A method of measuring acoustic impedance

An apparatus is described whereby acoustic impedances may be measured in terms of a known acoustic impedance and the complex ratios of two electrical 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 impedance Z is then calculated in terms of the known acoustic impedance Z
0
by means of the equation
$Z = Z_{0} {z_{1}-z_{2}\over z_{2}\over z_{3}-z_{2}},$
where z
1
, z
2
and z
3
are, respectively, 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, condenser transmitter and amplifiers (provided they are invariable) do not affect 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.