90 



ACOUSTICAL ELEMENTS 



meters from the throat has been made the same for the three horns as 

 shown in Fig, 5.3. The resistance and reactance characteristics for all 

 three horns are shown in Fig. 5.3. 



•l-l- 



oo .6 

 zz 



THROAT AREA 

 I SQ.CM. 



AREA = too SO. CM. 



1 PARABOLIC 



2 CONICAL 



3 EXPONENTIAL 



Fig. 5.3. Throat resistance r, and reactance ^, of infinite parabolic, conical and exponential 

 horns having the same throat area and the same cross section at a distance of 100 centi- 

 meters from the throat. 



5.19. Finite Conical Horn 2^. — The horns most commonly used for 

 sound reproduction are the conical and the exponential. Therefore, the 

 consideration of finite horns will be confined to these two types. 



The expression for the throat impedance of the conical horn is 



Zyll= — 



^1 



z AiSikhl CO?, \k{l — h)\ + {jpwhl — 2^2^2'^) sin [k{l — //)] 

 f/pco/ - 2^2^2(1 + kVh) sm[k{l - h)] +jpo:klh ~Y 

 \ -\-ZA2S2W- h)cosk{l~ h)\ 



5.50 



where Si = area, of the throat, in square centimeters, 

 *S'2 = area of the mouth, in square centimeters, 

 k = 27r/X, 



X = wavelength, in centimeters, 



/ = distance from the apex to the mouth, in centimeters, 

 CO = lirf, 

 f = frequency, in cycles per second, 



Olson, H. F., RC J Review, Vol. 1, No. 4, p. 68, 1937. 



