I 



and Distribution of Sound, 29)^ 



It may now be instructive to consider the case o£ a large 

 siren, such as the 7-iuch disk siren experimented upon at 

 St. Catherine's in 1901. The wind consumption here was 

 29 cubic feet, or 810 litres, per second. This average current, 

 for the purposes of a rough calculation, may be analysed 

 into a steady current of the same amount and an alternating 

 current whose extremes are represented by +810 litres per 

 second, the latter being alone effective for the production of 

 sound. The first question that arises is to what pressure 

 does this correspond, and is it a reasonable fraction of the 

 actual pressure employed ? 



The answer must depend upon the other circumstances of 

 the case, such as the character of the cone or other tubular 

 resonator associated with the siren. We shall begin by 

 supposing that there is nothing of this kind, so that the above 

 alternating flow takes place at the surface o£ a sphere of 

 radius r situated in the open. The velocity-potential and 

 the rate of total flow being given by (1) and (2) with o) equal 

 to 47r, we have for the maximum rate of that flow A^{ 1 + Fr^}, 

 or with sufficient approximation for our purpose A simply. 

 If s be the " condensation,'''' 



S/> = ays = — /3 dcfy/dt, 

 so that by (1) 



^'"^^=47ra7=2\^ ^^^ 



To obtain a numerical result we must make some supposition 

 as to the magnitude of r. Let us take kr = ^. Then 



47rA .(.. 



5max=-Yo-7 ...... (9) 



in w^hich A is the maximum flow, \ the wave-length, and a 

 the velocity of sound, /.^. 3x10* cm. per second. In the 

 experiments referred to, the pitch was low and such that 



X = S feet = 240 cm., 

 whence with A = 8'l x 10^ c.c. per second we find 



_ 1 

 ^"^""180* 

 The maximum condensation corresponding to the assumed 

 introduction of air is thus only jJq of an atmosphere. The 

 pressure is in the same proportion, and we see that it is but 

 an insignificant fraction of the pressure actually employed 

 (25 lbs. per square inch). We infer that no moderate 

 pressure can be utilized in this way, and that some cone or 



