272 



MEASUREMENTS 



The loud speakers are connected to two pipes, one of which is variable in 

 length and the other equipped with a means for attaching the unknown 

 impedance. At some distance beyond this point the two pipes are joined 

 by a small pipe which, in turn, is connected to another pipe leading to a 

 microphone and amplifier. Standing waves in the pipes are reduced by 

 the introduction of small tufts of felt. 



With the branch closed the voltage across the two loud speaker units 



,TUFTS or FELTv 



UNKNOWN 

 IMPEDANCE 



lQ 



jS^Kth m && ©"ffl ^ tS"'fe> Q <i9 &T!i t-S "^ eg ^ (MW' ^Sfc'ml^ 



ATTENUATORS . 



:ri)= 8 AMPLIFIER ~S?ETERJ 



OSCILLATOR 



MICROPHONE 



TELESCOPIC TUBING 



I iii'Tiii 



°nM LOUD SPEAKER 



UNIT 



Fig. 11.16. Schematic arrangement of an acoustic impedance bridge for measuring imped- 

 ance. (After Stewart.) 



and the length of the variable tube are adjusted until a minimum reading 

 is obtained in the output meter. The unknown impedance is now attached 

 and the process repeated. 



The unknown impedance can be obtained from the following equation 



2zau _ po 

 Izau + Ta P^ 



; (cos 6 + j sin d) 



11.14 



where Zau = unknown impedance, in acoustic ohms, 



fA = pc/^ acoustic resistance of the damped pipe, in acoustic 



ohms, 

 ^ = area of the pipe to which the branch is attached, in square 



centimeters, 

 p = density of air, in grams per cubic centimeter, and 

 c = velocity of sound, in centimeters per second. 

 The ratio po/po' can be determined from the following equation 



1^ 



£l£2_ 



11.15 



where ei and ^2 = the voltages applied to the loud speaker without the 

 branch, and 

 ei and ^2' = the voltages with the branch attached. 



