ON PHYSICS, OR NATURAL PHILOSOPHY.

No. XXIV.

(Continued from page 336.)

ACOUSTICS.

PRODUCTION, PROPAGATION, AND REFLECTION OF

SOUND.

Object of Acoustics.-The science of Acoustics has for its object the study of the laws of sound, and of the vibrations of elastic bodies. Music treats of sounds, with regard to the feelings and passions which they excite in us; acoustics only treats of the properties of sounds, the sensations which they produce not being taken into consideration.

Sound is a particular sensation excited in the organ of hearing by the vibratory motion of bodies, when this motion can be conveyed to the ear by an intervening medium. All sounds are not alike; they are distinguished by differences so sensible that we can compare them with each other and determine their ratios of intensity.

Noise, in general, is distinguished from sound. Sound, properly so called, is that which produces a continuous sensation, and of which we can appreciate the musical value; but noise is a sound too short in its duration to permit of its being appreciated, as the roar of a cannon; or rather it is a confused mixture of several discordant sounds, as the rolling of thunder or the dashing of the waves of the sea. Yet the difference between sound and noise is not always distinctly marked; there are some ears so finely organised that they can determine the musical value of the noise produced by the rolling of a carriage on the street.

Cause of Sound.-Sound is always the result of the rapid oscillations impressed on the particles of elastic bodies, when,

under the influence of a blow or of friction, the state of equi-heard. A diver who is at the bottom of the water of a river
librium among these particles has been disturbed. They tend can hear what is said on the bank. As to solids, their conduct-
then to resume their original position; but they cannot return
to this position at once, for they oscillate on each side of it by
vibratory or going and coming motions, which are extremely
rapid, and whose amplitude very quickly decreases.

ing power is so great that a very slight noise, as the scratch of
a pin, at the one extremity of a piece of wood is easily heard at
the other extremity. The ground conducts sound so well, that
at night, by applying the ear to it, the footsteps of horses and
other noises at a great distance can be distinctly heard.

A body which emits a sound is called sonorous; and the
motion which takes place among the particles of the sonorous Mode of the propagation of sound in air.-In order to simplify
body, and which consists of a go or a come of these particles, is the theory of the propagation of sound, let us first consider the
called a single oscillation or vibration; a double or complete vibra-case where it is propagated in an indefinite cylindrical tube.
tion consists both of a go and a come. The vibrations are easily
put to the test of experiment; if we throw a light powder on
a body emitting a sound, this powder will take a rapid motion,
and thus render the vibrations of the body visible; and if we
strike a long tense (stretched) cord, its vibrations will be appa-
rent to the eye.

Let MN, fig. 125, be such a tube filled with air at a constant
temperature and pressure; and in this tube let there be a
piston P oscillating with great velocity between a and A. This
piston when it passes from a to a compresses the air in the
tube; but by reason of the great compressibility of this fluid,
the condensation does not act throughout the whole length of
Sound not propagated in a vacuum.-The vibrations of elastic the tube, but only on a certain length A H, which is called the
bodies can only produce in us the sensation of sound by the condensed wave. All the parts of the condensed wave are not
intervention of a material medium placed between the ear equally condensed and their velocity is not the same; for the
and the sonorous body, and vibrating with it. This medium is piston in its oscillatory motion is animated with variable velo-
commonly the air; but gases, vapours, liquids, and solids also cities. The velocity at first is nothing at a, it increases pro-
transmit sound. In order to show that the presence of agressively to the middle of its course, then decreases to a, where
material medium is necessary to the propagation of sound, the it becomes nothing again.
following experiment is resorted to; place under the receiver Whence arise in the wave A н, variable densities of air and
of an air-pump, a bell which a small hammer strikes in a con- velocities, varying with the velocity of the piston. At A, where
tinuous manner, being put in motion by clock-work, fig. 124. the piston is at rest, the velocity of the air is nothing, and
While the receiver is full of air at the ordinary atmospheric this fluid has resumed its primitive density. At H, where
pressure, the sound of the bell under the strokes of the hammer the wave terminates, the velocity and density are the same as
is distinctly heard; but in proportion as the air is rarefied, the at A; but in the intervening points, these quantities increase
sound loses its intensity, and it ceases to be perceptible when from the point A to the middle section of the wave, and then
the receiver is exhausted. Whence, we conclude that sound decrease towards H. By conceiving the tube M N to be divided
is not propagated in a vacuum. In order that the experiment into equal lengths such as A H, and each of these lengths
may succeed well, the sonorous body should be placed on a divided into sections parallel to the piston, it can be demon-
cushion; for the pieces of metal of which the apparatus is made strated that at the moment when the first section of the wave
would otherwise transmit the sound to the platen of the air-A H is at rest, the first section of the part Hн' begins to parti-
pump, and the platen to the exterior air. The same experi- cipate in the motion; then, when the second section of the
ment can be made in a simpler manner by means of a glass wave A н is at rest, the motion is communicated to the second
globe, with a stop-cock, in which is suspended a little bell. If section of H '; and so on, section by section, in the parts н'н”,
we shake the globe when it is full of air, we distinctly hear the "H"", etc. The condensed wave proceeds therefore through
sound of the bell; but after the air within the globe has been the tube, each of its parts passing successively through the
exhausted, by means of the exhausting syringe, the bell is no same degrees of velocity and condensation.
longer heard.

VOL. IV.

When the piston moves in the contrary direction from a to
102

tained in the cylinder. In this apparatus, the cylinder must have a determinate depth, in order that the air which it contains may be in unison with the vessel A, otherwise the latter would vibrate alone. Vitruvius relates that the ancients placed sounding vessels in their theatres, in order to strengthen the sounds of the actors' voices.

Effect of tubes on the intensity of sound. The law above stated, that the intensity of sound is in the inverse ratio of the square of the distance, is not applicable to sounds transmitted through tubes, especially if they be cylindrical and straight. The sonorous waves are not then propagated under the form of increasing concentric spheres, and consequently the sound may be carried to a considerable distance without any very sensible alteration in its intensity. M. Biot has proved by experiment, that in one of the pipes employed for conducting the water in Paris, about 3,120 feet long, the voice lost so little of its intensity, that from one extremity of this tube to the other a conversation could be carried on in a low voice. Yet the diminution of the sound becomes sensible in tubes of great diameter, or in those in which the sides present many turnings and windings. Such effects are observed in vaults and long galleries. The property which tubes possess of conveying sounds to a distance first received its most useful application among our selves. The speaking-tubes used in our hotels and large establishments are well known. These tubes are made of caoutchouc, and of small diameter; they pass from one place to another through the walls of the house. If one speaks with a voice a little raised above the ordinary tone at one of the extremities of such a tube, it is very distinctly heard at the other extremity. According to the experiments of M. Biot already mentioned, it is evident that by means of acoustic tubes a correspondence with the living voice could be maintained between two towns at a given distance from each other. As sound passes over about 1,100 feet in a second, a distance of about 50 miles would be passed over in four minutes.

Velocity of sound in gases.-The propagation of sonorous waves being successive, sound is transmitted from place to place in an interval varying with their distance. On this principle, a great number of phenomena are explained. For example, the noise of thunder is heard a certain time after we have seen the flash of lightning, although the noise and the flash are produced simultaneously in the cloud.

sound in liquids is greater than in air.
Velocity of sound in liquids and solids.-The velocity of
MM. Colladon and
Sturm found, by experiments made in 1827, on the Lake of
Geneva, that the velocity of sound in water is about 4,708 feet
per second. This
This is more than four times its velocity in air.
In solids, the velocity is still greater. In experimenting on
the cast-iron pipes used in conducting water, M. Biot found
that sound is propagated in cast iron with a velocity ten and a
half times that of its velocity in air. The velocity of sound in
other solids has been determined theoretically by Chladni,
Savart, M. Masson and M. Wertheim, by means of the number
of longitudinal or transversal vibrations of the bodies, or by
means of their coefficient of elasticity. Chladni has found by
of sound is from ten to sixteen times greater than it is in air.
means of the longitudinal vibrations that in wood the velocity
In metals, this velocity is more variable; the velocities
varying from four to sixteen times greater than its velocity in

air.

retarded in their development, they are propagated under the Reflection of sound. So long as the sonorous waves are not form of concentric spheres; but when they meet an obstacle, they follow the general law of elastic bodies, they are thrown back upon themselves, and form new concentric waves, which seem to emanate from a second centre on the other side of the obstacle: this is expressed by saying that the waves are reflected. Fig. 127 represents a series of waves first incident Fig. 127.

Numerous experiments have been made in order to determine the velocity of sound in the air, that is, the space which it describes in a second. The latest appears to have been made in the summer of 1822, during the night, by the members of the French Board of Longitude. Two eminences were chosen as stations for this purpose, the one at Villejuif and the other at Montlhéry, near Paris. At each station, every ten minutes a cannon was fired. The observers at Villejuif heard very distinctly the twelve shots fired at Montlhéry; but those at the latter station heard only seven shots out of the twelve fired at Villejuif, the direction of the wind being contrary. At each station, the observers marked, by means of chronometers, the time which elapsed between the sight of the flash at the moment of explosion, and the hearing of the sound. This time was taken for that which the sound required in order to travel from the one station to the other; for the distance between the two stations was only 61066 127 feet, and we shall see, when we treat of Optics, that light takes an inappreciable time to describe a short distance like this. They found also that the mean duration of the propagation of sound from the one station to the other was 54.6 seconds. Now dividing the distance between the two stations by this number of seconds, we find that the velocity of the sound per second was about 1118 4 feet, at the temperature of 60°-8 Fahrenheit, which was that of the atmosphere at the time of the experiments. The velocity of sound in the air decreases with the temperature: at 50° Fahrenheit it is only about 1105-7 feet per second; and at 32° Fahrenheit it is about 1092.5 feet per second. But at the same temperature, this velocity is independent of the density of the air, and consequently of the pressure. Ating surface. the same temperature the velocity is the same for all sounds, According to these laws, the sound which in fig. 127 is proweak or strong, sharp or flat. M. Biot found in his experi- pagated along the straight line A c, takes after reflection the ments above-mentioned on the conductibility of tubes, that direction of the straight line CB; so that an observer placed at when a flute was played at the extremity of the tube 3,120 feet B, will hear, besides the sound proceeding from A, a second long, the sounds preserved their harmony at the other extre-sound, which will seem to him to be emitted from the point a.

on and then reflected from an obstacle PQ. If we consider, for instance, the incident wave M CD N, emitted from the centre A, the corresponding reflected wave is represented by the arc CKD, of which the point a is the virtual centre. If we join any point c of the reflecting body to the sonorous centre A, and draw cH perpendicular to the surface of this body, the angle ACH is called the angle of incidence, and the angle BCH formed by the production of a c, the angle of reflection. Whence the reflection of sound is regulated by the two following laws, which are also the same for light and for heat:

1st. The angle of reflection is equal to the angle of incidence.

2nd. The angle of reflection and the angle of incidence are situated in the same plane, which is perpendicular to the reflect

Future ;
Stim λυσ

First Aorist;
Stem ε-λυ-σο

LESSONS IN GREEK.-No. XXIV.
By JOHN R. BEARD, D.D.

But as

I proceed to exhibit in full an example of a verb pure, and take as my instance this verb Xvw, I loose, or unbind. the pure verbs do not possess the second tenses, that is, the second perfect active, the second pluperfect active, the second Verbs in w. The pure verb Xvw, I loose,—Active Voice. future passive, and the second aorist active, middle, and THE Greek Avw and the English loose are obviously connected passive; these second forms are taken from two mute verbs, in form as well as meaning. From the same root is our to | namely, τριβω, I ruo, and λειπω (root λιπ), I leave ; and from lose, which is the same word as loose, differently spelt and f one liquid verb, namely, φαιν-ω (root φαν), I show. By this pronounced; to lose is the result of loosing. means a complete example is presented.

I might loose.

λυ-ετε*
λυ-ετωσαν ο

όντων

λυ-οιμι

λυ-οις

λυ-οι

λυ-οιτον

λυ-οιτην

λυ-οιμεν

λυ-οιτε

λυ-οιεν

I would loose.

To be about to loose.
λυ-σ-ειν

About loosing. λυσεων

λυσ

λυ-σ

λυσ

λυ-σ

2 λυ-σ

λυσ

Loosing.

Present. Imperfect. Future. First Aorist. First Perfet. First Plug. Second Perfect. Second Plup. Second Aorist.

The Student should carefully copy out the whole several times. After he has learnt to recognise the connexion and derivation of the several parts, and so formed some idea of the beautiful harmony of the whole, let him commit the entire paradigm to memory; and let him not pass on until he has accomplished the task. The effort will save a world of trouble.

It is customary in Greek Grammar to give three parts of the verb, as the principal parts, or those parts from which the others may be formed, namely, the present, the future, the perfect. The connexion of the other parts with these hree is shown in the Table of Stems given above. I present

an example or two, as in τιω, I honour ; βουλευω, I advise; and λovw, I wash:--