94 ACOUSTICAL ELEMENTS 



Fig. 5.5/f . For example, the first maximum in the resistance characteristic 

 is 150 times the resistance of the succeeding minimum. 



By doubling the diameter of the mouth the maximum variation in the 

 resistance characteristic is 7.5, Fig. 5. SB. 



Figure 5.5C shows the impedance characteristic of a horn with a mouth 

 diameter of 30 inches. The maximum variation in the resistance charac- 

 teristic of this horn is 2. 



The impedance characteristic of a horn with a mouth diameter of 40 

 inches, Fig. 5.5D, shows a deviation in resistance of only a few per cent 

 from that of the infinite horn of Fig. 5.5E. 



These results show that as the change in impedance in passing from the 

 mouth to the free atmosphere becomes smaller by employing a mouth 

 diameter comparable to the wavelength, the reflection becomes corre- 

 spondingly less and the variations in the impedance characteristic are 

 reduced. 



The throat acoustic impedance characteristic as a function of the throat 

 size with the mouth and flare held constant is of interest in determining the 

 optimum length and a suitable matching impedance for the driving mecha- 

 nism. The impedance characteristics of four horns having a cutoff of 100 

 cycles, mouth diameter of 20 inches and throat diameter of 1, 2, 4 and 8 

 inches are shown in Fig. 5.6. A consideration of these characteristics shows 

 that the throat size has no appreciable effect upon the amplitude of the 

 variations in the impedance characteristics. However, the separation in 

 frequency between successive maxima is increased, as the throat becomes 

 larger, due to the decreased length of the horn. The frequency at which 

 the first maximum in the resistance characteristic occurs becomes progres- 

 sively higher as the length is decreased. 



5.22. Exponential Connectors. — A transformer is used in electrical 

 circuits to transfer between two impedances of different values without 

 appreciable reflection loss. In acoustical systems a horn may be used to 

 transfer from one impedance to another. As a matter of fact a horn may 

 be looked upon as an acoustical transformer, transforming large pressures 

 and small volume currents to small pressures and large volume currents. 

 It is the purpose of this section to show how an exponential horn or con- 

 nector may be used to transfer from one impedance to another. 



Figure 5.7 shows an exponential horn coupled to an infinite tube. The 

 acoustic impedance of an infinite tube is 



f 5.55 



02 



