THROAT IMPEDANCE CHARACTERISTICS 89 



where ^o = area at Xo, in square centimeters, 



xo = distance of throat from ;c = 0, in centimeters, 

 k = Itt/X, and 



X = wavelength, in centimeters. 

 5.17. Infinite Exponential Horn. — The equation expressing the cross- 

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



S = ^oe"*« 5.43 



where So = area at the throat, that is ;^ = 0, and 

 m = flaring constant. c3 — 

 The general horn equation for the exponential horn is 



(j) — c^m r — = 5.44 



dx dx^ 



The velocity potential, pressure and volume current are 



^ _ ^-(W2).[^,-.- 2 ^^Je^"' 5.45 



p = - ycope-<-/2) X ^j^-j 2 =^J e^"' 5.46 



U = - AS 



/4F _ j^2l _ rn 



m . /4^^ — 7n'^ I w„ , vw-m-^ ^ ^ ._^^ ^^^j 



The real and imaginary components of the acoustic impedance at the 

 throat are 



pc I m 



^^ = ^V'-4F "^ 



pc m 

 So 2k 



When m = 2k or 2Trf = mc the acoustic resistance is zero. This is 

 termed the cutoff frequency of the exponential horn. 



5.18. Throat Impedance Characteristics of Infinite Parabolic Conical 

 and Exponential Horns. — From the equations derived in Sees. 5.15, 5.16 

 and 5.17 the impedance characteristics of infinite horns may be computed. 

 In order to compare the characteristics of the infinite parabolic, conical 

 and exponential horns the throat area has been chosen the same for the 

 three horns (Fig. 5.3). In addition, the area at a distance of 100 centi- 



