6 BELL SYSTEM TECHNICAL JOURNAL 



of a wave-length before each measurement. A precise determination 

 of the point a quarter of a wave-length from the reflecting surface may 

 be made by placing a smooth metal block at the reflecting end and 

 finding then the position in the tube at which the pressure is a minimum. 

 In the other two methods it is relatively less important that the 

 temperature be maintained constant, for the ratio of pressures is 

 aff'ected very little by any temperature variations. In the third 

 method, where the length of the tube is varied, the expressions for R-i 

 and X^ are the same as in {b), except that in place of the ratio of 

 pressures they involve the square root of this ratio. For small values 

 of pressure ratios the precision is therefore somewhat greater. How- 

 ever, for high values of reflection the ratio becomes very large and 

 great care is required in the experimental set up to prevent errors 

 creeping into the measurements through extraneous vibrations and 

 stray electromotive forces in the measuring circuit. The main ad- 

 vantage of the method in which the pressure at the source only is 

 measured is that a short length of exploring tube is required. If 

 measurements down to a frequency of 60 cycles are made, the tube 

 length must be at least 8 feet. An exploring tube reaching the whole 

 length would ordinarily introduce too much attenuation if it were of 

 sufficiently small bore to prevent resonance effects at the lower fre- 

 quencies. 



Experimental Procedure 



In the case of the experimental results here reported the measure- 

 ments were all made by the method outlined in section (t), i.e., the 

 pressures were measured at the source while the length of the tube was 

 varied. The experimental set up is shown in Fig. 2. A piece of Shelby 



TO AMPLIFIER — 



Fig. 2 — -Diagram of apparatus 



Steel tubing, 9 feet long, of 3" internal diameter, and with 1/4" wall, 

 was fitted with a piston carrying the absorbing material. This piston 

 was made up of a brass tube one foot long with a wall 1/64" thick, the 

 far end of which was closed with a one-inch brass block. To insure the 

 propagation of plane waves and a constant velocity at the source, the 

 diaphragm at D had a diameter of 2J^", and a mass of about 100 

 grams. This was driven with a coil 2" in diameter situated in a radial 

 magnetic field. The annular gap between the edge of the diaphragm 



