No abstract

No abstract

Methods are presented for the calculation of wave forces on a vertically axisymmetric body arbitrarily placed within a channel. Integral representations of singular solutions of the Helmholtz equation, called channel multipoles here, are derived and these allow straightforward solution of the scattering problem for a vertical cylinder extending throughout the depth. In contrast to previous methods there is no need to sum series of images. These multipoles are also used in deriving an approximate solution valid when the radius of the cylinder is small relative to the wavelength and channel width.To solve for arbitrary shaped axisymmetric bodies, a plane-wave approximation is developed based on the assumption that the wavelength is much less than the channel width. Comparisons with the accurate solution for a vertical cylinder suggest that this approximate method performs well even when this assumption is clearly violated. The results of calculations of wave forces on a truncated cylinder are also given.All of the methods described may be applied just as easily to the case of an off-centre body as to a centrally-placed body.

A new method for the observation of ultrasonic field distributions is described, utilizing a starch plate in a dilute solution of iodine in a manner analogous to the use of photographic emulsions. Near-field diffraction patterns are shown as illustrative of results, which appear to be superior to those of other methods, and the advantages of the new method over previous techniques are described. Frequency 1073 kc/sec. Exposure time 1 min at 1.55 amp. Fro. 3. Pattern 2 cm from 2.88-cm diameter transducer, 1073 kc/sec, 2 min at 1.25 amp. FIG. 5. Pattern 5 cm from 2.88-cm diameter transducer, 1073 kc/sec, 10 min at 0.65 amp.Fro. 6. Pattern 3 cm from 1.99-cm diameter transducer, 2390 kc/sec, 3 min at 2.0 amp.

that this jet will often be accompanied by a fine mist of liquid droplets. Figure 1 is a photograph of the mist as it is produced above water by means of a 45-watt beam of 2.4-mc sound waves focused, using the concave surface of a spectacle lens as a reflector.The transducer used was a 1-inch disk of barium titanate ceramic mounted with air backing. The author discovered that if a bar of soap is placed in the water the fog production stops within about Light From Mercury •amp-'•i i' Brass Tube 12_ Oz C• Wate !i ater I"•1 i[ I'•Drop of Cover Gl:];s"•• r'='• Water /M ic roscope 16mm Oblechve FIG. 2. Apparatus used to examine visually and photograph the fog particles. The droplets falling vertically in the draft-free brass tube were viewed and photographed through the water drop at the bottom of the tube.one second and will start again only after the apparatus has been thoroughly rinsed and refilled with fresh water. The waterspout continues after the soap has been placed in the water but it is not accompanied by fog. If the fog is produced or collected in a closed vessel, it becomes so dense that the filament of a flashlight bulb cannot be seen through 10 cm of it. The total transmission of visible light (using an f/8 beam) through 10 cm of such fog has been measured to be less than one-half of one percent.Apparatus arranged as shown in Fig. 2 was used to obtain photomicrographs of the fog droplets so that the distribution of sizes could be determined. The water jacket for keeping the temperature in the inner tube constant was necessary in order to prevent convection currents. Thus particles in the inner tube fell toward the microscope objective under the influence of gravity and air viscosity. The water drop at the bottom of the tube provided an optical surface which the falling droplets could not fog. Illumination from a mercury lamp which passed through heat absorbing glass was applied only for brief periods of time and did not seem to be causing appreciable decrease of droplet size z 5 4 5 6 D•ometer Microns FIG. 3. Size distribution of the ultrasonically produced fog droplets. by evaporation. Five photographs showing 40 droplets in unmistakably good focus were taken at 1/150 sec on 3{X4{-inch film using a conventional photographic attachment to the microscope. Measurements of the images of the droplets on these photographs gave the drop size distribution shown in Fig. 3. This method of obtaining the distribution of drop sizes probably misses some of the smallest drops because a slightly out-of-focus drop appears too big and because the smallest droplets fall slowest and probably evaporate, join larger drops, or are lost on the walls before they can be photographed. ß * This research was supported by the U.S. Office of Naval Research. t Present address: Preliminary data of an extended program on acoustic birefringence are presented, showing the existence of such birefringence in poly-alphamethyl-styrene at a frequency of 1000 kc/sec, and that a linear relation exists between the magnitude of birefringence and t...