NEWTON S PBINCIPIA. 279 



in opposite directions. Of these one may often be con 

 sidered as the reflection of the other at the open or closed 

 end of the tube. These two waves will &quot; interfere &quot; as it 

 is called, and there will be in consequence two sets of 

 points in the tube, which possess remarkable properties. 

 At any point of one set there is no motion in the air, but 

 only a condensation. At any point of the other set there is 

 no condensation, but only motion. The first are called 

 &quot;nodes,&quot; the other &quot;loops.&quot; These points are placed in 

 regular order, alternately a node and loop at distances one 

 fourth the length of a wave. 



Suppose a tube closed at one end to be sounding a note 

 in unison with a vibrating plate at the other. Then clearly, 

 since the air must remain in contact with the tube at the 

 closed end, there can be no motion there. That point must 

 be a node. Since the air moves in consonance with the 

 vibrating plate, there must be no &quot;action or reaction&quot; 

 between the air and plate. If there were, the sounds would 

 not be in unison, and the note of both the tube and plate 

 would begin to change. The pressure of the air must 

 therefore be the same on each side of the plate; therefore 

 there is no condensation in front of the plate. That point 

 must be a loop. One end of the tube is therefore a loop, 

 the other a node. Hence the length ( I ) of the tube must 



be an odd multiple of j, where x is the length of a wave. 

 That is, 



That note which has the largest value of \ which can be 

 sounded from a given pipe is called the &quot; fundamental &quot; 

 note of that pipe. For this note n = 0, and we have 



The pitch of a note being determined by the length of the 



T 4 



