EXPONENTIAL HORNS 31 



source or a vibrating piston may be used to predict approximately the 

 directional characteristics of a direct radiator loud speaker. 



2.8. Exponential Horns. — The directional characteristics of a horn de- 

 pend upon the shape, mouth opening and the frequency. It is the purpose of 

 this section to examine and consider some of the factors which influence 

 the directional characteristics of a horn. 



The phase and particle velocity of the various incremental areas which 

 may be considered to constitute the mouth determines the directional 

 characteristics of the horn. The particular complexion of the velocities 

 and phase of these areas is governed bv the flare and dimensions and shape 

 of the mouth. In these considerations the mouth will be of circular cross 

 section and mounted in a large flat baflle. The mouth of the horn plays 

 a major role in determining the directional characteristics in the range 

 where the wavelength is greater than the mouth diameter. The flare is 

 the major factor in determining the directional characteristics in the range 

 where the wavelength is less than the mouth diameter. 



Figure 2.9 shows the effect of the diameter of the moutn for a constant 

 flare upon the directional characteristics ^^'^- of an exponential horn. At 

 the side of each polar diagram is the diameter of a vibrating piston which 

 will yield approximately the same directional characteristic. It will be 

 seen that up to the frequency at which the wavelength becomes compa- 

 rable to the mouth diameter, the directional characteristics are practically 

 the same as those of a piston of the size of the mouth. Above this fre- 

 quency the directional characteristics are practically independent of the 

 mouth size and appear to be governed primarily by the flare. 



To further illustrate the relative effects of the mouth and flare, Fig. 2.10 

 shows the effect of different rates of flare, for a constant mouth diameter, 

 upon the directional characteristics ot an exponential horn. These results 

 also show that for the wavelengths larger than the mouth diameter, the 

 directional characteristics are approximately the same as those of a vibrat- 

 ing piston of the same size as the mouth. Above this frequency the 

 directional characteristics are broader than that obtained from a piston 

 the size of the mouth. From another point of view, the diameter of the 



13 Olson, H. F., RCA Rede^, Vol. 1, No. 4, p. 68, 1937. 



^■* Goldman, S., Jour. Aeons. Soc. A-rner., Vol. 5, p. 181, 1934, reports the results 

 of an investigation upon the directional characteristics of exponential horns at 

 15,000 and 25,000 cycles. A comparison can be made with the results shown in 

 Figs. 2.9 and 2.10 by increasing the dimensions of the horns used by him to con- 

 form with those shown here and decreasing the frequency by the factor of increase 

 in dimensions. Such a comparison shows remarkable agreement between the two 

 sets of data. 



