moves backwards and forwards is called the amplitude of
the wave.
Suppose, in the next place, that instead of a merely transitory sound
like an explosion, we have a continuous musical sound, we have to
inquire what then will be the description of air-movement executed. The
experiments shown already will have convinced you that, in the case of
a musical sound, each air-particle must repeat the same kind of motion
again and again.
The precise nature of the displacement can be best illustrated by the
use of two models. Before you is placed a frame to which are slung a
series of golf-balls suspended by threads (see Fig. 4, Chapter I.).
Between each pair of balls there is a spiral brass spring, which
elastically resists both compression and extension. You will see that
the row of balls and springs, therefore, has similar properties to the
air. In virtue of the springs it resists compression and expansion, and
in virtue of the mass or inertia of the balls any ball, if displaced
and allowed to move back, overshoots its position of equilibrium
because it persists in motion. The row of balls, therefore, resists
extension and compression in consequence of the elasticity of the
springs, and each ball persists in movement in consequence of the
inertia of the ball.
If we then administer a little pat to the first ball, you will see a
wave-motion run along the line of balls. Each ball in turn moves to and
fro a little way, and its movement is handed on to its neighbours. We
have here an example of a longitudinal wave-motion which resembles that
of the air when it is traversed by a sound wave.
Another model which is of a more elaborate character shows us the
sort of motion made in a tube when a sound wave due to a continuous
musical sound is passing along it. It consists of a glass disc which is
blackened, and has the paint removed along certain excentric circular
lines. This disc is made to revolve in front of a wide slit in a piece
of metal. By means of an optical lantern we project on to the screen
an image of the slit, which you see is crossed by certain bright bars
of light, crowded together at some places and more spaced apart at
others. When the disc revolves, these bars of light each move to and
fro successively, and the result is that the crowded place moves along,
or is displaced.
A wave of compression is propagated along the slit, and the localities
where the bars of light are compressed or expanded continually change
their place. If we imagine the air in a tube to be divided into slices,
represented by these bars of light, the motion of the model exactly
represents the motion of the air in the tube when it is traversed by a
series of sound waves.
The distance from one place of greatest compression to the next is
called the wave-length of the sound wave. Hence, although a sound such
as that of an explosion may consist in the propagation of a single
layer of compression, the production of a continuous musical note
involves the transference of a series of equidistant compressional
zones, or waves.
These models will have assisted you, I trust, to form a clear idea of
the nature of a sound wave in air. It is something very different, in
fact, from a wave on the surface of water, but it is characterized
by the same general qualities of wave-motion. It is a state of
longitudinal periodic motion in a row of particles, which is handed on
from one to another. Each particle of air oscillates in the line of
propagation of the wave, and moves a little way backwards and forwards
on either side of its undisturbed position.
It will be seen, therefore, that a solitary sound wave is a state
of air-compression which travels along in the otherwise stationary
air. The air is squeezed more tightly together in a certain region,
and successive layers of air take up this condition. In the case of
water-surface waves the wave is a region of elevation at which the
water is raised above the general or average level, and this elevated
region is transferred from place to place on otherwise stationary
water. In the case of an air-wave train we have similar regions of
compression following each other at distances, it may be, of a fraction
of an inch or of several feet.
Thus in the case of ordinary speech or song, the waves are from 2 to
8 feet in length, that is, from one compressed region to the next. In
the case of a whistle, the wave-length may be 1 or 2 inches, whilst the
deepest note of an organ produces a sound of which the wave-length is
about 32 feet.
As in every other instance of wave-motion, air waves may differ from
each other in three respects. First, in _wave-length_; secondly, in
_amplitude_; and thirdly, in _wave-form_. The first determines what
we call the tone, _i.e._ whether the sound is high or low, treble or
bass; the second determines the intensity of the sound, whether faint
or loud; and the third determines its _quality_, or, as the Germans
expressively call it, the sound-colour (_Klangfarbe_).
We recognize at once a difference between the sound of a vowel, say
_ah_, sung by different persons to the same note of the piano and with
the same loudness. There is a personal element, an individuality, about
voices which at once arrests our attention, apart altogether from the
tone or loudness. This _sound-quality_ is determined by the form of the
wave-motion, that is, by the nature of the movement of the air-particle
during its little excursion to and fro in which it takes part in
producing a zone of compression or rarefaction in the air and so forms
a sound wave.
We have next to discuss the speed with which this air-compression
is propagated through the air. Every one knows that it is not
instantaneous. We see the flash of a gun at a distance, and a second
or so afterwards we hear the bang. We notice that the thunder is
heard often long after the lightning flash is seen. It would take too
long to describe the experiments which have been made to determine
precisely the speed of sound waves. Suffice it to say that all the
best experiments show that the velocity of a sound wave in air, at
the temperature of melting ice, or at 0° C. = 32° Fahr., is very
nearly 1087 feet per second, or 33,136 centimetres per second. This
is equivalent to 741 miles per hour, or more than ten times the speed
of an express train. At this rate a sound wave would take 4 hours to
cross the Atlantic Ocean, 16 hours to go half round the world or to the
antipodes, and some 2 minutes to cross from Dover to Calais.
An opportunity of observing this speed of sound waves on a gigantic
scale occurred about 20 years ago on the occasion of a great volcanic
eruption near Java. If you open the map of Asia and look for Java and
Sumatra in the Asiatic Archipelago, you will easily find the Sunda
Strait, and on a good map you will see a small island marked called
Krakatoa. This island possesses, or rather did possess, a volcano
which, until the year 1883, had not been known to be in eruption. In
that year, however, it again burst into activity, and after preliminary
warnings a final stupendous outburst occurred on August 27, 1883.
The roar of this volcanic explosion was probably the loudest noise
ever heard upon this earth. The pent-up volcanic gases and vapours
burst forth from some subterranean prison with such appalling power
that they created an air wave which not only encircled the earth, but
reverberated to and fro seven times before it finally faded away.
The zone of compressed air forming the mighty air wave as it passed
from point to point on the earth’s surface, caused an increase of
atmospheric pressure which left its record on all the self-registering
barometers, and thus enabled its steps to be traced. A diligent
examination of these records, as collected in a celebrated Report of
the Royal Society upon the Eruption of Krakatoa, showed exactly the
manner in which this great air wave expanded. Starting from Krakatoa
at 10 a.m. on the 27th of August, 1883, the air wave sped outwards in
a circle of ever-increasing diameter until, by 7 p.m. on the same
day, or 9 hours later, it formed a girdle embracing the whole world.
This stupendous circular air wave, 24,000 miles in circumference,
then contracted again, and in 9 hours more had condensed itself at a
point in the northern region of South America, which is the antipodes
of Krakatoa. It then rebounded, and, expanding once more, just like a
water wave reflected from the side of a circular trough, returned on
its own steps, so that 36 hours afterwards it had again reached the
point from whence it set out. Again and again it performed the same
double journey, but each time weaker than before, until, after seven
times, the echoes of this mighty air wave had completely died away.
This is no fancy picture, but a sober record of fact obtained from
the infallible records of self-registering air-pressure-measuring
instruments. But we have evidence that the actual sound of the
explosion was heard, 4 hours after it happened, on the other side of
the Indian Ocean, by human ears, and we have in this an instance of the
measurement of the velocity of sound on the largest scale on which it
was ever made.
There are many curious and interesting facts connected with the
transmission of a sound wave through air, affecting the distance at
which sounds can be heard. The speed of sound in air is much influenced
by the temperature of the air and by wind.
The speed of sound increases with the temperature. For every degree
Fahrenheit above the melting-point of ice (32° Fahr.) the speed is
increased by one foot per second. A more accurate rule is as follows:
Take the temperature of the air in degrees Centigrade, and add to this
number 273. In other words, obtain the value of 273 + _t°_ where _t°_
is the temperature of the air. Then the velocity of sound in feet per
second at this temperature is equal to the value of the expression—
1090√((273 + _t°_)/273)
There is one point in connection with the velocity of propagation of a
sound wave which should not be left without elucidation. It has been
explained that the velocity of a wave in any medium is numerically
given by the number obtained by dividing the square root of the
elasticity of the medium by the square root of its density. The number
representing the elasticity of a gas is numerically the same as that
representing its absolute pressure per square unit of surface. The
volume elasticity of the air may therefore be measured by the absolute
pressure it exerts on a unit of area such as 1 square foot. At the
earth’s surface the pressure of the air at 0° C. is equal to about
2116·4 lbs. per square foot. The absolute unit of force in mechanics
is that force which communicates a velocity of 1 foot per second to a
mass of 1 lb. after acting upon it for 1 second. If we allow a mass
of 1 lb. to fall from rest under the action of gravity at the earth’s
surface, it acquires after 1 second a velocity of 32·2 feet per second.
Hence the force usually called “a pressure of 1 lb.” is equal to 32·2
absolute units of force. Accordingly, the atmospheric pressure at the
earth’s surface is 2116·4 × 32·2 = 68,148 absolute units of force in
that system of measurement in which the foot, pound, and second are the
fundamental units.
The absolute density of the air is the mass of 1 cubic foot: 13 cubic
feet of air at the freezing-point, and when the barometer stands at 30
inches, weigh nearly 1 lb. More exactly, 1 cubic foot of air under
these conditions weighs 0·080728 lb. avoirdupois. If, then, we divide
the number representing the absolute pressure of the air by the number
representing the absolute density of air, we obtain the quotient
844,168; and if we take the square root of this, we obtain the number
912·6.
The above calculation was made first by Newton; and he was unable
to explain how it was that the velocity of the air wave, calculated
in the above manner from the general formula for wave-speed, gave a
value for the velocity, viz. 912·6, which was so much less than the
observed velocity of sound, viz. 1090 feet per second at 0° C. The
true explanation of this difference was first given by the celebrated
French mathematician Laplace. He pointed out that in air, as in all
other gases, the elasticity, when it is compressed slowly, is less
than that when it is compressed quickly. A gas, when compressed, is
heated, and if we give this heat time to escape, the gas resists the
compression less than if the heat stays in it. Hence air is a little
more resilient to a very sudden compression than to a slow one. Laplace
showed that the ratio of the elasticity under sudden compression was
to that under slow compression in the same ratio as the quantities of
heat required to raise a unit mass of air 1° C. under constant pressure
and under constant volume. This ratio is called “the ratio of the two
specific heats,” and is a number close to 1·41. Hence the velocity, as
calculated above, must be corrected by multiplying the number 844,168
by the number 1·41, and then taking the square root of the product.
When this calculation is made, we obtain, as a result, the number 1091,
which is exactly the observed value of the velocity of sound in feet
per second at 0° C. and under atmospheric pressure. The velocity of
sound is much affected by wind or movement of the air. Sound travels
faster with the wind than against it. Hence the presence of wind
distorts the shape of the sound wave by making portions of it travel
faster or slower than the rest.
These two facts explain how it happens that loud sounds are sometimes
heard at great distances from the source, but not heard at places close
by.
[Illustration: FIG. 47 (reproduced by permission of proprietors of
_Knowledge_).—Map of South of England, showing places (black dots) at
which sound of funeral guns was heard, February 1, 1901.]
Consider the case of a loud sound made near the surface of the earth.
If the air were all at rest, and everywhere at the same temperature,
the sound waves should spread out in hemispherical form. But if, as
is generally the case, the temperature near the ground is higher than
it is up above, then the part of the wave near the earth travels
more quickly than that in the higher regions of the air. It follows
that the sound wave will have its direction altered, and instead of
proceeding near the earth in a direction parallel to the ground, it
will be elevated, so as to strike in an upward direction. Again, it may
be brought down by meeting with a current of air which blows against
the lower portion and so retards that to a greater extent than it does
the upper part. So it comes to pass that a sound wave may, as it were,
“play leap-frog” over a certain district, being lifted up and then
let down again; and persons in that region will not hear the sound,
although others further off will do so. A very striking instance of
this occurred on the occasion of the funeral procession of our late
beloved Queen Victoria of blessed memory. The body was conveyed across
the Solent on February 1, 1901, between lines of battleships which
fired salutes with big guns. Arrangements were made to determine
the greatest distance the sound of these guns was heard. In a very
interesting article in _Knowledge_ for June, 1901, Dr. C. Davison has
collected the results of observation from eighty-four places, some of
which are indicated in the map (see Fig. 47), taken, by kind permission
of the editor of _Knowledge_, from that journal. Observations were
received from places as far distant as Alderton (Suffolk), 139
miles from the Solent. At several places the sound of the guns was
loud enough to make windows shake. This occurred at Longfield (56
miles), Sutton (58 miles), and Richmond Hill (61 miles). But whilst
there is clear evidence that the sound of the guns was heard even at
Peterborough (125 miles), most curious to say, the sound was hardly
heard at all in the neighbourhood of the Solent. The nearest place from
which any record was received was Horley, in Surrey (50 miles). Hence
it appears evident that the sound was lifted up soon after leaving the
Solent, and passed right over the heads of observers near, travelling
in the higher air for a considerable distance, probably 40 or 50 miles,
and was then deflected down again, and reached observers on the earth’s
surface at much greater distances. An examination of the wind-charts
for that day makes it tolerably clear that this was due to the manner
in which the wind was blowing at the time. Dr. Davison, _loc. cit._,
says—
“Now, on February 1, the wind at places to the west of Spithead
was generally light, and from the west or nearly so, though near
Lyndhurst there was a fresh breeze from about W.N.W. or N.W. At
Portsmouth, again, the wind is described as from the shore. On
the other hand, many of my correspondents at great distances
from Spithead state that the wind, when sensible, was southerly
in direction. Thus the sound-rays were first of all refracted by
contrary winds over the heads of observers between 10 and 45 miles,
and were afterwards brought down again by favourable upper currents,
so that the reports were clearly audible beyond 50 miles and up to
140 miles from Spithead, and were so loud at a distance of 84 miles
that labourers in the fields put down their spades and listened.”
The same explanation has been given of the extraordinary differences
that are found at various times in the distance at which lighthouse
fog-horns are heard by ships at sea. There is in this case, however,
another possible explanation, due to what is called interference of
sound waves, the explanation of which will be given presently. The
late Professor Tyndall, who was an authority on this subject, was of
opinion that in some states of the atmosphere there existed what he
called “acoustic opacity,” the air being non-uniform in temperature
and moisture; and through this very irregular medium, sound waves,
when passing, lost a great deal of their intensity by internal
reflection, or eclipses, just as light is stopped when passing through
a non-homogeneous medium like crushed ice or glass. At each surface
a little of the light is wasted by irregular reflection, and so the
medium, though composed of fragments of a transparent substance, is
more or less opaque in the mass.
On the subject of sound-signals as coast-warnings, some exceedingly
interesting information has recently been supplied by Mr. E.
Price-Edwards (see _Journal of the Society of Arts_, vol. 50, p. 315,
1902). The Lighthouse Boards of different countries provide the means
for making loud warning sounds at various lighthouses, as a substitute
for the light when fog comes on. The distance at which these sounds can
be heard, and the distance-traversing power of various kinds of sounds,
have been the subject of elaborate investigations.
The instrument which has been found to be the most effective in
producing very powerful sound waves is called a _siren_. It consists
of a tube or horn, having at the bottom a fixed disc with slits in it.
Outside this disc is another movable one which revolves against the
first, and which also has slits in it. When the second disc revolves,
the passage way into the horn is opened and closed intermittently and
suddenly, as the slits in the discs coincide or not. Air or steam
under a pressure of 10 to 40 lbs. on the square inch is blown into the
horn, and the rapid interruption of this blast by the revolving slits
causes it to be cut up into puffs which, when sufficiently frequent,
give rise to a very loud sound. The air under pressure is admitted to a
back chamber and awaits an opportunity to escape, and this is given to
it when the revolving disc moves into such a position that the slits
in the fixed and moving disc come opposite each other. In comparative
trials of different sound-producing instruments, nothing has yet been
found to surpass this siren as a producer of penetrating sounds.
It has been found very important that the frequency of the note given
by the siren should coincide with the fundamental tone of the trumpet
or horn. As will be explained in the next lecture, every column of air
in a tube has a particular natural time-period of oscillation. Suppose,
for instance, that for a certain length of trumpet-tube this is ¹⁄₁₀₀
second. Then the siren with that trumpet will be most effective if the
interruptions of the air-blast are 100 per second.
Lord Rayleigh has also shown that the shape of the mouth of the trumpet
is important, and that this should not be circular as usual, but
elliptical or oval, the shortest diameter of the ellipse being one
quarter of the longest one. Also that the mouth should occupy such a
position that the longer axis is vertical. Moreover, he considers that
the short axis of the oval should not exceed half the wave-length of
the sound being emitted. With a trumpet-mouth of such a shape, the
sound is prevented to some extent from being projected up and down,
but diffused better laterally—a result which is desired in coast
sound-signals.
The information accumulated as regards the distances at which sounds
can be heard is very briefly as follows:—
First as regards wind. The direction of the wind has a most remarkable
influence on the distance at which a given loud sound can be heard. In
one instance, the noise of a siren was heard 20 miles in calm weather;
whereas, with an opposing wind, it was not heard more than 1¹⁄₄ mile
away.
It has been found that for calm weather a low-pitched note is better in
carrying power than a high note, but in rough weather the opposite is
the case.
One thing that has been noticed by all who have experimented with this
subject is the curious occurrence of “areas of silence.” That is to
say, a certain siren will be well heard close to its position. Then a
little farther off the sound will be lost, but on going farther away
still it is heard again.
Many theories have been advanced to account for this, but none are
completely satisfactory. It is, however, a well-established effect, and
one with which it behoves all mariners to be acquainted.
One curious fact is the very great power that can be absorbed in
creating a loud siren note. Thus in one case, a siren giving a high
note was found to absorb as much as 600 horse-power when the note was
sounded continuously. The most striking and in one sense the most
disappointing thing about these loud sounds is the small distance
which they travel in certain states of the wind. As a general result,
it has been found that the most effective sound for coast-warnings
is one having a frequency of 100, or a wave-length of about 10 feet.
When dealing with the subject of waves in general, it was pointed
out that the velocity of a wave depended upon the elasticity and the
density of the medium in which it was being propagated. In the case of
a sound wave in air or any other gas, the speed of wave-transmission
is proportional to the square root of the elasticity of the gas, and
inversely proportional to the square root of the density.
At the same temperature the elasticity of a gas may be taken to be
the same as its pressure. Hence, at the same pressure, the speed of
sound-wave transmission through different gases varies inversely as
the square root of their densities. An example will make this clear. If
we take the density of hydrogen gas to be unity (= 1), then the density
of oxygen is 16. The ratio of the densities is therefore 1 to 16, and
the square roots of the densities are as √(1) to √(16), or as 1 to 4.
Accordingly, the velocity of sound waves in hydrogen gas is to that in
oxygen gas as 1 is to ¹⁄₄. In other words, sound travels four times
faster in hydrogen than it does in oxygen at the same temperature and
pressure. The following table shows the velocity of sound in different
gases at the melting-point of ice (= 0° C.) and atmospheric pressure (=
760 mm. barometer).
Gas. Velocity.
Hydrogen 4163 feet per second
Carbonic oxide 1106 ” ”
Air 1090 ” ”
Oxygen 1041 ” ”
Carbonic acid 856 ” ”
Accordingly, we see that the lighter the gas the faster sound travels
in it, pressure and temperature being the same. If the atmosphere we
breathe consisted of hydrogen instead of a mixture of oxygen, nitrogen,
and many other gases, a clap of thunder would follow a flash of
lightning much more quickly than it does in our present air, supposing
the storms to be at the same distance. Under present circumstances, if
20 seconds elapse between the flash and the peal, it indicates that the
storm is about 4 miles away, but if the atmosphere were of hydrogen,
for a storm at the same distance the thunder would follow the lightning
in about 5 seconds.
Furnished with these facts about the propagation of air waves, it is
now possible to point out some interesting consequences. It will be
in your recollection that in the first chapter it was pointed out
that a wave on water could be reflected by a hard surface, and that
it could be refracted, or bent, when it passed from a region where it
was moving quickly to one where it was moving more slowly. It will be
necessary now to prove experimentally that the same things can be done
with sound, in order that a body of proof may be built up in your minds
convincing you that the external cause of sound-sensation must be a
wave-motion in the air.
In the first place, I must describe to you, somewhat in detail, the
nature of the arrangements we shall employ for producing and detecting
the sound waves which will be used in these experiments.
It would not do to rely upon the ear as a detector because you cannot
all be so placed as to hear the sounds which will be produced, and we
shall, therefore, employ a peculiar kind of flame, called a _sensitive
flame_, to act as a detector.
If ordinary coal-gas stored in a gasometer is burnt at a small jet
under considerable pressure, we are able to produce a tall flame about
18 to 24 inches in height. The jet used is one with a steatite top and
small pin-hole gas exit about ¹⁄₂₅ inch in diameter. The pressure of
gas must be equal to about 10 inches of water, and it cannot be drawn
straight off the house gas-pipes, but must be supplied from a special
gasometer or gasbag under a pressure sufficient to make a flame 18
inches or so in height. If the pressure is too great, the flame roars;
if the pressure is slightly reduced, the flame can be made to burn
quietly and form a tall reed-like flame (A, Fig. 48). This flame, when
properly adjusted, is curiously sensitive to shrill, chirping sounds.
You may shout or talk loudly near it, and it takes no notice of your
voice, but if you chirrup or whistle in a shrill tone, or clink your
keys or a few coins in your hand, the flame at once shortens itself to
about 6 or 7 inches in height, and becomes possessed of a peculiarly
ragged edge, whilst at the same time it roars (B, Fig. 48). When in
adjustment, the clink of a couple of coins in the hand will affect this
sensitive flame on the other side of the room.[22] The flame is also
very sensitive to a shrill whistle or bird-call. It will be clear to
you, from previous explanations, that the flame responds, therefore, to
very short air waves forming high notes. The particular flame I shall
now use responds with great readiness to air waves of 1 inch to ¹⁄₂
inch in length.
[Illustration: FIG. 48.—A sensitive flame: A, quiescent; B, roaring.]
It may be well to explain that the sensitive portion of the flame is
the root, just where it emerges from the burner, and it is the action
of the sound wave in throwing this portion of the flame into vibration
which is the cause of its curious behaviour.
If you think what the action must be, you will easily see that the
operation of the sound wave is to throw the particles of the gas, just
as they escape from the hole in the jet, into vibration in a direction
transverse or at right angles to the direction of their movement in
the flame. The gas molecules are, when unacted upon by the sound wave,
rushing out of the jet, in an upward direction. When the sound wave
impinges on them they are, so to speak, caught, and caused to rock to
and fro in a direction across the flame. The combination of these two
motions results in a spreading action on the flame, so that instead
of being a thin lance-like shape, it becomes more blunt, stumpy, and
ragged at the sides. The flame acts, therefore, as a detector of
certain sounds. It is a very sensitive kind of ear which listens and
responds to the slightest whisper if only uttered in certain tones,
but is deaf to all other sounds. Its great use to us is that it
acknowledges the presence of air waves of short wave-length, and shows
at once when it is immersed in a stream of air waves or ripples of very
short wave-length.
In addition to this, I am provided with a whistle giving a very
shrill or high note, which is blown steadily by a current of air
supplied under constant pressure from a reservoir. If the whistle is
set in action, you will at once see the sensitive flame dip down and
acknowledge the presence of the air-waves sent out by the whistle.
The air waves sent out by this whistle proceed, of course, in all
directions, but for our present purpose we require to create what I may
call a _beam of sound_. You all know the action of a magnifying-glass,
or lens, upon a ray of light. What boy is there who has not, at some
time or other, amused himself by concentrating the rays of the sun by
a burning-glass, and by bringing them to a focus set light to a piece
of paper, or burnt his own or companion’s hand? In this case we use a
piece of glass called a lens, which is thicker in the middle than at
the edges, to converge parallel rays of light to a point or focus. We
also use such a lens in our optical lantern to render the diverging
rays from an electric lamp parallel, and so make a parallel beam of
light. I shall defer for a moment an explanation of this action, and
simply say here that it is possible to construct a _sound-lens_,
which operates in the same manner on rays of sound. I have had such a
sound-lens constructed for our present experiments, and it is made as
follows:—
It is possible to buy small balloons made of very thin material
called _collodion_, this latter consisting of gun-cotton dissolved in
ether and alcohol, and then poured out on a glass plate and allowed
to dry. If one of these balloons is purchased, it is possible with
great dexterity to cut from it two spherical segments or saucer-shaped
pieces. These have then to be cemented with _siccotine_ to a wooden
ring having two small pipes opening into it (see Fig. 49). By means
of these pipes we can inflate the lens-shaped bag so formed with
a heavy gas called carbonic acid gas, made by pouring strong acid
upon marble or chalk. The result of these operations, all of which
require considerable skill of hand, is to furnish us with a sound-lens
consisting of a collodion film in the shape of a magnifying-glass, or
double convex lens, filled with carbonic acid gas heavier than the air.
The sound-lens so made is fixed up against a hole in a glass screen of
the same size as the lens, and on one side of the lens is placed the
whistle, and on the other side the sensitive flame. These have to be
adjusted so that the whistle W, the centre of the lens L, and the jet
of the flame F are in one straight horizontal line perpendicular to the
glass plate.
[Illustration: FIG. 49.—A sound-lens focussing a divergent beam of air
waves.]
The distance of the whistle from the lens has then to be adjusted so as
to produce on the other side a nearly parallel beam of sound. In other
words, the whistle must be placed in the focus of the lens. A rule
for doing this is as follows: If the balloon from which the segments
of collodion were cut was nearly spherical, and had a diameter of 8
inches, then the whistle must be placed at slightly less than 8 inches
from the side of the lens next to it.[23] The exact distance, however,
will have to be found by trial, but it is somewhere near the point so
determined. The sensitive flame should be about 4 or 5 feet away from
the lens on the other side of the screen.
These arrangements having been made and the whistle set in action, it
will be found that the flame responds vigorously when it is placed on
the _axis-line_ of the lens, but if moved a few inches to right or
left of this line, it will cease to flare. This shows us that we have
formed a beam of sound, and with some little care it is possible to
make this a nearly parallel beam, so that when plunged in this stream
of air waves the flame dips, but by removing it just outside the stream
of sound it no longer flares. I have found it not difficult, when using
a sound-lens 6 or 7 inches in diameter, to make a beam of sound from a
whistle some 10 inches wide at about 4 feet from the lens.
Supposing the sound-lens and sensitive flame so adjusted, it is
then necessary for our purpose to provide a sound-prism, made in
the following manner: A zinc box is made in wedge form, and the two
inclined sides are cut out, and these windows are covered with thin
collodion film. The box has two pipes connected with it, by means of
which it can be filled with carbonic acid gas.
Provided with this apparatus, it is now possible to show you a
series of experiments which will leave no doubt in your minds that
the external agency which creates in us the sensation of sound is a
wave-motion in the air we breathe. Let me, in the first place, show
you that a sound-beam can be reflected. We adjust our sensitive flame
and set the whistle in action, and create, as described, by the lens,
a beam of sound. At a little distance, say a couple of feet, outside
the parallel beam we place the sensitive flame, and, being sheltered
from the direct action of the whistle, it remains perfectly quiescent.
Taking a sheet of glass in my hand, I hold it at an angle of 45° in
the sound-beam, and you see the flame at once roars. The beam has been
reflected on to the flame, but a very small angular movement of the
glass is sufficient to reflect the sound-ray past the flame without
touching it, and the flame then exhibits no agitation.
A few experiments of this kind with the flame in various positions
are sufficient to show that the sound-beam is reflected by the glass
in accordance with the law of reflection of wave-motion, viz. that
the angle of incidence is equal to the angle of reflection. We can
in the same way reflect the sound-beam by a wooden board, a piece of
cardboard, a looking-glass, or a sheet of metal. We can reflect it
from a wet duster, but not very well from a dry handkerchief. If we
place the flame in the direct beam, it is easy to show that all the
above good reflectors of sound are opaque to a sound-ray, and cast
an acoustic shadow. In fact, I can prevent the flame from roaring by
merely interposing my hand in front of it. A wet duster is found to be
opaque to these sound waves, but a dry linen handkerchief is fairly
transparent.
The collodion film used in making the lens and prism is also
exceedingly transparent to these short air waves. We may then go one
step further, and show that these air waves are capable of refraction.
It will be in your remembrance that, in speaking of water ripples, it
was shown by experiment that, when water ripples passed over a boundary
between two regions, in one of which they travelled more quickly than
in the other, a bending of the direction of ripple-motion took place.
We can show precisely the same thing with these air waves.
The collodion prism has been filled with a heavy gas called carbonic
acid. This gas is about half as heavy again as air, and it is this
heavy and poisonous gas which, by accumulating in old wells or brewers’
vats or in coal-mines after an explosion, causes the death of any man
or living animal immersed in it.
It has already been explained that the velocity of sound waves in
different gases varies inversely as the square root of their density.
Hence the speed of a sound wave in carbonic acid gas will be less than
that in air in the ratio of the square roots of the densities of these
gases. The density of carbonic acid gas is to that of air as 1·552 is
to 1. The square root of 1·552 is 1·246, or nearly 1¹⁄₄. Accordingly,
the speed of a sound wave in carbonic acid gas is to the speed in air
as 4 is to 5. A sound wave in air will therefore travel 5 feet or 5
inches in the same time that it travels 4 feet or 4 inches in carbonic
acid gas.
Let us now consider what must happen if a sound wave falls obliquely
upon the face of our carbonic acid prism.
[Illustration: FIG. 50.—The refraction of a wave by a prism.]
Let ABC be the prism (see Fig. 50) represented in plan, and let _ab_,
_ab_, _ab_, be a train of sound waves advancing against the face AC.
As soon as the left end _b_ of the wave _ab_ touches the face AC, and
enters the carbonic acid gas, its speed will begin to be retarded, and
in the time taken by the right end _a_ to move in air from _a_ to _c_,
the left end will have moved in carbonic acid gas, by a less distance,
_bd_, the distances _ca_ and _db_, being in the ratio of 5 to 4. Hence
it is clear that the wave-front _ab_ will be swung round, and when the
wave has wholly entered the prism, its direction of motion will have
been bent round to the left.
The same thing will happen at emergence. The right end, _e_, of the
wave _ef_ gets out into the air whilst the left end, _f_, is still in
carbonic acid. Accordingly, in the time taken for the end _f_ to move
to _h_, the end _e_ will have moved a greater distance, in the ratio
of 5 to 4, to _g_, and therefore we have again a bending round of the
wave-direction. It is evident, therefore, that this unequal retarding
of the two sides of the wave will result in a _refraction_, or bending,
of the wave-direction, and that whereas the sound-ray was proceeding,
before entering the prism, in the direction of the arrow on the right
hand, it is altered, after passing through the prism, so as to be
travelling in the direction of the arrow on the left-hand side. The
double bending of the sound-ray is therefore caused by, and is evidence
of the fact that, the sound wave travels more slowly in carbonic acid
gas than it does in air.[24]
Let us, then, bring these statements to the test of experiment. We
again start in action the whistle W, and place the sensitive flame in
the line of the lens-axis, and notice how violently the flame flares
(see Fig. 51). The flame is now at a distance of 4 feet from the lens.
I move the flame 1 foot to the left hand, and it is now outside the
beam of sound, and remains quiescent. The prism P, previously filled
with carbonic acid gas, is then inserted between the sound-lens and the
flame, and close to the former. When properly placed, the sensitive
flame F immediately dips and roars. It will be abundantly evident to
you that this can only arise because the prism has bent round the
sound-beam, and deflected it on to the flame. But if the beam is bent
round, then it follows that if the flame is now moved back to the
central position F′, the prism remaining in front of the lens, that the
flame will not now roar, and this we find to be the case. If, however,
the prism is then removed, the flame at once bursts into a roar.
[Illustration: FIG. 51.—The refraction of a sound-ray.]
This experiment proves to demonstration that we can refract waves of
sound just as we can refract ripples on water.
Having regard to what we have now seen, I do not think you will have
any difficulty in seeing how it is that the biconvex sound-lens,
filled with carbonic acid gas, is able to render divergent sound-rays
parallel; in other words, can convert a spherical sound wave into a
plane sound wave.
Consider what the effect really must be. Let the sound-lens be
represented in section by AB (see Fig. 49), and let W be the whistle
sending out spherical sound waves, represented by the dotted lines.
When the spherical wave meets the lens, the central portion of the wave
passes into a retarding medium, whilst the right and left wings of the
wave are still in air. Hence, as before, the wings gain on the centre.
Again, at emergence the wings emerge before the centre of the wave, and
hence again the wings gain on the centre. After complete emergence the
spherical wave-surface has been flattened out and made into a plane
wave. Hence the sound-rays diverging from the whistle are rendered
parallel or even convergent, provided that the whistle is properly
placed with regard to the lens.
You will see, therefore, that we can use a gas denser than the air,
contained in a transparent bag or vessel of collodion, as the means
of changing the form and direction of sound waves. We can make lenses
and prisms of carbonic acid gas which act on rays of sound just as do
lenses and prisms of glass on rays of light. There is, however, one
great difference between the operation of a carbonic acid prism on rays
of sound, and that of a glass or other prism on rays of light. In the
lectures on æther waves it will be made clear to you that what we call
light really consists in waves in a medium known as the æther. But
when such light waves are propagated through a transparent material
like glass, the speed of transmission depends on the wave-length, just
as in the case of water waves. But as regards sound waves there is no
difference between the velocity of propagation or speed with which
waves of different wave-lengths move. Hence a bass note travels just as
fast as a treble note, and the sound waves from a flute have a speed of
the same value as that from a trumpet or bassoon. If it were not so, it
would be impossible for us to hear music or song at a distance, because
the notes would arrive all in the wrong order, and the most familiar
melody would be unrecognizable. It follows from this that air waves, no
matter what their wave-length, are equally refracted on passing from
one medium to another of different density. We shall see later on that
this is not the case with waves of light and æther waves generally.
In the case of most transparent substances the æther waves which
constitute light are transmitted with different velocities, the longer
waves moving faster than the shorter ones. Hence we have the familiar
result of the decomposition of a ray of white light into its different
constituents by a glass prism. We cannot, however, perform a similar
experiment on a complex series of waves of sound by means of a carbonic
acid prism. In other words, a sound-prism refracts, but does not
disperse sound waves of various wave-lengths.
One thing, however, should be pointed out before dismissing this
experiment, and that is that to show successfully the experiment with
the prism, the length of the sound waves used must be small compared
with the dimensions of the prism. The reason for this is that otherwise
there would be too much bending of the waves round the obstacle. When
a train of waves, no matter whether waves in air or waves in water,
meets with an impervious body, there is always a certain bending of the
waves round it, which is technically called _diffraction_. We may see
this effect on a large scale when sea waves, rolling in, pass by some
large rock standing up like an island out of the water. The waves meet
it, pass round it, and, so to speak, embrace it and continue on the
other side. If there is to be any calm water on the leeward side, the
island must be large compared with the length of the waves. The same
thing holds good with regard to air waves.
In order that an object may form an acoustic or sound-shadow, it is
necessary that the construction shall be large compared with the length
of the wave.
Thus the hand held in front of the mouth does not much obstruct the
waves of the speaking voice, because these waves are about 2 to 4 feet
long. But as you have seen when using sound waves only 1 inch long, the
hand will form a very well-marked sound-shadow, as shown by its effect
when held between a whistle and a sensitive flame.
In order to complete our proof that the agency which affects our ears
as sound is really due to air waves, it is necessary to be able to
show that we can produce _interference_ with air waves, as in the case
of waves on water. The nature of the effect called interference by
which one wave is made to annihilate another has been already fully
explained. I will now endeavour to exhibit to you the interference
of two sound-wave trains in an experiment due to Lord Rayleigh, the
apparatus for which he has kindly lent to me.
It consists, as you see, of a stand, to which is fixed a jet, from
which we form a tall sensitive flame. Behind the flame is placed a
sheet of glass, which is held vertically, but can be slid towards or
from the flame. At a little distance we place a _bird-call_, or sort of
whistle, which produces, when blown with air, a note so shrill as to be
inaudible to human ears.
The air-vibrations so generated are at the rate of 33,000 per second,
which is beyond the limit of audition. Hence, even when blown strongly,
you hear no sound from this appliance.
It produces, however, as you can see, a very violent effect upon the
sensitive flame. Hence this flame _hears_ a note which we cannot hear,
and it suggests that perhaps some animals or insects may have a range
of hearing quite beyond the limits fixed for our human ears.
Such being the case, you will see that if the glass plate is placed
behind the flame at a certain distance, the flame at once stops flaring
and becomes quiescent. If, however, the plate is moved to or from the
flame by a very small distance equal to about the one-twelfth part of
an inch, the tall flame at once drops in height and begins to flare. If
we move the plate steadily backwards by equal small distances, we find
the flame alternately quiescent and waving.
The explanation of this effect is that it is due to the interference
between the direct and reflected sound-rays. The waves of air are
turned back when they meet the glass in such a manner that the crests
of the arriving waves are made to coincide with the hollows of the
reflected waves, or, to speak more correctly, the zones of condensation
of one are coincident with the places of rarefaction of the other.
When the glass is adjusted so that this happens, all air-wave motion
just in front of it is destroyed, and hence the sensitive detecting
flame remains quiescent. If, however, the glass is moved nearer to or
further from the flame, then the condensations of the reflected wave
may be made to fall in the same places as the condensations of the
arriving wave, and in that case the disturbance is doubled, and not
destroyed.
[Illustration: FIG. 52.]
A little model may be made which will help the reader to grasp this
point. Cut out a piece of paper in the form shown in Fig. 52 to
represent a wave. Bend back the paper on itself at the dotted line
_ab_, and let one half represent the arriving wave, and the other the
reflecting wave. It will be seen that in this case the crests of the
incoming wave are obliterated by the hollows of the returning wave.
If, however, the paper is bent back at _cd_, then the crests of the
reflected and incident waves conspire, and there is no interference.
Whenever we can produce _interference_ in this manner between two sets
of sound-rays, or light-rays, or rays of any other kind, we have the
strongest possible proof that we are concerned with a _wave-motion_;
because in no other way that we can understand is it possible that
a destruction of sound by sound can take place by, so to speak,
superimposing two sound-rays, or a destruction of light by bringing
together two rays of light.
We may, then, conclude our discussion of this part of our subject
by examining the manner in which vibrating bodies communicate a
different form of wave to the air. As already explained, we are by
our ears enabled to appreciate the fact that the air is thrown into a
wave-motion, and that this wave-motion may consist of waves of great
or small wave-length, and great or small amplitude. But we are able to
do something more—we are able to detect a difference between the form
of two waves, so that if represented by a wavy line of light, as you
have seen, the nature of the outline of that line impresses itself upon
our consciousness. Nothing is more remarkable than the extraordinary
delicacy of the ear in this respect. Amongst all our scores of friends
and acquaintances we recognize each by a _quality_ of voice which we
speak of as harsh, melodious, sympathetic, rasping, penetrating, or
clear. This is not altogether a matter of enunciation or vocalization,
for if different persons pronounce correctly the same vowel-sound, we
can detect a great difference between their voices. We have, then,
to ask wherein this difference consists when considered with respect
simply to what goes on outside of us in the air.
Great light was thrown on this by the invention and perfection of
the phonograph and telephone, and also a more recent and wonderful
invention, variously called the micro-phonograph or telegraphone. You
have all heard a phonograph speak, or sing, or reproduce music. In its
original form the Edison phonograph consisted of a cylinder covered
with tinfoil, against which pressed lightly a steel point attached to
the centre of a metal disc. In its modern form, as improved by Edison,
Bell, Tainter, and others, it is a far more perfect instrument for
recording and reproducing sound. It now consists of a cylinder covered
with a composition similar to very hard soap. This cylinder is carried
on a metal drum, and caused to revolve by clockwork slowly and very
uniformly. A metal arm carries an elastic metal disc called a receiving
diaphragm, and to the back of this is attached a very delicate
cutting-tool like a small chisel. By means of a screw the chisel and
diaphragm are made to travel along the cylinder, and if no vibration
is given to the disc the tool cuts a spiral on the recording cylinder,
which is a clean groove with smooth bottom ploughed out of the soft
composition. If, however, we speak or sing to the diaphragm, the air
waves cause it to vibrate, and this makes the tool cut a furrow, the
bottom of which is irregular, the undulations corresponding exactly to
the movements of the diaphragm. Thus, if we could look at the section
of the furrow, we should see it undulating like a miniature switchback
railway, each up-and-down corresponding with one vibration of the
diaphragm. In this manner we store up a record of air waves on the
hard-soap cylinder. In the next place, to reproduce the sound, another
diaphragm with a trumpet mouthpiece has at its back a little pointed
lever or set of levers, one extremity resting upon the bottom of the
irregular furrow.
Then, if the cylinder is so set that this reproducing diaphragm travels
over the record cut by the receiving diaphragm, we have a motion
communicated to it which is the exact facsimile of that which produced
the furrow. Accordingly, the reproducing diaphragm gives back to the
air impulses which reproduce the same wave-trains, and therefore the
same speech or song, as that which created the record.
We may in this manner record any human utterance and receive it again,
word-perfect, months or years after it was made.[25]
The action of the phonograph leads us to inquire how a disc of metal or
other elastic material responds to aerial vibrations which fall upon
it, and I shall conclude this lecture by showing you one experiment
of a kind to illustrate this point, which, though not very easy to
perform, is certainly one of the most attractive that can be shown.
There is on the table a brass tube, of a shape somewhat like a
square-shouldered funnel, and over the smaller end is loosely slipped
a wide indiarubber tube with a mouthpiece. It is essential that the
indiarubber tube shall not fit tightly, but shall be supported so that
an air space exists all round between it and the brass funnel tube. The
latter may be carried on a wooden stand. The wider end of the funnel
must have a diameter of about 2¹⁄₂ inches, and the lip must be quite
smooth. The interior of the funnel should be blackened. A soap solution
has then to be prepared as for blowing soap-bubbles. A good formula for
making this solution is given by Professor Vernon Boys, in his book,
“Soap Bubbles and the Forces which mould them,” and is as follows:
Fill a clean stoppered bottle three-quarters full of soft water. Add
one-fortieth part of its weight of oleate of soda, which will probably
float on the water. Leave it until it is dissolved. Then nearly fill
up the bottle with Price’s glycerine, and shake well. Leave the bottle
stoppered for a week in a dark place. Then syphon off the clear liquid
from the scum at the top. Add one or two drops of strong ammonia to
every pint of the liquid. Do not warm or filter the liquid, and keep it
carefully from exposure to the air. Do not expose the liquid to the air
more than necessary; but in blowing a bubble pour out a little of the
liquid into a saucer.
In default of this good solution a substitute may be found by
dissolving bits of clear yellow soap in soft water; but this soapy
water does not yield films which last so long as those made with the
Plateau solution above described.
By dipping the wide end of the funnel tube into some of the soap
solution placed in a saucer, it is easy to cover the end with a flat
soap film which will last a considerable time. This tube has then to
be fixed in front of an electric arc or lime-light lantern, so that
a powerful parallel beam of light can be directed on to the film by
a small flat mirror or looking-glass. A lens is also placed so as
to focus an image of the film on to a screen. In finding the right
position for the lens, it is a great help to place a piece of white
card with some bold black letters upon it over the brass funnel in the
place which will be occupied with the soapy film, and to focus this so
as to obtain a sharp image of the letters on the screen. When the soap
film is then substituted for the card, we should have on the screen a
reflection of the film surface, which at first will appear as a patch
of white light upon the screen. If we allow the film to stand for a
few seconds, it begins to get thinner at the upper part than at the
bottom, and the image on the screen will exhibit gorgeous bands of red
and green, called interference colours, which are due, like the colours
on a soap-bubble, to the interference of the rays of light reflected
from the inner and outer surfaces of the film. If the experiment is
skilfully performed, the appearance on the screen will then be very
beautiful. We shall have a patch of light which exhibits bands of
colours, becoming more intense the longer the film stands, and towards
the end having somewhat the appearance of an unusually lovely sunset.
Just before this condition of the film is reached, if we sing gently
into the mouthpiece of the indiarubber tube, the soap film will be
thrown into vibration. The image on the screen will exhibit a set of
regularly arranged concentric stationary ripples, which will alter in
appearance with every change in the note sung. The experiment requires
some care and practice to perform it properly, and should not be
attempted in public without many rehearsals; but when well shown it
is a most effective and interesting experiment. We see, therefore,
that so delicate an object as a stretched soap-film can take up the
vibrations of the air and be itself thrown into vibration. The reason
is that the soap-film, as already explained in the first lecture,
resists stretching, and behaves like a sheet of elastic indiarubber.
Hence, as each air wave falls upon it, the film is alternately pushed
out and pulled in, but being held at the edges, it can only accommodate
itself by stretching. We have, therefore, set up in the film a set of
stationary waves similar to those set up on a rope fixed at one end
when the loose end is regularly jerked up and down by the hand. The
experiment shows us clearly the way in which an elastic disc is set
in vibration when compressional waves fall upon it, and in the next
lecture we shall proceed to discuss the vibrations of this kind which
give rise to musical effects.