404 



SCIENCE. 



[N. S. Vol. XIV. No. 350. 



The rise of the sharpened note will natu- 

 rally depend on the pitch of the resonator. 

 For a shorter one giving d" to e" with in- 

 creasing blast, the above effect on the organ 

 pipe is an e" flat. A resonator of pitch d" 



sz^ 



6ZZ 



^^-d- 



to/" raises the organ pipe to e" or depresses 

 it to 6', as follows: c" at long ranges, h' 

 at a; = 1.2, about; h' flat at a;= 1.0 cm., 

 then suddenly e" at a;^.9 cm. Here I 

 thought I had detected two modes of vi- 

 bration of a system of two degrees of free- 

 dom ; yet as the butt end of the resonator 

 produced like depressions of tone, this is 

 probably referable to increased friction. 



A resonator of pitch a'-c", definitely be- 

 low that of the pipe, depressed the tone 

 from c" to c" flat. With the butt end the 

 depression was a whole tone. The same 

 resonator on top of the pipe showed just 

 perceptible sharpening. The effect seemed 

 to be the same whether the pitch of the 

 resonator was depressed by lengthening or 

 by reducing the size of the mouth. 



Remarks in Explanation. — As the note of 

 the organ pipe is always depressed when 

 the butt end of the resonator or any other 



obstacle is brought up to the lip, I think 

 that a rough explanation in terms of a 

 system of one degree of freedom will be ad- 

 missible. Thus the organ pipe is vibrat- 

 ing throughout under more or less resist- 

 ance. Its period may therefore be given by 

 2^= 2:rm/v^ma — b'\ where m is the inertia 

 of the vibrating body, a is Hooke's constant 

 and 2b the coeflBcient of friction. From an- 

 other point of view, T= 2/lm/6,if >i= Thj2m 

 is the logarithmic decrement. 



If the friction is increased by presenting 

 an obstacle at the lip, h is increased and 

 therefore T is increased or the tone is de- 

 pressed. If, however, the friction is de- 

 creased by presenting a negative obstacle — 

 i. e., the mouth of a resonator — near the 

 lip, which initially tugs and pushes synchro- 

 nously with the vibration of the lamina of 

 air from the lip, then h is decreased and T is 

 decreased. In other words, the tone is 

 sharpened. It is in this way that I have 

 presented this very striking phenomenon as 

 an illustration of the given equation, though 

 the full explanation cannot of course stop 

 with a single degree of freedom. 



As to the reasons for the absorption of the 

 organ-pipe note in the resonator, if its lid is 

 somewhat loose, it is clear that this cannot 

 be a case of ordinary interference ; for in 

 such a case there should be vibration in the 

 resonator, whereas none is manifest to the 

 touch at least. In other words, each succes- 

 sive vibration of the organ pipe is quenched 

 in the resonator, being completely damped 

 out. Hence the effective friction in the 

 resonator considered alone for the given 

 conditions is so large as to change the 

 harmonic type of decay in the exponential 

 type, the period becoming imaginary. Now 

 it is interesting to note that this takes place 

 at a particular distance, x, from the lip 

 within narrow limits, the resonator re- 

 sponding strongly to c" for larger values of 

 X, and to d" for smaller values. The whif- 

 fing suggests the impure octave h", while 



