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BELL SYSTEM TECHNICAL JOURNAL 



The value of the specific characteristic impedance Pojct/ioo becomes 

 on substituting in the value of a 



If we assume no dissipation, 7' = and Zj^ = -ylPoyp. In any case 

 at fairly high frequencies Z^ approaches V-PoTP. For example, for 

 air in a circular tube 1 centimeter in diameter, Zi^ departs from its 

 final value VAtp by less than 5 per cent at 100 cycles. The attenua- 

 tion constant a increases as the square root of the frequency, while the 

 phase constant b is little affected by the dissipation and at high fre- 

 quencies approaches the value cojC. 



II. Effect of a Junction or of a Change in Area of 

 THE Conducting Tube 



Suppose that we have a straight conducting tube, with a sidebranch 

 as shown in Fig. 1 . Let the excess pressure of the incoming plane wave 



Fig. 1 — An acoustic junction 



be pi. The ordinary assumption is that the width of the junction is 

 small compared with a wave-length and hence the pressure is practically 

 constant in the sidebranch, and main branch over the portion in im- 

 mediate contact with the sidebranch. It states also that the alge- 

 braic sum of the volume displacements at a junction of tubes is zero. 

 If Si is the area of the main conducting tube, S2 the area of the branch 

 tube, ii the linear velocity of the incoming wave in the conducting 

 tube, I2 the linear velocity of the outgoing wave from the junction and 

 77 the linear velocity in the branch tube at the junction, we can write 

 the equation 



^iSi = ^^Si + ^52 or Fi = F2 -f v. 



