ACOUSTIC IMPEDANCE. 19 



28.35, 47.05 cm., the impedance should be a minimum, and should fall 

 on the same axis, nearer to A. All these requirements are fairly well 

 met in the diagram of Figure 9. 



It is thus possible, by making purely electrical measurements of the 

 motional impedance of a telephone receiver, to arri^'c at the cor- 

 responding variations in acoustic impedance, when the acoustic load 

 is ^•aried, at constant impressed frequency. In the case of a simple 

 air tube of \'aried length, the acoustic impedance appears to follow 

 substantially the same quantitative behavior as the electric imped- 

 atice of an alternating-current line of correspondingly varied length. 



In the case of an electric line, we can always determine the \'alues 

 of the line angle d and the surge impedance z^, at a point, by succes- 

 sively grounding and freeing the line at the distant end, and measur- 

 ing the corresponding impedance Z„.i and Z/^ at the home end A. 

 The ratio of these two impedances is tanh-^^ and their product is Zo. 

 In the case of a tube or acoustic line, we can approximately free the 

 line, by plugging the tube at the far end with a smooth hard plug, 

 which is designed to serve as a perfect sound reflector; but no means 

 are at present available for "grounding" the acoustic line. With the 

 tube wide open at the distant end, there is still an appreciable acoustic 

 impedance in and beyond the open end. If the tube opens into a 

 room or walled space, this terminal acoustic impedance will, in general, 

 possess some reactance due to reflections from the walls; but if the 

 tube terminates in the open air, the terminal acoustic impedance is 

 likely to have only a small reactive component or slope. If the 

 amount of the terminal acoustic impedance a of a tube opening out of 

 doors, could be ascertained from the geometry of the tube, it would be 

 readily possible to compute d and z^ from the acoustic impedance Z/.4 

 with the distant end plugged, and Z^4 with the distant end open to the 

 free air. Until a can be satisfactorily predetermined, it will be neces- 

 sary to measure d and z^ by indirect electrical methods, and to deter- 

 mine (T from the differences between Z/i and Z^a- Such investiga- 

 tions might lead to the experimental determination of cr, the open-end 

 terminal acoustic impedance of a tube of given dimensions. 



Kfccfs of different Apertarcfi at the Far End of the Tube on the Acoudic 

 Impedance at the Sending End: Figure 10 shows several motional 

 impedance diagrams for the case of a fixed length of the same air- 

 tube (87.8 cm.), each diagram being taken at constant impressed 

 frequency, and with different sizes of circular aperture in the plug at 

 the distant end of the tube. The tube was closed with a flat slab of 

 fiber 0.62 cm. thick, (^ircular holes marked Nos. 1, 2, 3, and 4 were 



