Francis E. Fox

Gas Bubbles with Organic Skin as Cavitation Nuclei

The hypothesis discussed that the cavitation nuclei consist in gas bubbles. Due to surface tension, small bubbles would dissolve in a very short time. If the bubbles are larger than 5×10−3 cm, or if the liquid is supersaturated, they may last longer or even be stable, but then no cavitation threshold exists.The hypothesis expressed that the nuclei are very small bubbles, stabilized by an organic skin, which mechanically prevents loss of gas by diffusion. The cavitation occurs when the skin breaks and the threshold is determined by the breaking strength of the film and the size of the bubble.

Phase Velocity and Absorption Measurements in Water Containing Air Bubbles

The phase velocity and absorption of a continuous train of sound waves in water containing air bubbles were measured as functions of frequency from 10 kc/sec to 1 mc/sec. The data are in fairly good agreement with theories by Meyer and Skudrzyk and Carstensen and Foldy. For the bubbles investigated which constituted 0.02 percent of the volume, phase velocity varied from 500 m/sec to 2500 m/sec and peak absorption was over 30 db/cm.

Experimental Investigation of Ultrasonic Intensity Gain in Water Due to Concave Reflectors

This paper discusses a method of producing high intensity sound waves in liquids. A beam of ultrasonic waves (4.25 mc, 15 × 12 mm cross section, acoustic power≃2 watts) was focused with an ordinary watch glass (6.8 cm radius of curvature). The intensity in the focal region is large enough to raise an ultrasonic fountain 10 cm high accompanied by a spray of fog droplets. The distribution of intensity in the focal region was determined by measuring the screening effect of properly placed obstacles. The sound intensity in the focal region and in the plane wave was measured by the radiation pressure on beads of convenient size. The absolute intensity in the plane wave was also calculated from the driving potential and the measured mechanical Q of the crystal, and reasonable agreement was found with the direct measurement. A gain in intensity by a factor of about 70 was measured where simple diffraction theory predicts 74. For the highest voltages used the extrapolated negative peak pressure was 41 atmospheres...

Ultrasonic Absorption in Water

The coefficient of absorption (2αν−2) of ultrasonic waves was measured by a radiation pressure method at frequencies from 7 to 50 Mc. The average value is given for each frequency. These cluster closely around 43.1 × 10−17, and there is no indication of a drop in 2αν−2. Errors entering into absorption measurements are discussed.

Ultrasonic Dispersion in Water Solutions of Magnesium Sulfate

In a dispersive medium the relative phases of the components of a complex sound wave change with path length. The present article describes a method of measuring dispersion in which the change in relative phases of a complex wave consisting of a fundamental and a selected harmonic are measured as a function of the path length. Sensitivities, in measuring difference in velocity, of one part in 105 with a probable error of 3 parts in 105 were obtained experimentally. Dispersion measurements made in water solutions ofMgSO4 below one megacycle show linear dependence upon concentration up to 0.5 mole per liter and agree with those calculated from absorption data. The data indicate total dispersion of 13.6×10−4 per mole per liter, with a relaxation frequency of 160 kc at 24°C.

Resonant Acoustic Interferometry with Air‐Liquid Reflecting Surface

An ultrasonic interferometer has been developed using an air‐liquid surface as a reflector. Because of certain simplifications that occur, it is found advisable to recast the mathematical interpretation of the results along different lines than previously. The effect of a loaded piezoelectric crystal at resonance is taken as a variable resistance, and the measured values of this resistance are interpreted to calculate absorption in the liquid.

An Ultrasonic Stroboscope for Measuring Sound Wave‐Length in Liquids

A stroboscopic method discussed by Bar for using a sound wave as a light shutter and viewing the same wave train with the modulated light is modified so as to permit observations to be made with a very simple optical system without lenses. This results in a method of measuring relative or absolute acoustic wave‐lengths in liquids with a precision limited only by that of measuring lengths of the order of a meter and the spacing of lines on a photographic plate.

Theory of Ultrasonic Intensity Gain Due to Concave Reflectors

A concave reflector can be used to concentrate a beam of plane ultrasonic waves in the focal region, where the intensity If is much larger than the intensity Ii in the plane wave. When the sound wave‐length is small compared to the dimensions of the beam and reflector, one can use the well‐known Fraunhofer diffraction formulas to calculate the intensity gain, i.e., If/Ii. Expressions are derived for the maximum and average intensity gain in the zero‐order image when the ultrasonic beam is circular or rectangular, together with formulas giving the total intensity falling upon circular or rectangular areas of arbitrary dimensions in the focal region.

Ultrasonic Absorption in Magnesium Sulfate Solutions

The ultrasonic absorption coefficients in water solutions of magnesium sulfate were measured at 30 Mc as a function of temperature and concentration. Temperatures from 0 to 30°C and concentrations from 0.05 to 2.00 molarity were used. Measured data were used to calculate Q, the absorption cross section per molecule of magnesium sulfate at several temperatures. Q is defined by (2αM/ν2)/N where N is the number of molecules of magnesium sulfate per cc, ν is the frequency, and αM is the amplitude absorption coefficient caused by the magnesium sulfate. These are constant for concentrations up to 1‐molarity but decrease by 50 percent for 2‐molarity concentration. The constant values of Q×1037, 25 at 25°C, 30 at 20°C and 37 at 15°C indicate an activation energy for the magnesium sulfate absorption process at 30 Mc of 6.8 kcal/mole°K.

An Ultrasonic Source of Improved Design: Optical Studies of Ultrasonic Waves in Liquids

After discussing the production of sound radiation suitable for ultrasonic interferometry in liquid media, a source is described in which a piezoelectric quartz plate mounted at a nodal plane for its principal vibration mode has one vibrating face exposed directly to the liquid media so that its motion may approximate that of a piston radiating into a semi‐infinite medium. A review is given of some of the optical methods using continuous illumination that can be used in the investigation of ultrasonic radiation fields in liquids. Both progressive and standing sound wave systems are used with plane and divergent light. Photographs are included and bring out in a striking manner phenomena discussed in optics and acoustics.