SOUND TRANSMISSION IN TUBES 



97 



A horn consisting of three rates of flare is shown in Fig. 5.8. The im- 

 pedance characteristic at the throat of the small horn is obtained in stages. 

 First, the throat impedance characteristic for the large horn is obtained by 

 using equation 5.53. The throat impedance obtained for the large horn 

 now becomes the mouth impedance of the intermediate horn. The im- 

 pedance of the throat of the intermediate horn is obtained by employing 



(n|o-.9 



Fig. 5.8. Throat acoustic impedance characteristic of a multiple flare exponential horn of 

 three sections. The cutoffs due to flare of the three horns are 25, 100 and 1400 cycles. 

 In this example the impedance is referred to 6"!. r, resistive component at the throat of 

 the small horn, x, reactive component at the throat of the small horn. 



equation 5.53. For the frequency corresponding to ^ = of the inter- 

 mediate horn the impedance at the throat of the intermediate horn becomes 

 indeterminate. The expression can be evaluated as shown in Sec. 5.22 on 

 exponential connectors. Next, the throat impedance at the throat of the 

 small horn is obtained by again employing equation 5.53. The mouth 

 impedance of the small horn is the throat impedance just obtained for the 

 intermediate horn. The impedance characteristic of Fig. 5.8 shows three 

 distinct steps depicting the surge impedance of each section. 



5.24. Sound Transmission in Tubes ^7. 28, 29^ — jj^g effect of viscosity 

 upon the characteristics of small holes and slits was considered in Sees. 5.3 

 and 5.4. The transmission loss in tubes of circular section is of interest 



-^ Crandall, " Vibrating Systems and Sound," D. Van Nostrand Co., New York. 



^* Lamb, " Theory of Sound," E. Arnold, London. 



2^ Raleigh, " Theory of Sound," Macmillan and Co., London. 



