Lord Rayleigh on the Theory of Resonators. 423 



opposite sources; the representation of the complete tuning- 

 fork will require at least four simple sources. The fact is that 

 the simple source of theory, or even a reasonable approximation 

 thereto, is rarely met with in practice. When a solid body, 

 such as a string, bar, or bell, vibrates, there is usually but little 

 change of volume; and thus the algebraic sum of the sources is 

 approximately zero, the effect depending mainly on the different 

 situation of the positive and negative parts. It is true that the 

 resonance-board of a musical instrument may be regarded as 

 more nearly a simple source, in the sense that the principal 

 component parts have the same sign ; but the diffusion would 

 generally be great enough to separate it considerably from the 

 ideal simple source concentrated in one point. 



In order to see how materially the action of a resonator de- 

 pends upon the character of the source, we need only take the 

 case of a double source, whose components are sufficiently far 

 apart to be dealt with separately, but not so far that the interval 

 amounts to a sensible fraction of the wave-length. In conse- 

 quence of the last supposition, the joint effect at a moderate dis- 

 tance is but a very small part of what would be due to either 

 component separately ; the fluid emitted by the one is instantly 

 sucked up by the other, and vice versd. Now suppose that a 

 resonator of the same pitch is presented to one of the component 

 sources. Its effect, we have seen, will be to neutralize the 

 source in question, and thus to leave the other free. The result 

 is a considerable augmentation of loudness, which, however, to 

 the eye of theory still appears as the absorption rather than as 

 the production of sound. 



In general, whenever a resonator is so situated that there 

 would be at its mouth, supposed to be closed, a sensible varia- 

 tion of pressure due to external sources, the opening of the 

 mouth will entail a great alteration in the mechanical conditions. 

 There will be developed such a transfer of air backwards and 

 forwards through the mouth as would, if it existed alone, pro- 

 duce a variation of pressure at the mouth equal and opposite to 

 that above spoken of. Until this condition of things is attained 

 (that is, until the total pressure at the mouth is constant) the 

 vibration of the resonator must increase. Now the characteristic 

 of a resonator is that vibrations escape from it slowly, that a 

 large vibration within it corresponds to but a small variation of 

 pressure at the mouth. Hence it follows that, under the sup- 

 posed circumstances, there will be a large flow of air through the 

 mouth, or, in other words, that the resonator will behave as a 

 simple source of considerable power. If the system of external 

 sources be of such a character as to produce by itself little effect, 

 the operation of the resonator is attended by an augmentation of 



