24 ACOUSTICAL RADIATING SYSTEMS 



The total power, in ergs, emitted by a doublet source is 



P = ff^ dS 2.20 



J J pc 



where p = pressure, in dynes per square centimeter, 

 p = density, in grams per cubic centimeter, 

 c = velocity of sound, in centimeters per second, and 

 dS — area, in square centimeters, over which the pressure is ^. 

 Taking the value of p from equation 2.9 (for r very large) the total 

 average power in ergs per second emitted by a doublet source is 



Pt = Lirr- I cos-^ a sm a da 2.21 



Jo 2r2 



Pt = lirpck^A^ 2.22 



where p = density, in grams per cubic centimeter, 

 k = 27r/X, 



X = wavelength, in centimeters, 



c = velocity of sound, in centimeters per second, and 

 A is defined in the first paragraph of this section. 

 The power output from a simple source (equation 2.6) is proportional 

 to the square of the frequency, while the power output from a doublet 

 source (equation 2.22) is proportional to the fourth power of the frequency. 

 For this reason the power output of a direct radiator loud speaker falls off 

 rapidly with frequency when the dimensions of the baffle are small com- 

 pared to the wavelength. See Sec. 7.7. 



2.4. Straight Line Source. — A straight line source may be made 

 up of a large number of points of equal intensity on a line separated by 

 equal and very small distances. The directional characteristic^'^-'^' of such 

 a line is 



'rnrd 

 sm I si 



in a ) 



1 — sm « I 

 \X / 



Ra = -7—, T 2.23 



n sin 



where Ra = ratio of the pressure for an angle a to the pressure for an 

 angle a = 0. The direction a = is normal to the line, 



5 Wolff, I., and Maker, L., Acous. Soc. Amer., Vol. 2, No. 2, p. 201, 1930. 



6 Stenzel, H., Elek. Nach. Tech., Vol. 4, No. 6, p. 239, 1927. 



7 Stenzel, H., Elek. Nach. Tech., Vol. 6, No. 5, p. 165, 1929. 



