ACOUSTIC IMPEDANCE, 15 



It is important that the frequency and the temperature in such a 

 test should be held as nearly constant as possible. The frequency 

 should be near to the resonant frequency f^. If the frequency is 

 remote from the resonant frequency, the mechanic reactance of the 

 diaphragm is likely to be so large that the addition of the acoustic load 

 to be measured will not affect the vector motional impedance materi- 

 ally; whereas at resonance, a small change in added acoustic load will 

 be likely to affect the motional impedance considerably. 



The variations in R and X indicated in Figure 7, represent corre- 

 sponding variations in the electric impedance Z = R -1- j X. These 

 are due to variations in the acoustic impedance Zo, which is the subject 

 of investigation. The curves of R and X in Figure 7, represent total 

 apparent resistance and reactance, in the receiver, at varying air- 

 column lengths. The values Hd and Xd indicated on the left-hand 

 side of the figure, are respectively the damped resistance and react- 

 ance of the receiver at this frequency. With reference to the imped- 

 ance Zd = Rd -f- j Xd, as origin, the values of motional impedance Z', 

 corresponding to the successive air-columns, are plotted vectorially in 

 Figure 8. The numbers marked on this spiral are air-column lengths 

 in cm. It will be seen that at L = cm., or with the piston within 

 1.5 mm. of the diaphragm, the motional impedance was 12.5^ 75 ?4 

 ohms. This value was nearly repeated with L — 19 cm. At L = 10 

 cm., however, the motional impedance had increased to 142. S'V 42.1 

 ohms. The curve is a slowly contracting spiral, with a pitch of 18.7 

 cm., which is half a wave length at 921 <>5 ; since the velocity of sound 

 at 20°C being 34,430 cm. per sec, the wave length X = 34,430/921 = 

 37.38 cm. 



In order to utilize the motional-impedance diagram of Figure 8 for 

 determining the acoustic impedance of the load in front of the receiver 

 diaphragm, we may refer to equations (16) and (19). Equation (16) 

 shows that we must find Y', the vector reciprocal of the motional 

 impedance, and multiply by the square of the vector constant A of the 

 receiver, in order to derive the total mechanic impedance z' on the 

 diaphragm. This means that we must invert the diagram of Figure 8, 

 or find the locus of the reciprocal spiral. 



If we operate upon the graph of motional admittance by the vector 

 factor A2, where A = 5.138 X 10« V 27!8 (the value measured for 

 this particular receiver)^; i.e., multiplying each vector admittance 



9 In order to determine the value of the vector force factor A, it is necessary 

 to measure the amphtude of receiver diaphragm vibration at resonance, as has 

 been described in preceding papers, Bibhography 9. 



