PHYSIOLOGICAL ACOUSTICS 285 



There are one or two questions, however, relating principally 

 to Ohm's Law ( 1), to which some reference is necessary. The 

 first point on which the student should satisfy himself is that 

 the various simple-harmonic vibrations which are as a rule 

 combined in the production of a musical note are really 

 represented by independent elements in the resulting sensation ; 

 that the latter can in fact be resolved into a fundamental tone 

 and a series of harmonics. For this a slight course of education 

 is necessary. A series of resonators of the type shewn in 

 Fig. 80, p. 261, tuned to the overtones which it is desired to 

 detect, are of great service for this purpose*. But such 

 assistance is not indispensable, and a good deal can be effected 

 with the piano or monochord. Take for instance the note c, 

 whose harmonics are c', g f , c", e", g ', If on the piano one 

 of these, say g' } be gently sounded, and the key then released, 

 so that the vibration is stopped, and if immediately afterwards 

 the note c be struck with full intensity, it is not difficult to 

 recognize in the compound sensation the presence of the 

 element previously heard. This is often more perceptible as 

 the sound dies away, the overtones being apparently extinguished 

 more slowly than the fundamental. A more immediately 

 convincing series of experiments can be made with the 

 monochord, or with a piano whose strings are horizontal and 

 therefore easily accessible. If a string be set into vibration 

 whilst damped at a nodal point of one of the harmonics by 

 contact with a hair-pencil, the fundamental tone and all the 

 harmonics of lower rank may be reduced in intensity or 

 altogether extinguished, according to the degree and duration 

 of the pressure applied. In this way a whole series of types 

 of vibration can be produced in which the harmonic in question 

 is accompanied by a varying admixture of the fundamental, &c. 

 The occurrence throughout of the corresponding sensation as 

 an independent element in the resulting sound is in this way 

 easily appreciated. The piano also lends itself readily to the 



* It may be noted that the external ear-cavity is itself a resonator, 

 responding most intensely to a certain tone, which varies for different 

 individuals but is usually in the neighbourhood of ff* g ir . The aperture 

 being relatively large, the damping and consequently the range of resonance 

 is considerable. 



