« ΠροηγούμενηΣυνέχεια »
ON PHYSICS, OR NATURAL PHILOSOPHY.
Sound is propagated in all elastic bodies.--If in the two experie ments 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
(Continued from page 336.)
Fig. 124. 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. Musio 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 conductthen to resume their original position; but they cannot return ing 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 a piñ, at the one extremity of a piece of wood is easily heard at vibratory or going and coming motions, which are extremely the other extrenaity. The ground conducts sound so well, that rapid, and whose amplitude very quickly decreases.
at night, by applying the ear to it, the footsteps of horses and A body which emits a sound is called sonorouw; and the other noises at a great distance can be distinctly heard. 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 Let M N, fig. 125, be such a tube filled with air at a constant pụt to the test of experiment; if we throw a light powder on temperature and pressure; and in this tube let there be a a body emitting a sound, this powder will take a rapid motion, piston P oscillating with great
velocity between a and A. This and thus render the vibrations of the body visible; and if we piston when it passes from a to a compresses the air in the 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.
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 a gressively to the middle of its course, then decreases to 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 H, 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 , 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 demoncushion; 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 ! a' begins to partipump, 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 H 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 n'; and so on, section by section, in the parts H' H", we shake the globe when it is full of air, we distinctly hear the 1" !", 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.
When the piston moves in the contrary direction from A to
a, 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 in motion by clock-work under the receiver of an air-pump, we is expanded. Then the following section or stratum expand hear the intensity of the sound diminishing as the air becomes ing in its turn, the first returns to its primitive state of conden- rarefied. In hydrogen, which is about fourteen times rarer sation, and so on from section to section, or from stratum to than air, the sound has much less intensity, although the presstratum; so that when the piston has reached the point a, sure be the same. In carbonic acid, on the contrary, of which there is produced an expanded or dilated wave of the same length the density is about one and a half times that of air, the sound as the condensed wave, and immediately following it in the is more intense. On high mountains, where the air is much cylindric tube, where they are propagated in succession, the rarefied, we must speak with considerable effort in order to corresponding sections of the two waves having equal and be heard, and the explosion of a gun produces but a weak contrary velocities. These two waves taken together constitute sound. one undulation ; that is, that an undulation comprises the part 4th. The intensity of sound is modified by the agitation of of the column of air which is modified during a go and come of the air and the direction of the winds. It is found that in the piston; the length of the undulation is the space which the calme weather sound is always more easily propagated than in sound describes during the time of a complete vibration of the windy weather; and that, in the latter case, the sound is more body which produces it. This length diminishes with the intense, at the same distance, when heard in the direction of rapidity of the vibrations,
the wind than when heard in the opposite direction.
From the consideration of the motion of sonorous waves in 5th. Sound is increased in the vicinity of a sonorous body. a cylinder, we may now pass to that of their motion in a The string of an instrument stretched in free air, yields but a medium indefinite in extent in all directions. By supposing feeble sound when it is made to vibrate at a distance from what has been said regarding a moveable piston in a tube to every sonorous body; but if it be stretched above a sonorous be applied in every direction to the particles of vibratory case, as in the guitar, the violin, or the violoncello, it emits a bodies, we shall be enabled to arrive at the explanation of full and strong sound, because that the case and the air vibrate this case also. On this supposition, there will be produced in unison with the string. Hence arises the use of sonorous around every centre of disturbance a series of spherical waves cases in stringed instruments. alternately condensed and rarefied. These waves being .con- Apparatus for increasing sound.–To demonstrate the power of tained between two spherical concentric surfaces whose radii cases or vessels full of air to increase the intensity of sound, are gradually increasing, whilst the breadth of the waves M. Savart constructed the apparatus shown in fig. 126. It remains the same, their mass will increase in proportion as they recede from the centre of disturbance; whence the velo
Fig. 126. city 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 them
А selves across each other, without having either their length or their velocity inodified. 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 consists of a hemispherical vessel A, made of bell-metal, which intensity of the vibrations of the air being, in every spherical is made to vibrate by means of a strong bow; near it is placed wave, in the inverse ratio of the square of the radius of the a hollow cylinder B made of paste-board, open at the anterior sphere, that is, of the square of the distance from the point of extremity and closed at the other. By means of a handle, this disturbance, this is necessarily the case also with the intensity cylinder is turned at pleasure on a support fixed in an arm C, of the sound.
which slides freely in the stand of the apparatus; thus the 2nd. The intensity of sound increases with the amplitude of cylinder B can be easily turned aside from the vessel A. The the vibrations of the sonorous body; and consequently, with apparatus being arranged as shown in the figure, when it is the velocity of the oscillation of the waves. The connection made to vibrate, the sounds emitted take a force and a fulness which exists between the intensity of sound and the ampli- of which no idea can be formed without hearing them; but tude of the vibrations is easily proved by means of vibrating the sound loses almost all its intensity if the cylinder be turned cords; they show that when the amplitude of the oscillations aside, and it is gradually diminished as the cylinder is drawn diminishes, the intensity of the sound is diminished also. back; an experiment which proves that the increase in the
3rd. The intensity of sound depends on the density of the intensity of the sound arises from the vibrations of the air con.
tained in the cylinder. In this apparatus, the cylinder must | mity, which indicates that the different sounds were propagated have a determinate depth, in order that the air which it con- with equal velocity. tains may be in unison with the vessel A, otherwise the latter The velocity of sound varies in different gases, although would vibrate alone. Vitruvius relates that the ancients the temperature be the same in all. By making the same pipe placed sounding vessels in their theatres, in order to strengthen of an organ sound with different gases, Dulong found that at the sounds of the actors' voices,
32° Fahrenheit the velocities in these gases were as follows: Effect of tubes on the intensity of sound. The law above stated,
second that the intensity of sound is in the inverse ratio of the square
1040:1 of the distance, is not applicable to sounds transmitted through
1092.5 tubes, especially if they be cylindrical and straight. The
1105.7 sonorous waves are not then propagated under the form of
4163.5 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 sound in liquids is greater than in air.
Velocity of sound in liquids and solids. - The velocity of experiment, that in one of the pipes employed for conducting Sturm found, by experiments made in 1827, on the Lake of
MM. Colladon and the water in Paris, about 3,120 feet long, the voice lost so little Geneva, that the velocity of sound in water is about 4,708 feet of its intensity, that from one extremity of this tube to the other a conversation could be carried on in a low voice. Yet In solids, the velocity is still greater. In experimenting on the diminution of the sound becomes sensible in tubes of great the cast-iron pipes used in conducting water, M. Biot found diameter, or in those in which the sides present many turnings that sound is propagated in cast iron with a velocity ten and a and windings. Such effects are observed in vaults and long half times that of its velocity in air. The velocity of sound in galleries.
other solids has been determined theoretically by Chladni, The property which tubes possess of conveying sounds to a
Savart, M. Masson and M. Wertheim, by means of the number distance first received its most useful application among our- of longitudinal or transversal vibrations of the bodies, or by establishments are well known. These tubes are made of means of their coefficient of elasticity. Chladni has found by caoutchouc, and of small diameter; they pass from one place of sound is from ten to sixteen times greater than it is in air.
means of the longitudinal vibrations that in wood the velocity to another through the walls of the house. If one speaks with In metals, this velocity is more variable; the velocities a voice a little raised above the ordinary tone at one of the varying from four to sixteen times greater than its velocity in extremities of such a tube, it is very distinctly heard at the
air. other extremity. According to the experiments of M. Biot already mentioned, it is evident that by means of acoustic retarded in their development, they are propagated under the
Reflection of sound. So long as the sonorous waves are not tubes à correspondence with the living voice could be main- form of concentric spheres; but when they meet an obstacle, tained between two towns at a given distance from each other. they follow the general law of elastic bodies, they are thrown As sound passes over about 1,100 feet in a second, a distance back upon themselves, and form new concentric waves, which of about 50 miles would be passed over in four minutes.
seem to emanate from a second centre on the other side of the Velocity of sound in gases. The propagation of sonorous obstacle: this is expressed by saying that the waves are waves being successive, sound is transmitted from place reflected. Fig. 127 represents a series of waves first incident to place in an interval varying with their distanse.
On this principle, a great number of phenomena are explained.
Fig. 127, 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.
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 MCD N, emitted from the centre treat of Optics, that light takes an inappreciable time to des- A, the corresponding reflected wave is represented by the arc cribe a short distance like this. They found also that the CKD, of which the point « is the virtual centre. mean duration of the propagation of sound from the one point c of the reflecting body to the sonorous centre A, and station to the other was 54.6 seconds. Now dividing the draw ch perpendicular to the surface of this body, the angle distance between the two stations by this number of Ach is called the angle of incidence, and the angle Bch formed seconds, we find that the velocity of the sound per second by the production of a c, the angle of reflection. Whence the was about 1118.4 feet, at the temperature of 60°.8 Fahrenheit, reflection of sound is regulated by the two following laws, which was that of the atmosphere at the time of the experi- which are also the same for light and for heat: ments. The velocity of sound in the air decreases with the 1st. The angle of reflection is equal to the angle of incitemperature : at 50° Fahrenheit it is only about 1105-7 feet per dence. second; and at 32° Fahrenheit it is about 1092-5 feet per second. 2nd. The angle of reflection and the angle of incidence are But at the same temperature, this velocity is independent of situated in the same plane, which is perpendicular to the reflectthe density of the air, and consequently of the pressure. At ing surface. the same temperature the velocity is the same for all sounds, According to these laws, the sound which in fig. 127 is pro. weak 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.
LESSONS IN GREEK.No. XXIV.
proceed to exhibit in full an example of a verb pure, and
take as my instance this verb \vw, I loose, or unbind. By JOHN R. BEARD, D.D.
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 low 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, toußw, I rub, and XELT-W (root dır), I leave ; and from lose, which is the same word as loose, differently spelt and one liquid verb, namely, patv-w (root pav), I show. By this pronounced; to lose is the result of loosing.
means a complete example is presented.
S. 1 ε-λιπ-ον
take the λιπ-ε like the
Opt. Impf. Pres. Imperat.
The connexion of the parts will become obvious if I put the Stems together.
Present. Imperfect. Future. First Aorist. First Perfect. First Plup. Second Perfect. Second Plup. Second Aorist. λυ ελν λυσ ελυσ λελυκ ελελυκ πεφην επεφην
ελιπ, The Stems arrange themselves in pairs, thus
The first thing which I advise the Student to do, is to an example or two, as in τιω, I honour» και βουλευω, Ι ααυεse; and make himself familiar with the stems. Having got the stems Lovw, I wash: he will easily acquire the rest.
Perfect. times. After he has learnt to recognise the connexion and derivation of the several parts, and so formed some idea of the
βε-βουλευκα beautiful harmony of the whole, let him commit the entire
λε-λουκα. paradigm to memory; and let him not pass on until he has acoomplished the task. The effort will save a world of trouble, ,
I present the same parts in their stems :It is customary in Greek Grammar to give three parts of Present Stein. , Future Stem. Perfect Stem. 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
βε-βουλευκhree is shown in the Table of Stems given above. I present