HORNS 



85 



The above equation is the impedance of a closed pipe when there is no 

 end correction as, for example, when the pipe is used in a closed system. 



When the open end is free and terminated in a large baffle the total 

 acoustic impedance is the sum of equations 5.12 and 5.19, 



2pc 



Zat 



wp 



kR ) •' lirR'k^ 



PC 



K,{2kR) -j-^^cotkl 



5.20 



The ratio of the pressure at the closed end of the tube to the free space 

 pressure is useful in predicting the performance of pipes and cavities. 

 The ratio of the pressure at the closed end to that in free space is 



cos kl — 



wR' 

 pc 



Xa sin kl 



+ — — TT ^4 sm^ k/ 



5.21 



where p = pressure at the closed end, and 



po = pressure in free space ta and Xa of equation 5.12. 





-f 



/_ / °<=3^>— ■\\ 



Fig. 5.2. Ratio of the pressure at the bottom of a cylindrical cavity to the free space pressure 



in the incident sound wave. 



The characteristics of Fig. 5.2 depict the ratio of the pressure at the 

 closed end to that in free space as a function of the dimensions of the cavity 

 and the wavelength. 



5.13. Horns. — A horn is an acoustic transducer consisting of a tube of 

 varying sectional area. Horns have been widely used for centuries for 



