EX TRA NEO US FREQ UENCIES 



171 



(17) and (19). The attenuation due to viscosity and heat loss in the 

 horn has been neglected. 



A number of measurements at various microphone positions in 

 front of the horn, shown by the dotted circles, indicate the difficulty 

 of obtaining accurate results in a room. The average of the measure- 

 ments at a number of random positions in front of the horn at a con- 

 stant sound power output and the measurements at a single position 

 for various sound outputs gives the plotted curve which is probably 

 not greatly different from that which would be obtained in open air. 



Figure 8 shows the measured and calculated ratios of the second 

 harmonic pressure to the fundamental pressure for various funda- 

 mental frequencies. 



500 600 800 1000 2000 3000 



FUNDAMENTAL FREQUENCY IN CYCLES PER SECOND 



4000 5000 



Fig. 8 — 2nd harmonic generated in an exponential horn vs. fundamental frequency 

 (sound output = 10 watts). 



Demonstration of Extraneous Frequencies 



Almost two hundred years ago Sorge, a German organist, and 

 Tartini, an Italian violinist, discovered independently, apart from all 

 theory, that the union of two loud independent tones produced a 

 difference tone. That this is not entirely a subjective tone produced 

 by the ear but is actually present in the air was demonstrated by 

 others some years later by the use of a tuned resonator. With modern 

 apparatus consisting of power amplifiers, oscillators and tuned electro- 

 mechanical vibrators it is a relatively simple matter to show not only 

 the difference tone but the summation and harmonic tones as well. 



An exponential horn was attached to the open end of the 1566 cm 

 tube previously described but with the damping material removed. 

 A moving coil microphone placed in front of the horn picked up the 

 complex tone produced when two equal pure tones of 600 and 940 



