14 



from one wave of the two being either totally intercepted 

 or, at least, diminished in force, and the loudness of the 

 sound is proportional to the difference of the intensity of the 

 two waves when they affect the ear. 



All instruments for increasing sound, and producing re- 

 sonance, act upon this principle. 



The following facts will illustrate these principles in de- 

 tail. A tuning fork is a centre of four 

 waves, two -f and two — , but unless it be 

 - very close to the ear, no sound is heard from 

 it ; because the centre of all the four waves 

 being very close, all act on the ear with 

 equal force, and the difference is 0, (approxiniatively.) 



Now, if an open tube, of the same length as a one-phase 

 wave from the fork, be approached to one centre, as a, in 

 the adjoining figure, the air in it commences to vibrate in 

 unison with the fork, from being set in motion by the first 



wave which passes into it : 

 the vibration of the tube is, 

 however, a phase behind 

 that of the fork, and hence, 

 when a — wave passes from 

 the centre a, it meets a -f- wave from the end of the tube e> 

 and both are destroyed. The — centre, c, destroys also a 

 -f centre, as D, and there remain only the centres of -f 

 waves, B from the fork, and f from the tube, and these acting 

 in concert on the tympanum produce the sound that we 

 hear. 



If the tube be closed, and of only one-half the length, 

 the -f- wave, which emanates from the centre a, passes in, 

 and being reflected from the bottom, issues again at the 

 moment when the next — wave from a is about to enter; e 

 and A then destroy each other, and c and d also interfering, 

 there results only the -f wave b, which acts unimpeded on 



