THE MEASUREMENT OF ACOUSTIC IMPEDANCE 



(a) Pressure Measured at Two Points in the Tube 



It has already been pointed out that the impedance Z2 can be deter- 

 mined if the relative phase and magnitude of the pressures at any two 

 points in the tube are known. However, from the standpoint of con- 

 venience and precision it appears best to measure the pressures at the 

 reflecting surface and at a point a quarter of a wave-length away. We 

 then have at the reflecting surface x = I and 



P2 = Rki 



i?2 + iX2 



R cos jS/ + iZi sin /3/ 



and for the point x = I — -^ = I 



so that 



Hence 



Pi 



IT 



iR 



R cos jS/ -f iZ2 sin ^l 

 X2 - iRi 



]• 



R 



Ae"^. 



R2 = 



X2 = 



AR sin (pA 

 AR cos (f, y 

 AR. J 



If the coefficient of reflection is expressed as * 



/^ i* _ ^2 ~ R 



" 1 -f 2^ sin ^ + ^^ 

 _ 1 — 2^ sin ^ + A'^ _ 



we get 



C = 



where 



(f = tan 



_j 2A cos (f 

 A^ + 1 



(3) 



(4) 



(5) 



The absorption coefficient, which is generally defined as the ratio of 

 absorbed to incident power, is equal to 1 — \C\-. 



{b) Tube of Constant Length; the A bsolute Value of the Pressure Measured 

 at Points along the Tube 



The method discussed under this section is that adopted by H. O. 

 Taylor for measuring the absorption coefficient of porous materials. 

 ^ I. B. Crandall, "Theory of Vibrating Systems and Sound," page 168. 



