TESTING OF LOUD SPEAKERS 267 



factor is imaginary it becomes rather complicated to employ the motional 

 impedance method. 



The efficiency n, in per cent, by the motional impedance method is 

 given by 



^ = '^ X 100 11.13 



Ten 



where Tem = ^en — fsD motional resistance, in ohms, 



J'EN = resistive component with the system in the normal state, in 



ohms, and 

 Ted = damped resistance with the vibrating system blocked, in 



ohms. 



This equation describes the simplest method of determining the effi- 

 ciency from motional impedance measurements when the electromechani- 

 cal coupling factor is real. See Chapters VI, VII and VIII. It assumes 

 that the entire value of the motional resistance may be attributed to 

 radiation resistance. This method adds the radiation from both sides 

 of the diaphragm and, therefore, assumes that the radiation from both 

 sides is useful. It assumes that there are no mechanical losses in the 

 diaphragm and suspension system. These losses can be determined 

 from the measurements of the motional impedance in a vacuum. Of 

 course, in this case, the load on the diaphragm is not normal and the losses 

 may be quite different from those which obtain under actual operating 

 conditions. This method also assumes that there are no losses due to 

 viscous air friction. Since the amplitude of the vibration of a voice coil is 

 normally small at the higher frequencies, the problem of blocking the 

 voice coil against motion is not a simple matter. Obviously, any motion 

 will introduce an error in the determination of the efficiency. 



E. Phase Distortion Characteristic. — The phase distortion character- 

 istic of a loud speaker is a plot of the phase angle between the sound output 

 and some reference sound as a function of the frequency. 



Two microphones and separate amplifiers and a cathode oscillograph 

 may be used as outlined in Sec. 11. 2D, Fig. 11.5. A reference sound may 

 be set up by a separate loud speaker, in which the phase shift is small, 

 and picked up by one microphone. A reference voltage source may be 

 substituted for the reference microphone. The sound from the loud 

 speaker to be tested may be picked up on the other microphone. The phase 

 difference may be determined as outlined in Sec. 11. 2Z). The phase dis- 

 tortion is of importance in the overlap region of the multiple channel sys- 



