392 Prof. C. V. Raman on the " Wolf-note" 



unusual degree; and it appears to have been realized that the 

 difficulty of: maintaining the note steadily is due in someway 

 to the sympathetic resonance of the instrument*. In a 

 recent paper f , Q\ W. White has published some interesting 

 experimental work on the subject, confirming this view. The 

 most striking effect noticed is the cyclical variation in the 

 intensity o£ the note when the instrument is forced to speak 

 at this point. White suggests as an explanation of these 

 fluctuations of intensity that they are due to beats which 

 accompany the forced vibration impressed on the resonator 

 when the impressed pitch approaches the natural pitch of 

 the system. The correctness of this suggestion seems open 

 to serious criticism. For, the beats which are produced 

 when a periodic force acts on a resonator are of brief 

 duration, being merely due to the superposition of its forced 

 and free oscillations, and when, as in the present case, the 

 resonator freely communicates its energy to the atmosphere 

 and the force itself is applied in a progressive manner and 

 not suddenly, such beats should be wholly negligible in 

 importance, and should, moreover, vanish entirely when the 

 impressed pitch coincides with the natural pitch.. In the 

 present case the essential feature is the persistency of the 

 fluctuations of intensity and their markedness over a not 

 inconsiderable range; and it is evident that an explanation 

 of the effect has to be sought for on lines different from those 

 indicated by White. I had occasion to examine this point 

 when preparing my monograph on the " Mechanical Theory 

 of the Vibrations of Bowed Strings," which will shortly be 

 published, and the conclusions I arrived at have since been 

 confirmed by me experimentally. 



From the mechanical theory, it appears that when the 

 pressure with which the bow is applied is less than a certain 

 critical value, proportionate to the rate of dissipation of 

 energy from the vibrating string, the bow is incapable of 

 maintaining the ordinary mode of vibration in which the 

 fundamental is dominant, and the mode of vibration should 

 progressively alter into one in which the octave is the pre- 

 dominant harmonic J. In the particular case in which the 

 frequency of free oscillation of the string coincides very 

 nearly with that of the bridge of the violin and associated 

 masses, the mode of vibration of the string is initially of the 

 well-known type in which the fundamental is dominant. 



* Guillemin, "The Application of Physical Forces," 1877. 

 t a. W. White, Proc. Camb. Phil. Soc. June 1915. 

 % Compare with the observations of Helmholtz, ' Sensations of Tone/ 

 English Translation by Ellis, p. 85. 



