Chap, xxxin.] RESONATORS. 443 



quarter wave length. If the column of air were 

 longer the condensation would not have travelled 

 through the jar till after the recoil of the fork (the 

 rarefaction) had begun, and thus the two would not 

 harmonise. Such a jar, then, open at only one end 

 must be equal to a quarter the wave length of the 

 vibration of the fork if it is to vibrate in harmony 

 with it. If a fork vibrating more rapidly be used, 

 its wave length is shorter and a shorter column of 

 air is required to be in harmony with it. This may 

 be obtained by pouring more water into the tall jar 

 till the proper length is secured, or by using a shorter 

 jar. The column of air in a tube open at both ends 

 will also vibrate in harmony with a given sound. A 

 tube open at both ends must be twice the length of a 

 tube closed at one end, in order to vibrate synchro- 

 nously with the same note. A tube open at both ends 

 is called briefly an open tube or pipe, and one closed at 

 one end is called a stopped tube or pipe. We have seen 

 that a stopped pipe must be a quarter the wave length 

 of a given vibration if it is to vibrate in harmony with 

 it, so an open pipe must be half the wave length to be 

 in harmony. If an open pipe is the same length as 

 a stopped pipe, it will vibrate in harmony with the 

 octave of the note of the stopped pipe, for it can only 

 be half the wave length of a vibration which is half as 

 short as that to which the stopped pipe responds ; 

 that is, the vibration to which the open pipe responds 

 must have twice the rapidity of the vibration of the 

 note to which the stopped pipe responds ; it must be 

 its octave. 



Forms of resonators. The fact of resonance 

 is made use of for practical purposes. Thus, tuning 

 forks are usually mounted upon boxes, of such a 

 length that the column of air in the box will vibrate in 

 harmony with the note of a particular fork, and with 

 none other. The sound is thus rendered audible to a 



