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SKCT. XVI. INTERFERENCE OF SOUNDS. 133 



light, in passing from a dense to a rare medium, are not 

 only refracted, but suffer total reflection at veiy oblique 

 incidences (N. 184). 



The laws of interference extend also to sound. It is 

 clear that two equal and similar musical strings will be 

 in unison, if they communicate the same number of 

 vibrations to the air in the same time. But if two such 

 stiings be so nearly in unison, that one performs a hun- 

 dred vibrations in a second, and the other a hundred 

 and one in the same period during the first few vibra- 

 tions, the two resulting sounds will combine to form one 

 of double the intensity of either, because the aerial waves 

 will sensibly coincide in time and place ; but one will 

 gradually gain on the other till at the fiftieth vibration it 

 will be half an oscillation in advance. Then the waves 

 of air which produce the sound being sensibly equal, but 

 the receding part of the one coinciding with the advan- 

 cing part of the other, they will destroy one another and 

 occasion an instant of silence. The sound will be re- 

 newed 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 alternations 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 coexistence of two undula- 

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

 And as the magnitude of an undulation may be dimin- 

 ished by the addition of another transmitted in the same 

 direction, it follows that one undulation may be abso- 

 lutely 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 instrument vibrates, its two branches alter- 

 nately recede from and approach one another ; ach 

 communicates its vibrations to the ah*, 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 

 M 



