30 KENNELLY AND 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 



■ m=Sp .-^^^^ (25) 



hnear 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 sq. cm. 



The fimdamental dynamic equation expressing the instantaneous 



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



grams is 



m .r d\= - (W dvnes Z (26) 



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

 above that on the near side; or 



5F dvnes , ,-^. 



m X = Sp.r = - ^ p^ ^ (-'0 



dl linear cm. 



and^^ 



dp dynes/sq. cm. , . 



px = — -T7 —r. ^ {-^) 



dl linear cm. 



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 



, = ,.?£ 1^5/ (29) 



(91- sec. 



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

 axis, in kines. 



From (26) and (24) 



OF = — X (jrcio)) d\ rms. dynes Z (30) 



This expresses the relation between a small difference of alternating 

 pressure dF across an elementary length d\ of the tube conductor, and 

 the simultaneous vibratory velocity x of the element. It corresponds 

 to the well known relation between the difference of alternating 



16 Lamb's Hydrodynamics, p. 458, Eq. (.3). 



17 " •' ■ p. 458, Eq. (6). 



