﻿578 Simultaneous Vibration- Curves of String and Air. 



Figures 2-5 show the effects when bowing at 1/5, 1/14, 

 1/14, and 1/5 respectively, thus affording a test o£ the uniform 

 working of the apparatus. In fig. 2 the bowing was bad as 

 seen by the crinkles in the string's record. 



Figures 6-9 form a series in which the string was plucked 

 throughout, but at 1/14, 1/10, 1/5, and 1/7 respectively. 

 These allow of comparisons with the former cases of bowing 

 and with fig. 10 of the previous paper "*, which showed the 

 motion of the sound-box when the string was plucked at 1/7. 



Figures 10-13 form a set all bowed at 1/14, but with 

 pitches ascending by about 1/3 of a tone, the frequencies 

 being 128, 134, 139, and 145 per second respectively. The 

 curves for the air exhibit an instructive and gradual change 

 through this series. 



The above 13 figures constitute the first column on the 

 Plate. 



Columns 2 and 3 should be viewed side by side as the 

 pitches then correspond, but the figure in any line in col. 2 

 shows the effects of bowing at 1/10 for a particular pitch, 

 while the figure on the same line in col. 3 shows the effect of 

 plucking at 1/10 obtained without altering the pitch. Of 

 course the bowing and plucking were made near opposite 

 ends of the string so that the resin would not be greased by 

 the thumb and finger. 



In each of the cols. 2 and 3 the pitches vary throughout 

 an octave and constitute the tempered chromatic scale. The 

 actual frequencies are given between the columns on the 

 Plate, and are the same as those used in the former paper. 



Thus these two columns of the present paper show the 

 variation due to pitch changing, and allow the effects of 

 bowing and plucking to be contrasted side by side. Further, 

 by comparing these with the corresponding figures of the 

 former paper, the distinction between the motions of the belly 

 and those of the diaphragm can be discerned. 



It is perhaps too early yet to make generalizations on this 

 distinction, but so far the tendency seems to be towards 

 greater simplicity (fewer Fourier components) in the motion 

 of the sound-box than in that of the air, the latter being 

 apparently able to follow more closely the highly complicated 

 motion of the string which, when well bowed, may be 

 regarded as a Fourier series to infinity. 



University College, Nottingham, 

 July 26, 1906. 



* Phil. Masr. July 1905. 



