Lord Rayleigh on the Theory of Resonators. 425 



it directly. This experiment succeeds perfectly: however 

 strongly the bar be excited, there is but little sound heard. If 

 about a second after the stroke the resonator be suddenly with- 

 drawn, the swelling out of the sound is very striking, and proves 

 conclusively that the presence of a resonator does not always 

 augment the loudness of a sound. The second resonator may 

 be held in such a position that it would by itself have little effect. 

 The experiment may also be made with a tuning-fork held in the 

 hand, or by some soft support. 



The reader may perhaps be inclined to suppose, as I did at 

 first, that the theory might be tested in the case of a simple 

 tone produced in one room and heard in the next through a 

 hole in the intervening wall. But a little consideration will 

 show that the requirements of theory are not properly satisfied 

 by this arrangement, in fact that the intensity of the source (at 

 the hole) is itself largely dependent on the presence or absence 

 of the resonator. Thus, if we suppose that the hole is small and 

 the original source distant, the pressure in the neighbourhood 

 of the hole on the first side of the wall will be nearly the same 

 as if the hole were stopped ; so that if the inertia of the air near 

 the hole can be neglected, we have on the second side a given 

 pressure, and not, as the theory assumes, a given flow. With a 

 tuning-fork mounted on a resonance-box and held rather close 

 to the hole, I have, however, succeeded in proving that the sound 

 coming through the wall may sometimes be diminished by the 

 neighbourhood of a resonator. 



In order to obtain more exact ideas of the operation of a re- 

 sonator, let us take one whose mouth is furnished with an infinite 

 flange, and which vibrates in response to a source of any kind 

 at a distance. The whole potential outside the resonator may 

 be divided into two parts — one of which is the same as if the 

 mouth of the resonator were closed, and the other the same as 

 if there were no external source, but the motion at the mouth 

 were maintained according to the same law as actually obtains. 

 Over the area of the mouth, which is supposed small, the poten- 

 tial of the former part will be nearly constant, and may be de- 

 noted by y}r . For the second part, <£ , we have already had 

 occasion to form the expression 



00 = 



27rJJdx r " 2tt iJJ^o r J J dx Q °J 



_ -— 1 CC d(f) dv i/c - 

 ~~ 2tt JJoVqT + 2^ ' 



if X represent the total current. Of these two terms the first 

 depends upon the inertia of air outside the mouth, whose effect 

 is equivalent to an addition to the mass of the vibrating parts 



