:294: Lord Rayleigh on the Production 



resonating tube is a necessity. It may be remarked that the 

 radius r of the sphere^ on which the introduction of air is 

 supposed to take place, is 1/4/: or X/Stt, that is in the case 

 taken 4 inches or 10 cms. 



Cones and Resonators, 



The next question is what improvement in the direction 

 of utilizing higher pressures can be attained by the associa- 

 tion of cones and resonators ? But to this it is at present 

 difficult to give a satisfactory answer. Theory shows that, 

 apart from friction and other complications perhaps not very 

 important, the efficiency of a small source may by these 

 means be increased to any extent. Thus, in the case of the 

 cone, if it be the maximum velocity of a progressive wave at 

 a point w^here the section is <7, conservation of energy requires 

 that (TV? be constant. The maximum total flow [oru) is there- 

 fore proportional to o-z, i, e. to the linear dimension of the 

 section. If the vibrations are infinitesimal, we may begin 

 with as small a diameter as we please and end with a large 

 one. and thus obtain any desired multiplication of the source. 

 For it is the total flow at the open end of the cone which 

 measures the power of the source for external purposes. If, 

 however, the quantity of air periodically introduced at the 

 small end can no longer be treated as infinitesimal, this 

 <irgument fails ; and it is probable that the advantage 

 derivable from the cone diminishes. In an extreme case 

 we can easily recognize that this must be so. For the most 

 that the cone could do would be to add its own contents 

 to that of the air forcibly introduced. As the latter increases 

 without limit, the addition must at last become relatively 

 unimportant, and then the cone might as well be dispensed 

 with. Similar considerations apply to the use of a resonator. 



There is no reason to doubt that great advantage accrues 

 from the use of the conical trumpet in existing fog-signalling 

 apparatus, although probably it falls short of what would be 

 expected according to the theory of infinitely small vibra- 

 tions. If it be a question of striving to augment still further 

 the force of the sound, we must remember that the applica- 

 tion of power has already been carried to great lengths. 

 The utilization of more power might demand an increase in 

 the scale of the apparatus. This in itself would present no 

 particular difficulty, but we must not forget that everything 

 has relation to the wave-length of the sound, and that this 

 is to a great extent fixed for us by the nature of the ear. It 

 may well be that we are trying to do more than the con- 

 ditions allow, and that further advance would require a 



