[ 125 ] 



XYII. JSfotes on tlieTheory of Sound. By R. H. M. BoSAN- 

 QUET, Fellow of St. Johns College^ Oxford. 



[Continued from p. 39.] 

 6. The Unsymmetrical Divergence of Sound in Air, 



THE most complete example of unsymmetrical divergence 

 is formed by a disturbance, covering an element of sur- 

 face so small as to be sensibly plane, advancing through the 

 air with lateral expansion, so that its edges trace out a cone 

 of small vertical angle. 



It has generally been assumed that when sound issues from 

 the end of a tube whose diameter is small compared with the 

 wave-length, it diverges after a time in an approximately sphe- 

 rical form. Helmholtz, for instance, assumes that at consi- 

 derable distances from the orifice the motion may be expressed 

 by the velocity potential of symmetrical spherical (or sectorial) 

 divergence. I have endeavoured to pave the way in the ex- 

 amination of the details of the action by an experimental study 

 of the motion of the air in the case of uniform flow from the 

 end of a pipe ; and in the case of outward flow it is quite 

 clear that no approximation to a symmetrical divergence takes 

 place at any moderate distance from the orifice. 



It is clear that, according to the rigorous treatment of sym- 

 metrical spherical divergence in Part I., the motion in the 

 case of a periodic slowly changing flow is ultimately of the 

 same nature, at any given instant, as that of a steady flow. 

 The general reasoning by which the similarity of the two mo- 

 tions at any instant was independently deduced in that case 

 holds also in this. 



Under these circumstances we may treat the phenomena of 

 steady flow, w^hich are easily observed in a rough manner, as 

 affording information as to the nature of the motion in the 

 case of a periodic flow whose wave-length is great in compa- 

 rison with all the dimensions concerned. The cases of air 

 issuing from and entering the orifice of a tube present differ- 

 ent forms. First, as to air issuing from an orifice. 



The simplest way of observing the form of motion of the 

 issuing air is to blow smoke out from the rounded aperture of 

 the m.outh with a slight but steady pressure. The issuing 

 smoke in this case forms a cone whose vortical angle is some- 

 where about 20° to 30°. Vertical movements take place 

 which we leave out of consideration. 



An india-rubber tube was attached to an acoustic bellows 

 and caused to give forth from its end a horizontal blast. The 

 pressure used was that of the bellows alone with all weights 



