III-55 



Silberman made measurements of phase velocity and attenuation for 

 sound traveling through air bubble-water mixtures in vertical pipes. The pipes 

 were made of steel with inside diameters of 2 and 3 inches and lengths of 8 and 

 6 feet, respectively. Because of the small pipe size and the frequencies used, 

 the pipe diameter was less than half a wavelength; consequently the sound could 

 be viewed as plane waves. 



Two configurations of experimental equipment were used. In the first, 

 the pipe was fastened to a base containing the sound generator, and bubbles were 

 introduced by a tube through the base. In the second apparatus, the bottom of 

 the tube was open, and the sound generator was supported independently. Bub- 

 bles were generated by a number of needle orifices positioned outside the tube. 

 The entire apparatus was suspended in a water tank. Problems arising in bubble 

 production were responsible for changing from the first apparatus to the second. 

 With the first, there was considerable difficulty in obtaining bubbles of uniform 

 size and spatial distribution. 



Measurements were made by recording the pressure at various points 

 along the tubes. For standing waves, the pressure at a point x is given by 



, , - -d^ r ,3 ,p X P 2TTf ,, ,li/3 



p(x) = 2e cosh^ a (-t - x) - c 



— (^-x)J 



where 



a = attenuation constant 



-i = length of the column 



f - frequency of the sound 



c = velocity of sound 



Using this equation and the pressure measurements, the experimental 

 attenuation constant can be determined. Phase constants were determined by 

 measuring the half wavelength distances between successive nodes or antinodes, 

 and the phase velocity was calculated from the equation 



= fX 



where A. is the measured wavelength. The effects of elasticity of the pipe wall 

 and of viscosity were small enough to be neglected. Corrections were made to 

 allow for the variation in hydrostatic pressure at various points along the tubes. 



artIiurJl.lLlttlp.3lnt. 



S-7001-0307 



