A METHOD OF MEASURING ACOUSTIC IMPEDANCE 



405 



Since the differential equations of acoustics are analogous to those 

 of electrical lines and networks, the theorem may be applied to the 

 action of this apparatus with a considerable saving in labor.* 



By Thevenin's theorem then, the tube, loud speaker, oscillator, etc. 

 may be replaced by one pressure and one impedance. The pressure is 

 the "open-circuit" pressure at the end of the tube, or in other words 

 the pressure that would be exerted on a rigid wall if placed there. 

 The impedance is the complex ratio of pressure to velocity at the end 

 of the tube which would exist if acoustic energy were sent into it toward 

 the loud speaker, the oscillator being shut off-. In electrical terms, this 

 would be called the impedance looking into the source. The velocity 

 or acoustic current that flows into an impedance attached to the end is 

 then the current that would flow in an analogous circuit composed of 

 this vibromotive force or pressure and the two impedances in series. 

 This impedance diagram is given in Fig. 3. 



Fig. 3 — -Impedance diagram for Thevenin's theorem. 



E is the open-circuit voltage or pressure, T the impedance looking 

 into the source of sound at the junction, and Z the attached impedance. 

 The pressure e at the junction of T and Z is, of course, the velocity- 



current ^ in the loop, multiplied by Z. The three equations for 



three values of attached impedance are 



Z — Zo, 



Z = QO, 



Z = Z, 



ei = 



EZ, 



T + Z,' 



62 = E, 



EZ 



ez = 



T + Z 



The two unknown quantities, E and T, can be eliminated giving one 

 equation 



Z_ 



Zo 



62 



ei 



- 1 



£2 



- 1 



* A more direct proof of Thevenin's theorem as applied to acoustics is given by 

 W. P. Mason in 5. 5. r. /., 6, 291 (1927). 



