BEATS. 405 



will be louder than the sound of each when heard alone. 

 But since the rate of vibration is not exactly the same for 

 both sounds, the condensations and rarefactions of air 

 which are produced by the two sonorous bodies cease to 

 take place at the same time. After a short time the 

 condensation produced by one body coincides with the 

 rarefaction produced by the other body, and vice versa- 

 both sounds mutually destroy one another, and this 

 happens when one body has performed just half a vibra- 

 tion more than the other. If one body is in advance of 

 the other by a whole vibration, the condensations and 

 rarefactions again take place at the same time, and the 

 intensity of the sound is again increased ; if it is in ad- 

 vance by one vibration and a half, the sound is again 

 destroyed, and so on. The number of times per second 

 that the condensation due to one sound coincides with 

 the condensations or rarefactions respectively due to 

 the other, that is, the number of beats, or of alterna- 

 tions of loudness and faintness, is equal to the differ- 

 ence between the numbers of vibrations per second cor- 

 responding to the two sounds employed. 



That the beats are the more frequent, the greater the difference 

 in pitch of the two notes producing them, may be shown by means 

 of the monochord with two strings. Both strings are first tuned 

 in unison, and then the sound of one is gradually heightened or 

 lowered ; beats are thus obtained which follow one another more 

 and more rapidly. In order to obtain slow beats the note of one 

 string may be lowered by weighting the strii g slightly in the 

 middle without altering the tension ; for this p rpose a piece of 

 softened copper or brass wire, about O mm '5 thick and 10 mm long, is 

 wound in close turns round the middle of the string, precisely like 

 the strings used for the bass notes of a piano-forte. 



To render the beats distinctly perceptible, it is best to pluck -both 

 strings simultaneously with the first and second fingers of the right 

 hand, applying the fingers exactly in the middle of the strings, for 



