88 ACOUSTICAL ELEMENTS 



throat are 



PC 2 

 ta = — 5.34 



Sq irkXfiJi^^kxQ) -\- Y-^^kxo)] 



pC Jo{kXo)Ji{kXo) + Yo(kXo)Yi{kXo) 



""^ ~ So Jr'ikxo) + Yi\kxo) 



where Jo, /i = Bessel functions of the first kind of order zero and one, 



Yo, Yi = Bessel functions ^^ of the second kind of order zero and one, 

 p — density of the medium, in grams per cubic centimeter, 

 c = velocity of sound, in centimeters. 

 So = area at Xo, in square centimeters, 

 Xo = distance of the throat from x = 0, in centimeters, 

 k = 27r/X, and 



X = wavelength, in centimeters. 

 5.16. Infinite Conical Horn. — The equation expressing the cross- 

 sectional area as a function of the distance along the axis is, 



S = Sox^ 5.36 



The general horn equation for the conical horn is 



ci>- ^-^2^ = 5.37 



X dx dx^ , 



The velocity potential, pressure and volume current are 



5.38 



5.39 



5.40 



x' 



The real and imaginary components of the acoustic impedance at the 

 throat are 



pc kW c .. 



Ta = — -: T—T 5.41 



Xa 



So 1 + kW 

 pc kXo 



Yo 1 + kw 



5.42 



22 Jahnke and Emde, " Tables of Functions," Teubner, Berlin. 



