366 



Studies in Acoustics. 



[Feb. 27, 



27. It follows from this investigation as far as it has gone, that our 

 knowledge of vowel sounds is not perfect. The principal proof of this 

 is the fact that vowels cannot be reproduced exactly by mechanical 

 means. Something is always missing — probably the noises due to the 

 rush of air through the teeth, and against the tongue and lips. 



28. The curves (fig. 10) arrived at synthetically do not differ very 

 materially from those arrived at analytically by Helmholtz (fig. 6). 

 They principally differ in the prominence of the prime. But the 

 prime can be dispensed with altogether. Curves produced by the 

 synthetic machine, compounded of the different partials without their 

 prime, show that there exist beats or resultant sounds. A vowel sound 

 of the pitch of the prime may be produced by certain partials alone, 

 without sounding the prime at all. The beat in fact becomes the 

 prime. This point is clearly illustrated, orally, by the automatic 

 phonograph, and graphically by the sketch (fig. 11), drawn by the 

 synthetic curve machine. In fact, every two partials of numbers 

 indivisible by any common multiple, if sounded alone, reproduce by 

 their beats the prime itself- Thus, the third and the fifth partials, 

 or the second and the third, &c, will result in the reproduction 

 of the prime. In fact, fig. 11 illustrates not only this, but it shows 

 that when the number of partials introduced is increased, the beats 

 become more and more pronounced. 



II. — The Loudness of Sound. 



29. Another point remaining for investigation arising out of this 

 inquiry, is the true theory of the loudness of sound. It is thought by 

 the authors that loudness does not depend upon amplitude of vibration 

 only, bat also upon the quantity of air put into vibration ; and, therefore, 

 there exists an absolutely physical magnitude in acoustics analogous to 

 that of quantity of electricity or quantity of heat, and which may be 

 called the quantity of sound. This can be shown experimentally by con- 

 structing three disks like those in fig. 1, whose diameters increase in 

 arithmetical ratio. When these disks are vibrated by the same curve 

 by the automatic phonograph, or when they are thrown into vibra- 

 tion by tuning forks, it will be found that the intensity of sound 

 increases in a surprising ratio. The amplitude remains just the same ; 

 the area under vibration alone increases. Thus, in the automatic 

 phonograph, for two notes, one of which is an octave higher than the 

 other, the area ought probably to be diminished one-half for the 

 higher to produce equal loudness. Similarly for the same note, if 

 we increase the area to be vibrated in its reproduction, it will be 

 found that, as the area increases, so does the loudness of the sound 

 emitted. In fact, in the automatic phonograph the diameter of the 

 sounding disk ought, if it were possible, to vary with the pitch of 

 each note, to produce equal intensity of sound. 



