154 INTERFERENCE OF SOUNDS. [SECT. xvr. 



the succession of sounds will be more rapid and intense, and, 

 if the lightning describe a circular curve round a person, the 

 sound will arrive from every point at the same instant with 

 a stunning crash. In like manner the subterranean noises, 

 heard during earthquakes like distant thunder, may arise 

 from the consecutive arrival at the ear of undulations pro- 

 pagated at the same instant from nearer and more remote 

 points ; or, if they originate in the same point, the sound may 

 come by different routes through strata of different densities. 



Sounds under water are heard very distinctly in the air 

 immediately above ; but the intensity decays with great 

 rapidity as the observer goes farther off, and is altogether 

 inaudible at the distance of two or three hundred yards. So 

 that waves of sound, like those of light, in passing from a 

 dense to a rare medium, are not only refracted, but suffer 

 total reflection at very 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 strings be so nearly in 

 unison that one performs a hundred vibrations in a second, 

 and the other a hundred and one in the same period during 

 the first few vibrations, 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 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 alternations 



