in Bowed Stringed Instruments. 393 



But the vibrations of the string excite those of the instrument, 

 and, as the vibrations of the latter increase in amplitude, the 

 rate of dissipation of energy increases continually till it 

 outstrips the critical limit, beyond which the bow fails to 

 maintain the usual type of vibration. As a result of this, the 

 mode of vibration of the string progressively alters to a type 

 in which the fundamental is subordinate to the octave in 

 importance. The vibration of the belly then begins to decrease 

 in amplitude, but, as may be expected, this follows the change 

 in the vibrational form of tbe string by a considerable interval. 

 The decrease in the amplitude of the vibrations of the belly 

 results in a falling off of the rate of dissipation of energy, 

 and, when this is again below the critical limit, the string- 

 regains its original form of vibration, passing successively 

 through similar stages, but in the reverse order. This is then 

 followed by an increase in the vibrations of the belly, and 

 the cycle repeats itself indefinitely. The period of each cycle 

 is approximately twice the time in which the vibrations of 

 the belly would decrease from the maximum to the minimum, 

 if the bow were suddenly removed. 



The foregoing indications of theory are amply confirmed 

 by the photographs reproduced in Plate IX., which show the 

 simultaneous vibration-curves of the belly and string of a 

 'cello at the wolf-note pitch. It will be seen that the form 

 of vibration of the string alters cyclically in the manner pre- 

 dicted by theory, and that the corresponding changes in the 

 vibration-curve of the belly follow those of the string by 

 an interval of about quarter of a cycle. That the two sets 

 of changes are dynamically interconnected in the manner 

 described is further confirmed by the prominence of the 

 octave in both curves at the epochs of minimum amplitude. 

 The explanation of the cyclical changes given above is also 

 in accordance with the observed fact that they disappear and 

 are replaced by a steady vibration when the ratio of the 

 pressure to the velocity of bowing is either sufficiently 

 increased or sufficiently reduced. In the former case the 

 string vibrates in its normal mode, and in the latter case 

 the fundamental disappears altogether and the string divides 

 up into two segments. 



Effect of Muting on the " Wolf-note" 



Since the pitch of the wolf-note coincides with that of a 

 point of maximum resonance of the belly, we should expect 

 to find that by loading the bridge or other mobile part of the 

 body of the instrument important effects are produced. 



