A Method of Measuring Acoustic Impedance * 



By P. B. FLANDERS 



An apparatus is described whereby acoustic impedances may be measured 

 in terms of a known acoustic impedance and the complex ratios of two elec- 

 trical potentiometer readings to a third. As a known impedance, there is 

 chosen the reactance of a closed tube of uniform bore which is an eighth 

 wave-length long. The electrical readings are obtained by balancing the 

 amplified output of a condenser transmitter against the electrical input of 

 the source of sound. The condenser transmitter picks up the acoustic 

 pressure at the junction of the sound-source and the attached impedance. 

 A balance is made for each of three successively attached impedances: (1) 

 a closed tube an eighth wave-length long, (2) a rigid closure of the sound- 

 source, and (3) the impedance to be measured. The unknown acoustic im- 

 pedance Z is then calculated in terms of the known acoustic impedance Zo 



by means of the equation Z = Zo , where 3i, Z2 and 23 are, respectively, 



23—22 



the three electrical impedance settings of the potentiometer. As indicated 

 by this equation, the constants of the electrical circuit are involved only as 

 ratios, so that the response characteristics of the source of the sound, con- 

 denser transmitter and amplifiers (provided they are invariable) do not afifect 

 the measurement. 



Illustrations are given of impedance measurements on a closed tube of 

 uniform bore, a conical horn, an exponential horn, an " infinite " tube, and a 

 hole in an " infinite " wall. 



THE progress in acoustics during the past few years has caused 

 acoustic impedance measurement to have the same relative 

 importance that impedance measurement in electrical work has had 

 for many years. The concept of acoustic impedance is derived from 

 the analogy ^ that exists between electrical and acoustic devices, as 

 shown by the analogous differential equations describing their action. 

 Acoustic impedance is usually defined as the complex ratio of pressure 

 to volume velocity (or flux) but it is sometimes more convenient to 

 deal with ratios of pressure to linear velocity or force to linear velocity. 

 The magnitudes of these are interrelated, of course, by powers of the 

 area involved. 



The earliest efforts to measure acoustic impedance seem to have been 

 made by Kennelly and Kurokawa.^ In their method, electrical 

 measurements were made of the motional impedance of a telephone 

 receiver, with and without an attached acoustic impedance. Except 

 for frequencies near resonance, the method was inaccurate because 

 the acoustic impedance was associated with a relatively large mechani- 

 cal impedance. 



* Presented before Acous. Soc. Amer., New York City, May 3, 1932. 



1 This analogy was first pointed out by A. G. Webster in Nat. Acad, of Science, 5, 

 275 (1919). 



2 Proc. Am. Ac. Arts and Sc, 56, 1 (1921). 



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