SOUND 



581 



and drums are familiar instances of vibrating 

 bodies ; but if these are made to vibrate in vacua 

 no sound will be heard. Vibrating in air they 

 give forth their appropriate sounds. In the Siren 

 (q.v.) we have an instrument which produces 

 sound by breaking up a continuous blast of air 

 into a succession of pulses. The instrument is 

 valuable as proving that the pitch of a note 

 depends on the number of pulses per second. The 

 faster the siren spins, the more quickly the pulses 

 follow each other, the greater is the frequency or 

 number of pulses per second, and the higher is the 

 pitch, as the ear at once tells us. The same fact 

 can lie proved by holding the edge of a card against 

 the teeth of a revolving toothed wheel. If the 

 wheel is going fast enough, the successive noises 

 of the card as it frees itself from each tooth and 

 impinges itself on the next succeeding are no 

 longer distinguishable, but coalesce to produce a 

 note of definite pitch which rises as the wheel 

 rotates faster. Now it may be shown that, when 

 the ear is satisfied that the notes produced by a 

 siren and a tuning-fork have the same pitch, the 

 number of pulses given by the siren in one second 

 is exactly equal to the number of vibrations of the 

 tnning-fork in the same time. Thus the vibrating 

 tuning-fork transfers to the air a series of pulses 

 timing accurately with the vibrations. It is not 

 difficult to see how this takes place. As the forks 

 vibrate to and fro they push the air first on one 

 side and then on the other; and just as a hand 

 moved slightly to and fro in water starts a series 

 of waves travelling outwards along the surface, so 

 the tuning-fork starts in the air a series of waves 

 of condensation and rarefaction which travel out- 

 wards through the air. In the case of the water- 

 waves gravitation supplies the force which, by its 

 tendency to keep the surface level, gives the power 

 of recovery that is indispensable to all wave- 

 motion. In the case of the sound-waves the air's 

 own Elasticity (q.v.), or power of resisting change 

 of bulk and of recovering completely its original 

 density, is the essential factor in producing and 

 sustaining the wave-motion (see WAVE). 



The essential features of the wave-motion in the 

 air may be indicated by the behaviour of a row of 

 points, each of which oscillates to and fro about its 

 mean position. The time or period of oscillation 

 is the same for all ; and we shall suppose the 

 oscillations to be of the simplest type Known as 

 Simple Harmonic Motion (see WAVE). When at 

 rest the points are all at equal intervals apart, as 

 in fig. 1, a. When in motion so that each point 

 moves through its mean position a little later than 



d. 



Fig. 1. 



does the immediately preceding point, then the 

 points will be crowded together in some regions 

 and widely distributed at others (fig. 1, 6). As 

 the points continue their oscillations the configur- 

 ation will not remain steady, but will move along 

 among the points (fig. 1, c and d). Any given 

 region will become alternately more crpwdeu and 

 less crowded, a region now of condensation, now of 

 rarefaction. This ever-changing condition, which 

 we have supposed to be the characteristic of a row 

 of points, may easily be imagined to be possessed 

 by a swarm of space-filling particles ; and, from 

 the analogy of the circular ripples which expand 

 outwards over the surface of a lake which has been 

 disturbed by a stone being dropped into it, we can 

 readily picture a succession of spherical waves of 

 condensation and rarefaction radiating out through 



air from the source of disturbance, in the present 

 instance the source of sound. The mode by which 

 the condensation or rarefaction is passed on from 

 one region of air to another may be explained as 

 follows : Because of its elasticity air resists com- 

 pression and will tend to recover its original 

 density as soon as the compressing force is removed. 

 But because of its inertia it will, if left perfectly 

 free, overdo the recovery just as a pendulum 

 when drawn aside and let go swings to the other 

 side of its natural position of rest. Now if any 

 small region of air undergoes rarefaction it can 

 only do so by itself expanding and thereby com- 

 pressing the surrounding layer of air. But as it, 

 so to speak, swings back through its condition of 

 normal density to a state of condensation, the 

 surrounding layer will swing from its state of 

 condensation to a state of rarefaction, that is, 

 expansion, compressing thereby in its turn the 

 next encompassing layer of air. This second layer, 

 having thus acquired an oscillatory character, will 

 in the same way impress the next layer with a 

 like character, and so on indefinitely. 



Returning to the case of the tuning-fork, we see 

 how the energy of its vibrations is gradually trans- 

 ferred to the air and transmitted through it to the 

 farthest limits at which the sound is heard, if not 

 farther. Thus the motion of the tuning-fork 

 gradually decays, and the intensity of the sound 

 heard at any given distance simultaneously dimin- 

 ishes. Ultimately the sound dies away, and the 

 tuning-fork conies to rest. What is called the 

 intensity of a sound depends in some way upon 

 the degree of agitation communicated to the air 

 in accurate language, upon the vibratory energy 

 existing in the air at the place where the sound fs 

 heard. Now it is a familiar experience that with 

 great variations of intensity the pitch of a sound 

 remains unchanged. The pitch depends upon the 

 number of vibrations per second, and the intensity 

 upon the energy of vibration. We find then that 

 within wide limits the extent or amplitude of the 

 vibration, or (as in air) the range tnrongh which 

 the density may vary, does not affect the periodic 

 time of the vibration. The quantitative relation 

 between the energy and the amplitude, and there- 

 fore between the intensity and the amplitude, 

 is that the former varies as the square of the 

 latter. With double the amplitude we have four 

 times the intensity, with half the amplitude one- 

 fourth the intensity. That the intensity falls off 

 at a much quicker rate than the amplitude is at 

 once evident to any one closely inspecting the 

 diminishing range of motion of a tuning-fork and 

 at the same time paying attention to the decreasing 

 loudness of the tone. The ear is by no means so 

 sensitive in comparing intensities as it is in com- 

 paring pitches. When two notes are of very 

 different pitch it is often difficult to say which is 

 the louder. 



We now pass to the consideration of the quality 

 of a musical sound. A tuning-fork gives a colour- 

 less inexpressive sound, whose one useful property 

 is the constancy of the pitch. When sounding the 

 same note the pianoforte, the violin, the trumpet, 

 the clarionet, and the human voice all impart their 

 own peculiar flavour, which is readily recognised 

 by the ear. Not only so, but we can distinguish 

 different pianofortes, different violins, different 

 voices, and so on. These differences of quality 

 cannot depend on the frequency or number of 

 vibrations per second, for that determines the 

 pitch ; nor upon the energy of vibration, for that 

 determines tne intensity. Quality, in fact, can 

 depend only on the internal nature of the vibration. 

 This may be sho%vn synthetically, as Konig has 

 done, by making siren discs, each perforated with 

 its own peculiar shape of hole, but all identical as 



