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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.

Sound is propagated in all elastic bodies.-If in the two experiments just mentioned, after having made the vacuum, we introduce into the receiver or into the globe any gas or vapour, the sound of the bell is again heard, which proves that sound is propagated in gases and vapours, as in common air. Sound is also propagated in liquids. When two bodies strike against each other under water, the sound of the shock is distinctly Fig. 124.

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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 conductthen to resume their original position; but they cannot returning power is so great that a very slight noise, as the scratch of 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.

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 body, and which consists of a go or a come of these particles, is called a single oscillation or vibration; a double or complete vibration 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-tube; but by reason of the great compressibility of this fluid. rent to the eye.

Mode of the propagation of sound in air.-In order to simplify the theory of the propagation of sound, let us first consider the case where it is propagated in an indefinite cylindrical tube. Let м N, 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 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 velocommonly the air; but gases, vapours, liquids, and solids also cities. The velocity at first is nothing at a, it increases protransmit 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 of an air-pump, a bell which a small hammer strikes in a continuous manner, being put in motion by clock-work, fig. 124. While the receiver is full of air at the ordinary atmospheric pressure, the sound of the bell under the strokes of the hammer is distinctly heard; but in proportion as the air is rarefied, the sound loses its intensity, and it ceases to be perceptible when the receiver is exhausted. Whence, we conclude that sound is not propagated in a vacuum. In order that the experiment may succeed well, the sonorous body should be placed on a cushion; for the pieces of metal of which the apparatus is made would otherwise transmit the sound to the platen of the air-A H is at rest, the first section of the part н H' begins to partipump, and the platen to the exterior air. The same experiment can be made in a simpler manner by means of a glass globe, with a stop-cock, in which is suspended a little bell. If we shake the globe when it is full of air, we distinctly hear the sound of the bell; but after the air within the globe has been exhausted, by means of the exhausting syringe, the bell is no longer heard.

VOL. IV.

Whence arise in the wave A н, variable densities of air and velocities, varying with the velocity of the piston. At A, where the piston is at rest, the velocity of the air is nothing, and this fluid has resumed its primitive density. At H, where the wave terminates, the velocity and density are the same as at A; but in the intervening points, these quantities increase from the point A to the middle section of the wave, and then decrease towards H. By conceiving the tube M N to be divided into equal lengths such as AH, and each of these lengths divided into sections parallel to the piston, it can be demonstrated that at the moment when the first section of the wave cipate in the motion; then, when the second section of the wave A H is at rest, the motion is communicated to the second section of H H'; and so on, section by section, in the parts I'н", н"H", etc. The condensed wave proceeds therefore through the tube, each of its parts passing successively through the same degrees of velocity and condensation.

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

in motion by clock-work under the receiver of an air-pump, we hear the intensity of the sound diminishing as the air becomes rarefied. In hydrogen, which is about fourteen times rarer than air, the sound has much less intensity, although the pres sure be the same. In carbonic acid, on the contrary, of which the density is about one and a half times that of air, the sound is more intense. On high mountains, where the air is much rarefied, we must speak with considerable effort in order to be heard, and the explosion of a gun produces but a weak sound.

, it produces behind it a vacuum in which the section or | air in the place where it is produced. If we place a bell put stratum of air in contact with the posterior face of the piston is expanded. Then the following section or stratum expanding in its turn, the first returns to its primitive state of condensation, and so on from section to section, or from stratum to stratum; so that when the piston has reached the point a, there is produced an expanded or dilated wave of the same length as the condensed wave, and immediately following it in the cylindric tube, where they are propagated in succession, the corresponding sections of the two waves having equal and contrary velocities. These two waves taken together constitute one undulation; that is, that an undulation comprises the part of the column of air which is modified during a go and come of the piston; the length of the undulation is the space which the sound describes during the time of a complete vibration of the body which produces it. This length diminishes with the rapidity of the vibrations.

4th. The intensity of sound is modified by the agitation of the air and the direction of the winds. It is found that in calm weather sound is always more easily propagated than in windy weather; and that, in the latter case, the sound is more intense, at the same distance, when heard in the direction of the wind than when heard in the opposite direction.

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From the consideration of the motion of sonorous waves in a cylinder, we may now pass to that of their motion in a medium indefinite in extent in all directions. By supposing what has been said regarding a moveable piston in a tube to be applied in every direction to the particles of vibratory bodies, we shall be enabled to arrive at the explanation of this case also. On this supposition, there will be produced around every centre of disturbance a series of spherical waves alternately condensed and rarefied. These waves being contained between two spherical concentric surfaces whose radii are gradually increasing, whilst the breadth of the waves remains the same, their mass will increase in proportion as they recede from the centre of disturbance; whence the velocity of vibration imparted to the particles will be gradually diminished, and the intensity of the sound lessened in the same proportion. It is the spherical waves thus alternately condensed and rarefied, which, in spreading themselves through space, become the medium for the propagation of sound. If, at several points of space, disturbances take place at the same time, there will be produced around each, a system of waves similar to the preceding. Now all these waves spread themselves across each other, without having either their length or their velocity modified. Sometimes the condensed or rarefied waves are placed upon others of the same kind in such a manner as to produce an effect equal to their sum; sometimes they meet and produce an effect equal to their difference. The coexistence of waves is rendered visible to the eye, by disturbing smooth water at several points of its surface.

Causes of variation in the intensity of sound.-Several causes modify the force or intensity of sound, such as the distance of the sonorous body, the amplitude of the vibrations, the density of the air in the place where the sound is produced, the direction of the currents of the air, and the vicinity of other sonorous bodies. 1st, The intensity of sound is in the inverse ratio of the square of the distance of the sonorous body from the ear. This law, demonstrable by analysis, is the consequence of the mode of the propagation of sonorous waves. Indeed, the intensity of the vibrations of the air being, in every spherical wave, in the inverse ratio of the square of the radius of the sphere, that is, of the square of the distance from the point of disturbance, this is necessarily the case also with the intensity of the sound.

2nd. The intensity of sound increases with the amplitude of the vibrations of the sonorous body; and consequently, with the velocity of the oscillation of the waves. The connection which exists between the intensity of sound and the amplitude of the vibrations is easily proved by means of vibrating cords; they show that when the amplitude of the oscillations diminishes, the intensity of the sound is diminished also.

3rd. The intensity of sound depends on the density of the

5th. Sound is increased in the vicinity of a sonorous body. The string of an instrument stretched in free air, yields but a feeble sound when it is made to vibrate at a distance from every sonorous body; but if it be stretched above a sonorous case, as in the guitar, the violin, or the violoncello, it emits a full and strong sound, because that the case and the air vibrate in unison with the string. Hence arises the use of sonorous cases in stringed instruments.

Apparatus for increasing sound.-To demonstrate the power of cases or vessels full of air to increase the intensity of sound, M. Savart constructed the apparatus shown in fig. 126. It Fig. 126.

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consists of a hemispherical vessel A, made of bell-metal, which
is made to vibrate by means of a strong bow; near it is placed
a hollow cylinder в made of paste-board, open at the anterior
extremity and closed at the other. By means of a handle, this
cylinder is turned at pleasure on a support fixed in an arm c
which slides freely in the stand of the apparatus; thus the
cylinder B can be easily turned aside from the vessel A. The
apparatus being arranged as shown in the figure, when it is
made to vibrate, the sounds emitted take a force and a fulness
of which no idea can be formed without hearing them; but
the sound loses almost all its intensity if the cylinder be
be turned
aside, and it is gradually diminished as the cylinder is drawn
back; an experiment which proves that the increase in the
intensity of the sound arises from the vibrations of the air con-

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.

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Velocity of sound in liquids and solids.-The velocity of sound in liquids is greater than in air. 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 is more than four times its velocity in air. În 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 means of the longitudinal vibrations that in wood the velocity of sound is from ten to sixteen times greater than it is in air. In metals, this velocity is more variable; the velocities varying from four to sixteen times greater than its velocity in

air.

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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 on and then reflected from an obstacle PQ. If we consider, stations was only 61066 127 feet, and we shall see, when we for instance, the incident wave M CD N, emitted from the centre treat of Optics, that light takes an inappreciable time to des-A, the sorresponding reflected wave is represented by the arc cribe 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. At the same temperature the velocity is the same for all sounds, weak or strong, sharp or flat. M. Biot found in his experiments above-mentioned on the conductibility of tubes, that when a flute was played at the extremity of the tube 3,120 feet long, the sounds preserved their harmony at the other extre

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 reflecting surface.

According to these laws, the sound which in fig. 127 is propagated along the straight line A c, takes after reflection the direction of the straight line CB; so that an observer placed at B, will hear, besides the sound proceeding from A, a second sound, which will seem to him to be emitted from the point a.

Imperfect; Stem ε-λυ

Future; Stem λυ-σ

Present; Stem λυ

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

Verbs in w. The pure verb Xvw, I loose,-Active Voice. THE Greek Avw and the English loose are obviously connected in form as well as meaning. From the same root is our to lose, which is the same word as loose, differently spelt and pronounced; to lose is the result of loosing.

I proceed to exhibit in full an example of a verb pure, and take as my instance this verb Xvw, I loose, or unbind. But as the pure verbs do not possess the second tenses, that is, the second perfect active, the second pluperfect active, the second future passive, and the second aorist active, middle, and passive; these second forms are taken from two mute verbs, namely, τριβω, I rub, and λειπ-ω (root λιπ), I leave; and from one liquid verb, namely, φαιν.ω (root φαν), I show. By this means a complete example is presented.

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Loose thou, &c.

To loose.

Loosing.

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λυπτεν

I would loose.

λυ-σ-οιμι
λυ-σ, &c. like the
Imperfect

To be about to loose. λυ-σ-ειν

λυσ

λυσ

λυσ

λυσ

λυσ

λυσ

I loosed.

I may have loosed. I might have loosed.

Loose thou.

δ. 1 ε-λυσα

Av-o-w**

2 ε-λυ-σας

λυ-στης like the

3 ε-λυ-σ-ε

λυ-σ

Pres. Subj.

|λυ-σ-αιμι λυσ-αις οι ειας λυ-σ-αι* οι ειε

To have loosed. λυσαι

λυ-στον

λυ-σ-ατω

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λυ-σ-αιτον

λυ-σ-ατον

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First Aorist; Stem ε-λυ-σ

δ. 1 λε-λυ-κα

2 λε-λυ-κ-ας
3 λελυκε

Δ. 2 λε-λυ-κ-ατον

3 λελυ-κ-ατον Ρ. 1 λελυ-κ αμεν

2 λελυ-κ-ατε

3 λελυκᾶσι

I may have loosed.

λε-λυ-κ-ω λεολυ-κ-ης,&c. like the Pres. Subj

λε-λυ-κ

λελυ-κα

λε-λυ-κ

λε-λυκ

λε-λυκο

λελυκ

λυ-σ-αιεν οι ειαν

λε-λυκε λε-λυ-κ-ετω λελυ κ ετον λελυ-κ-ετων

λελυ-κ-ετε

λελυ κ ετωσαν

or οντών

About loosing. λυστων

Having loosed. λυ-σας

Το have loosed,

Haring loosed.

λελυ-κ εναι

λε-λυ-κ ως

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Present. Imperfect. Future. First Aorist. First Perfect. First Plur. Second Perfect, Second Plup, Second Aorist.

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The first thing which I advise the make himself familiar with the stems. he will easily acquire the rest.

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Student to do, is to an example or two, as in τιω, I honour ; βουλεύω, I advise ; and
Having got the stems | λούω, I wash:

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

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