146 BELL SYSTEM TECHNICAL JOURNAL 



efficiency that the receiver would have under this condition, by any 

 method whatever, it is necessary to connect the receiver to a tube hav- 

 ing the same acoustic impedance as a tube of this character. This 

 impedance for a tube 2.45 sq. cm. in area is 16.7 c.g.s. units. A tube 

 of finite length but of the same area will have an impedance of this 

 value provided the sound wave reflected at the far end has a relatively 

 small amplitude when it reaches the sending end. To satisfy this con- 

 dition a tube 50 feet long was terminated in an acoustic resistance 

 unit having an impedance appro.ximately equal to 16.7 +jl6a;-10~'* 

 c.g.s. units. The essential elements of this resistance unit comprised 

 a number of short narrow annular slits; its impedance was determined 

 experimentally by a method described in another paper.* As this im- 

 pedance at low frequencies is practically the same as the characteristic 

 impedance of the tube, the amplitude of the reflected wave in this 

 region is small; at the higher frequencies the reflected wave is atten- 

 uated sufficiently in the 50-foot tube to produce a negligible effect on 

 the sending end impedance. This tube with the resistance unit was 

 connected to the receiver during the following series of measurements. 



Efficiency 



One of the simplest methods of determining the power efficiency 

 of a loud speaker is to measure the electrical impedance, first, when the 

 receiver is in operating condition, and, secondly, when the diaphragm is 

 constrained from moving so that no back e.m.f. is generated. The 

 difference between these impedances is known as the motional im- 

 pedance.^ The resistance component of this motional impedance 

 when multiplied by the square of the current gives the power that is 

 generated by the motion of the diaphragm. If there is a negligible 

 amount of power lost in viscosity and mechanical hysteresis, the ratio 

 of the motional impedance to the free impedance can be taken as the 

 efficiency of the receiver, i.e., the ratio of the acoustic power output to 

 the total power input. This method of measuring efficiency is well 

 known to the art, but for most commercial receivers the efficiency is so 

 low that the motional impedance cannot be determined with a high 

 degree of accuracy over an extended frequency range. However, for 

 this receiver we have had no difficulty in determining the efficiency in 

 this way up to 8,000 p.p.s. The values so obtained are given by the 

 circles in Fig. 7. 



On account of the uncertainty of the magnitude of the mechanical 



^ Wente and Bedell, Bell System Technical Journal, January 1928. 

 ^ Kennelley and Pierce, "The Impedance of Telephone Receivers as Affected by 

 the Motion ol their Diaphragms," Proc. A. A. A. S., Vol. 48, No. 6, September 1912. 



