170 



BELL SYSTEM TECHNICAL JOURNAL 



where 



x' = (1 - e-"'^'^)l{ml2). 



(20) 



Equations (19) and (20) indicate that the second harmonic at the 

 mouth of an exponential horn of length x is equivalent to the second 

 harmonic at the end of a tube of length x' and of uniform section, 

 equal to the area of the throat of the horn. Thus the second harmonic 

 in the mouth of a horn having an index of taper m — 0.075 cm~\ cut- 

 off frequency 200 c.p.s. and length 78 cm is equal to the second har- 

 monic at the end of a straight tube 25 cm long and of the same diameter 

 as the throat of the horn. 



Exponential Horn Measurements 



Measurements of the output of a horn attached to a moving coil 

 receiver were made in an acoustically damped room. The horn had a 

 throat diameter of 3.8 cm, a length of 78 cm and a cut-off frequency of 

 200 c.p.s. The diaphragm of the loud speaker was coupled to the 

 throat of the horn through a straight tube 13 cm long. A filtered 

 single frequency tone was impressed on the loud speaker and the sound 

 was picked up by a small microphone in front of the horn. The funda- 

 mental and second harmonic voltages from the microphone amplifier 

 were separated by means of a band-pass filter and measured. 



The approximate acoustic power at the throat of the horn was 

 calculated from the known efficiency of the loud speaker and the 

 electrical voltage and current supplied. 



The measured and calculated ratios of the second harmonic pressure 

 to the fundamental pressure at the mouth of the horn, including the 

 effects of generation of second harmonic in both the horn and the 

 straight tube coupling the receiver and the throat of the horn, are 

 shown in Fig. 7 in terms of the sound output in watts. See equations 



0.3 0.4 0.5 0.6 0.8 1.0 2 3 4 5 6 



SOUND OUTPUT IN WATTS 



Fig. 7 — 2nd harmonic generated in an exponential horn vs. sound output. 



