Belas — On the Structure of Water- Jets. 207 



Now, if we break up the jet in a regular manner by a fork, a 

 drop will be thrown off with each complete vibration, and hence, 

 instead of a confused noise, a musical note will be heard — the note 

 that the fork is yielding. The sound can be made very loud and 

 penetrating, its quality depending on the nature and tension of the 

 diaphragm and the pressure of the water. 



If the latter be suitably adjusted, a note will be emitted by the 

 membrane without any fork being used ; for the impacts of the 

 drops will set up vibrations in the membrane which communicate 

 themselves to the jet, and effect its regular resolution ; and the 

 note, when once established, will be maintained. If the pressure 

 be increased, several notes may be obtained in succession, the pitch 

 rising with the pressure. 



An interesting example of the Doppler effect may here be 

 noticed. If the membrane be rapidly moved nearer the orifice, 

 the pitch of the note will be raised during the motion ; and on 

 lowering the membrane, the pitch will be lowered. 



There is an experiment that can be performed in connection 

 with this singing membrane that is very striking, and of some 

 theoretical interest. Suppose the fork Ut 4 , making 512 complete 

 vibrations per second, be placed on the stand. The membrane 

 will respond to that note. Let it now be removed, and Sol 3 , 

 giving 384 vibrations, substituted. The membrane again re- 

 sponds, this time to Sol 3 . Place the two together on the stand, 

 and a deep, powerful note of Ut 2 , or 128 vibrations, will be 

 heard. It is, in fact, the difference-tone, or grave harmonic of 

 the two forks. 



There has been for some years a controversy amongst physicists 

 as to whether these difference-tones had an objective existence or 

 not, that is whether there do really exist in the air vibrations of that 

 period. Some held that they were purely subjective, and produced 

 within the ear, owing largely to a peculiarity of construction of 

 that organ, while others held that they existed in the external air. 

 It would take too long to enter into the details upon which 

 the respective arguments were based ; but Helmholtz showed, from 

 mathematical considerations, that when a mass of air is set in 

 motion by two simple sources of sound, in certain cases vibrations 

 will arise with a frequency equal to the difference of frequencies of 

 the generating tones. If such vibrations exist objectively (he 



