30 KENNELLY AXD KUROKAWA. 



These equations indicate that in the steady state, the acceleration 

 is in leading quadrature to the velocity, which, in turn, is in leading 

 quadrature to the displacement. 



The linear mass, or mass of air normally occupying 1 cm. length of 



tube will be 



o'ln 

 m = Sp ,. " (25) 



Imear cm. 



where p is the density of the quiescent air in the tube at its actual 

 temperature and its normal pressure intensity p^ dynes per sci. cm. 

 The fundamental dynamic equation expressing the instantaneous 

 acceleration of a thin layer of air dl cm. long, and having a mass m dl 

 grams is 



m x dl= - OF dynes Z (26) 



where + dY is the excess of total pressure on the far side of the layer 

 above that on the near side; or 



m .V = bp.r = — ":;7 t'- ^ ^-') 



and^^ 



p.r = 



(28) 



where p is the excess of the pressure intensity p^ dynes per sq. cm. on 

 the far side of the layer above that on the near side. 

 It is also a well known acoustic condition ^'^ that 



.,: = r?';^ "^Z (29) 



or sec. 



where v is the velocity of transmission of sound in the tube, along its 

 axis, in kines. 



From (26) and (24) 



dF = — .r (jmco) ai rms. dynes Z (30) 



This expresses the relation between a small dift'erence of alternating 

 pressure aF across an elementary length ai of the tube conductor, and 

 the simultaneous A'ibratory \elocity x of the element. It corresponds 

 to the well known relation between the difference of alternating 



16 Lamb's Hvdrodvnaniics, p. 4.5S, Eq. (.3). 



17 " ■ "■ ]). 458, E(i. (6). 



