84 ACOUSTICAL ELEMENTS 



5.10. Impedance of a Circular Orifice in a Wall of Infinitesimal Thick- 

 ness. — The impedance of a circular orifice in a wall of infinitesimal thick- 

 ness may be considered to be the same as that of the air load upon a piston 

 of infinitesimal thickness and zero mass set in the opening. Then the 

 acoustic impedance of a circular aperture in a thin wall is obtained from 

 equation 5.12 by multiplying by 2. 



5.11. Impedance of an Open Pipe with Large Flanges. — In this case 

 it will be assumed: that the mouths of the pipe are fitted with freely moving 

 massless pistons and that the length of the pipe is small compared to the 

 wavelength. The impedance is the sum of the mass reactance of the air 

 between the pistons and the impedance of the air load upon the pistons. 



The acoustic reactance of the column of air between the two pistons, 



from equation 5.3, is 



p/ 

 ^A = ~^^ 5.17 



where p = density of air, in grams per cubic centimeter, 

 / = length of the pipe, in centimeters, 

 R — radius of the pipe, in centimeters, 

 CO = 27r/", and 



/ = frequency, in cycles per second. 

 The acoustic impedance of the entire system Is 



5.12. Closed Pipe with a Flange. — The impedance of a pipe closed at 

 one end and equipped with a flange at the open end may be considered to 

 be the sum of the impedance of the pipe and the end correction. It will 

 be assumed that the open end of the pipe is equipped with a massless piston. 



The acoustic input impedance at the piston ^" of the above system is 



zao = - ^.cotkl 5.19 



where / = length of the pipe, in centimeters, 

 R = radius of the pipe, in centimeters, 

 p = density, in grams per cubic centimeter, 

 c = velocity of sound, in centimeters per second, 

 k = 27r/X, and 

 X = wavelength, in centimeters. 



12 Olson and Massa, " Applied Acoustics," P. Blakiston's Son and Co., Philadelphia. 



