SECT. XVI. INTERFERENCE OF SOUNDS. 139 



on the other till at the fiftieth vibration it will be half an oscil- 

 lation in advance. Then the waves of air which produce the 

 sound being sensibly equal, but the receding part of the one 

 coinciding with the advancing part of the other, they will destroy 

 one another, and occasion an instant of silence. The sound will 

 be renewed immediately after, and will gradually increase till 

 the hundredth vibration, when the two waves will combine to 

 produce a sound double the intensity of either. These intervals of 

 silence and greatest intensity, called beats, will recur every 

 second ; but if the notes differ much from one another, the alter- 

 nations will resemble a rattle ; and if the strings be in perfect 

 unison, there will be no beats, since there will be no interference. 

 Thus by interference is meant the co-existence of two undula- 

 tions in which the lengths of the waves are the same. And as 

 the magnitude of an undulation may be diminished by the addi- 

 tion of another transmitted in the same direction, it follows that 

 one undulation may be absolutely destroyed by another when 

 waves of the same length are transmitted in the same direction, 

 provided that the maxima of the undulations are equal, and that 

 one follows the other by half the length of a wave. A tuning- 

 fork affords a good example of interference. "When that instru- 

 ment vibrates, its two branches alternately recede from and 

 approach one another ; each communicates its vibrations to the 

 air, and a musical note is the consequence. If the fork be held 

 upright about a foot from the ear, and turned round its axis 

 while vibrating, at every quarter revolution the sound will 

 scarcely be heard, while at the intermediate points it will be 

 strong and clear. This phenomenon arises from the interference 

 of the undulations of air coming from the two branches of the 

 fork. When the two branches coincide, or when they are at 

 equal distances from the ear. the waves of air combine to rein- 

 force each other ; but at the quadrants, where the two branches 

 are at unequal distances from the ear, the lengths of the waves 

 differ by half an undulation, and consequently destroy one 

 another. 



