Direct Absolute Measurement of Acoustic Impedance

The uniqueness of this method of measuring acoustic impedance (ratio of pressure to volume-current, lies in the fact that it involves the measurement of no other mechanical impedance, such as that of a telephone diaphragm. The computations involve values of the acoustic frequency and of the density of an sound velocity in the medium (air in this instance), and these are assumed to be known with sufficient accuracy. The only observations actually made are the readings of a centimeter scale and of relative resistances, and the disappearance of audible intensity. All measurements can thus be referred to units of mass, length and time. The method is based upon the knowledge of the effect of acoustic impedance upon the incident wave when inserted as a branch of an acoustic conduit.Theory.---With the impedance as a branch the values of its two components can be ascertained by Z₁=(ρa2S)·A(A²+B²) and Z₂=(ρa2S)·B(A²+B²) wherein ρ and a are the density of and velocity of sound in the medium, S, is the area of the conduit and A and B are known functions of the incident and transmitted pressure amplitudes and of the difference of phase between them.Method.---A common source actuated two telephone receivers, one serving as a source of sound and the other as a comparison instrument. The apparatus was so constructed that the transmitted wave was matched in intensity by one from the comparison receiver. This was done by reducing the effect of the addition of the two waves at the ears to zero. The adjustment enabled the phase relation to be measured at the same time.Application.---Illustrations are given of the accuracy obtainable by measuring Z₁ and Z₂ for an orifice, a Helmholtz resonator and an infinite tube. Satisfactory comparisons are made with the theoretical values. The components of a conical horn are also given. The method can be used for any sort of acoustical impedance in a fluid medium and is simple, direct and accurate.