208 hertz's experiments. 



we approach it we get the reflected taps earlier and the incident ones 

 later than when we were at the source. How far must we go toward 

 the reflector in order that the original and reflected taps may again ap- 

 pear simultaneous*? We must go half the distance that a tap is propa- 

 gated during the intervnl between two taps — half the distance, because 

 in going away from the source we are approaching the reflector and so 

 make a double change — we not only get the original ones later, but we 

 also get the reflected ones earlier, and so coincidence will have again 

 been reached when we have gone half the distance between any pair 

 of compressions travelling in the air. Now, if the taps succeed one 

 another slowly, the distance in the air between any two of them trav- 

 elling through it will be considerable; any one of them will go a con- 

 siderable distance from the source before its successor is started after 

 it. If, on the contrary, they succeed one another rapidly, the distance 

 between the travelling taps will be small. 



In general, if v be the velocity with which a tap travels, and t be 

 the interval of time between successive taps, the distance apart of the 

 taps travelling in the air will be X = vt. By arranging, then, that the 

 taps shall succeed one another very rapidly, /. e., by making t small, 

 we can arrange that A may be small, and that consequently the ois 

 tauce between our source of sound and the reflecting wall may be 

 small too, and yet large enough to contain several places at distances 

 of ^X apart between the source and the reflector where the incident 

 and reflected taps occur simultaneously. Now, a very rapid succes- 

 sion of taps is to us a continuous sound, and where the incident and 

 reflected taps coincide we hear simply an increased sound, while at 

 the intermediate jflaces where the incident taps occur in tlie inter- 

 vals between the reflected tai)s we do not hear this eftect at all. In 

 the case of a succession of sharp taps we would hear in this latter 

 place the octave of the original note, but if the original series be, 

 instead of taps, a simple vibration of the air into and out from the 

 reflector, the in and out motions of the incident waves will in some 

 l)laces coincide with the in and out motions of the reflected wave, and 

 then thei'e will be an increased motion, while at intermediate places 

 the in and out motions of the incident wave will coincide with rhe 

 out and in motions of the reflected wave, and no motion, or silence, 

 Avill result, so that at some places the sound will be great and at inter- 

 mediate ])laces small. 



This whole eflect of having an incident and reflected wave travel- 

 ling simultaneously along a medium can be simply and beautifully 

 illustrated to the eye by sending a succession of waves along a chain 

 or heavy limp rope or an India-rubber tube fixed at the far end so as 

 to reflect the waves back again. It will then be found that the 

 chain divides up into a series of places Avhere the motion is very 

 great, called loops, se})arated by points Avhere the motion is very 

 small, called nodes. The former are the places where the incident and 



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