In the following pages I have tried to render the science of Acoustics interesting to all intelligent persons, including those who do not possess any special scientific culture.
The subject is treated experimentally throughout, and I have endeavored so to place each experiment before the reader that he should realize it as an actual operation. My desire, indeed, has been to give distinct images of the various phenomena of acoustics, and to cause them to be seen mentally in their true relations.
I have been indebted to the kindness of some of my English friends for a more or less complete examination of the proof-sheets of this work. To my celebrated German friend Clausius, who has given himself the trouble of reading the proofs from beginning to end, my especial thanks are due and tendered.
There is a growing desire for scientific culture throughout the civilized world. The feeling is natural, and, under the circumstances, inevitable. For a power which influences so mightily the intellectual and material action of the age could not fail to arrest attention and challenge examination. In our schools and universities a movement in favor of science has begun which, no doubt, will end in the recognition of its claims, both as a source of knowledge and as a means of discipline. If by showing, however inadequately, the methods and results of physical science to men of influence, who derive their culture from another source, this book should indirectly aid in promoting the movement referred to, it will not have been written in vain.
SOUND
CHAPTER I
The Nerves and Sensation—Production and Propagation of Sonorous Motion—Experiments on Sounding Bodies placed in Vacuo—Deadening of Sound by Hydrogen—Action of Hydrogen on the Voice—Propagation of Sound through Air of Varying Density—Reflection of Sound—Echoes—Refraction of Sound—Diffraction of Sound; Case of Erith Village and Church—Influence of Temperature on Velocity—Influence of Density on Elasticity—Newton’s Calculation of Velocity—Thermal Changes Produced by the Sonorous Wave—Laplace’s Correction of Newton’s Formula—Ratio of Specific Heats at Constant Pressure and at Constant Volume deduced from Velocities of Sound—Mechanical Equivalent of Heat deduced from this Ratio—Inference that Atmospheric Air Possesses no Sensible Power to Radiate Heat—Velocity of Sound in Different Gases—Velocity in Liquids and Solids—Influence of Molecular Structure on the Velocity of Sound
§ 1. Introduction: Character of Sonorous Motion. Experimental Illustrations
THE various nerves of the human body have their origin in the brain, which is the seat of sensation. When the finger is wounded, the sensor nerves convey to the brain intelligence of the injury, and if these nerves be severed, however serious the hurt may be, no pain is experienced. We have the strongest reason for believing that what the nerves convey to the brain is in all cases motion. The motion here meant is not, however, that of the nerve as a whole, but of its molecules or smallest particles.8
Different nerves are appropriated to the transmission of different kinds of molecular motion. The nerves of taste, for example, are not competent to transmit the tremors of light, nor is the optic nerve competent to transmit sonorous vibrations. For these a special nerve is necessary, which passes from the brain into one of the cavities of the ear, and there divides into a multitude of filaments. It is the motion imparted to this, the auditory nerve, which, in the brain, is translated into sound.
Applying a flame to a small collodion balloon which contains a mixture of oxygen and hydrogen, the gases explode, and every ear in this room is conscious of a shock, which we name a sound. How was this shock transmitted from the balloon to our organs of hearing? Have the exploding gases shot the air-particles against the auditory nerve as a gun shoots a ball against a target? No doubt, in the neighborhood of the balloon, there is to some extent a propulsion of particles; but no particle of air from the vicinity of the balloon reached the ear of any person here present. The process was this: When the flame touched the mixed gases they combined chemically, and their union was accompanied by the development of intense heat. The heated air expanded suddenly, forcing the surrounding air violently away on all sides. This motion of the air close to the balloon was rapidly imparted to that a little further off, the air first set in motion coming at the same time to rest. The air, at a little distance, passed its motion on to the air at a greater distance, and came also in its turn to rest. Thus each shell of air, if I may use the term, surrounding the balloon took up the motion of the shell next preceding, and transmitted it to the next succeeding shell, the motion being thus propagated as a pulse or wave through the air.
The motion of the pulse must not be confounded with the motion of the particles which at any moment constitute the pulse. For while the wave moves forward through considerable distances, each particular particle of air makes only a small excursion to and fro.
Fig. 1.
The process may be rudely represented by the propagation of motion through a row of glass balls, such as are employed in the game of solitaire. Placing the balls along a groove thus, Fig. 1, each of them touching its neighbor, and urging one of them against the end of the row: the motion thus imparted to the first ball is delivered up to the second, the motion of the second is delivered up to the third, the motion of the third is imparted to the fourth; each ball, after having given up its motion, returning itself to rest. The last ball only of the row flies away. In a similar way is sound conveyed from particle to particle through the air. The particles which fill the cavity of the ear are finally driven against the tympanic membrane, which is stretched across the passage leading from the external ear toward the brain. This membrane, which closes outwardly the “drum” of the ear, is thrown into vibration, its motion is transmitted to the ends of the auditory nerve, and afterward along that nerve to the brain, where the vibrations are translated into sound. How it is that the motion of the nervous matter can thus excite the consciousness of sound is a mystery which the human mind cannot fathom.
Fig. 2.
The propagation of sound may be illustrated by another homely but useful illustration. I have here five young assistants, A, B, C, D, and E, Fig. 2, placed in a row, one behind the other, each boy’s hands resting against the back of the boy in front of him. E is now foremost, and A finishes the row behind. I suddenly push A, A pushes B, and regains his upright position; B pushes C; C pushes D; D pushes E; each boy, after the transmission of the push, becoming himself erect. E, having nobody in front, is thrown forward. Had he been standing on the edge of a precipice, he would have fallen over; had he stood in contact with a window, he would have broken the glass; had he been close to a drumhead, he would have shaken the drum. “We could thus transmit a push through a row of a hundred boys, each particular boy, however, only swaying to and fro. Thus, also, we send sound through the air, and shake the drum of a distant ear, while each particular particle of the air concerned in the transmission of the pulse makes only a small oscillation.
But we have not yet extracted from our row of boys all that they can teach us. When A is pushed he may yield languidly, and thus tardily deliver up the motion to his neighbor B. B may do the same to C, C to D, and D to E. In this way the motion might be transmitted with comparative slowness along the line. But A, when pushed, may, by a sharp muscular effort and sudden recoil, deliver up promptly his motion to B, and come himself to rest; B may do the same to C, C to D, and D to E, the motion being thus transmitted rapidly along the line. Now this sharp muscular effort and sudden recoil is analogous to the elasticity of the air in the case of sound.