172 BELL SYSTEM TECHNICAL JOURNAL 



c.p.s. were impressed on the air. The microphone voltage was 

 ampHfied and impressed on six torsional vibrators tuned to 340, 600, 

 940, 1200, 1540 and 1880 c.p.s. Spherical mirrors attached to the 

 vibrators produced on a screen bands of light the amplitudes of which 

 were approximately proportional to the relative pressures of the 

 various frequencies in the complex tone. 



For the higher power inputs to the loud speaker used in the experi- 

 ment, the presence of the sum and difference frequencies and the har- 

 monic frequencies was easily observed. At these power outputs the 

 quality of the sound was very disagreeable and the fundamental tones 

 could hardly be distinguished. 



Conclusion 



The theoretical and experimental determinations of the extraneous 

 frequency waves generated in the air within a tube are in good agree- 

 ment as regards the variation in magnitude with frequency, distance 

 from the source and magnitude of the primary tones. The magnitude 

 of the second harmonic is very nearly proportional to the distance 

 from the source, to the fundamental frequency and to the square of 

 the amplitude of the fundamental pressure. When there are two 

 primary tones, the extraneous frequencies generated in the air include, 

 as well as the harmonics of the primary tones, frequencies which are, 

 respectively, the sum and the difference of the primary frequencies 

 and also other higher order tones. The magnitudes of the summation 

 and difference tones are very nearly proportional to the distance from 

 the source, to the product of the magnitudes of the two primary 

 pressures, and in each case, to the frequency of the particular com- 

 bination tone. As regards the absolute magnitudes of the generated 

 tones in the tube all of the measured values are about 3 db lower 

 than the theoretical values. 



Good agreement was obtained also between the experimental and 

 theoretical determinations of the second harmonic generated in the air 

 within an exponential horn, as regards proportionality to the funda- 

 mental frequency and power and also as to absolute magnitude. In 

 fact the agreement in absolute magnitude was closer for the horn than 

 for the tube, but not much significance should be attached to this fact, 

 as the horn theory is developed from the theoretical solution for the 

 tube and the horn measurements are known to be less reliable than 

 the tube measurements, 



