LAWS OF SONOROUS VIBRATIONS. 825 



the sound will become appreciable and progressively more intense as the surrounding 

 medium is increased in density. 



If we produce a single sound, or shock, in a free atmosphere, we may suppose that 

 the waves are transmitted equally in every direction ; and this is accomplished in the 

 following manner : An imaginary sphere of air receives an impulse, or shock, from the 

 body which produces the sound. This shock is, in its turn, communicated to another 

 spherical stratum of air ; this, to a third, and so on. The elasticity of the air, however, 

 produces a recoil of each imaginary sphere of air, and it is a portion of the last stratum 

 which strikes the tympanum, throwing it into vibration. If but a single impulse be 

 given to the air, we may suppose that all of the different strata, after a single oscillation, 

 return to their original quiescent condition. The first stratum receives the shock, and 

 the last communicates the shock to the ear. The oscillations of sound, produced in this 

 way, are to and fro in the direction of the line of conduction and are said to be longi- 

 tudinal. In the undulatory theory of light, the vibrations are supposed to be at right 

 angles to the line of propagation, or transversal. A complete oscillation to and fro is 

 called a sound-wave. 



It is evident that vibrating bodies may be made to perform and impart to the atmos- 

 phere oscillations of greater or less amplitude. The intensity of the sound is in propor- 

 tion to the amplitude of the vibrations. If we cause a tuning-fork to vibrate, the sound 

 is at first loud, or intense ; but the amplitude gradually diminishes, and the sound dies 

 away until it is lost. In a vibrating body capable of producing a definite number of 

 waves of sound in a second, it is evident that, the greater the amplitude of the wave, the 

 greater is the velocity of the particles thrown into vibration. It has been ascertained by 

 experiment, that there is an invariable mathematical relation between the intensity of 

 sound, the velocity of the conducting particles, and the amplitude of the waves ; and 

 this is expressed by the formula, that the intensity is proportional to the square of the 

 amplitude. It is evident, also, that the intensity of sound is diminished by distance, as 

 the amplitude of the waves and the velocity of the vibrating particles become weaker, 

 the farther we are removed from the sonorous body. The sound, as the waves recede 

 from the sonorous body, becomes distributed over an increased area. The propagation 

 of sound has been reduced also to the formula, that the intensity diminishes in propor- 

 tion to the square of the distance. 



Sonorous vibrations are subject to many of the laws of reflection which we have 

 studied in connection with light. Sound may be absorbed by soft and non-vibrating 

 surfaces, in the same way that certain surfaces absorb the rays of light. It is in this way 

 that we explain the deadening of sound in apartments furnished with carpets, curtains, 

 etc., and its reflection from smooth, hard surfaces. By carefully-arranged convex sur- 

 faces, the waves of sound may be readily collected to a focus. These laws of the reflec- 

 tion of sonorous waves explain echoes and the conduction of sound by confined strata of 

 air, as in tubes. We thus explain the mechanism of speaking-trumpets, the collection of 

 the waves by the pavilion of the ear, and their transmission to the tympanum by the 

 external auditory meatus. To make the parallel between sonorous and luminous trans- 

 mission more complete, it has been ascertained that the waves of sound may be refracted 

 to a focus by being made to pass, through an acoustic lens, as a balloon filled with car- 

 bonic-acid gas. The waves of sound may also be deflected around solid bodies, when 

 they produce what have been called by Tyndall, shadows of sound. 



Any one observing the sound produced by the blow of an axe can note the important 

 fact that sound is transmitted with much less rapidity than light. At a short distance, 

 our view of the body is practically instantaneous ; but there is a considerable interval 

 between the blow and the sound. This interval represents the velocity of the sonorous 

 conduction. This fact is also illustrated by the interval between a flash of lightning and 

 the sound of thunder. The velocity of sound depends upon the density and elasticity of 

 the conducting medium. The rate of conduction of sound by atmospheric air at the 



