Ultrasonic Plane Wave Research Articles

The influence of progressive light diffraction in Debye-Sears phenomena

Two previous theories of Debye-Sears diffraction of light by plane ultrasonic waves are summarized. The theories assume that significant modulation of the light wave occurs in both phase and amplitude. In our own approach account is taken of both curvature of the light rays inside the ultrasonic beam and diffraction of the system alone at the exit plane, neglecting any diffraction effect in the liquid itself. In the Hargrove's method progressive diffraction in the medium is considered. Results from these theories are compared with experimental data obtained at a frequency of 5 MHz with ultrasonic waves having large amplitude and beamwidth (50 mm).

Propagation of ultrasonic waves in a piezoresistive and piezoelectric medium

The propagation of an ultrasonic plane wave in a piezoresistive and piezoelectric medium subject to a d.c. current is studies in two typical cases : (1) Propagation along the d.c. current (longitudinal case); (2) Propagation normal to the d.c. current (transverse case). It is shown that in both configurations the propagation constant is modified by piezoresistive effect. However, in the longitudinal case, the piezoresistive coupling is generally small compared to the usual field coupling. Specific cases are discussed in which the piezoresistive coupling may be of practical interest.

Analysis of the Liquid Surface Motion in Liquid Surface Acoustical Holography

A linear partial differential equation is obtained that describes the motion of a liquid surface when impinged upon by pulsed ultrasonic waves. The case of two pulsed plane ultrasonic waves incident upon the liquid surface over the same area at equal but opposite angles is treated. A particular solution of the equation is obtained and separated into a ripple displacement superimposed on a uniform displacement, both of which oscillate. Numerical values of frequencies of oscillation and displacements are obtained for various liquids. The theoretical analysis is compared with experimental results. In addition, the transfer function relating the liquid surface displacement to the acoustic radiation pressure, and the scattering coefficient, for the light reflected from the liquid surface as a function of surface displacement, are obtained.

Successive Diffraction Theory for Diffraction of Light by Ultrasonic Waves of Arbitrary Waveform

A theory is developed for the diffraction of light by arbitrary, periodic, ultrasonic plane waves of sufficiently high frequency, large amplitude, and/or beamwidth that significant refraction of light occurs within the ultrasonic beam and that the Raman-Nath approach is no longer applicable. Under such conditions, the emerging-light wavefront is significantly amplitude-modulated in addition to the phase-modulation considered in the Raman-Nath approach. The final diffraction spectrum is considered to result from N successive diffractions by N adjacent sections of the ultrasonic beam. The results are expressed in a form suitable for computation by iterations using a high-speed computer.

Mode conversion of ultrasonic waves at flat boundaries

The energy partition between reflected and refracted plane ultrasonic waves at water-solid and solid-water boundaries is considered. Some general features are discussed and applications of the results to velocity measurements are pointed out. Results of calculations for a Plexiglas-water boundary show that the curves one obtains are quite dissimilar if one either considers or neglects the shear wave in the Plexiglas.

Interference Patterns of Ultrasonic Optical Gratings*

In general, a medium disturbed by plane ultrasonic waves becomes a combined amplitude and phase grating for the light passing through this medium. A theory for the interference pattern in the Fresnel region is developed in terms of the light wavefront emerging from any arbitrary periodic grating. The images formed in the Fresnel field repeat at regular distances. The periodicities of these images are discussed for all periodic gratings.

Diffraction of Light by Ultrasonic Waves of Various Standing Wave Ratios

The theory for the diffraction of light by plane ultrasonic waves of various standing wave ratios is derived. The liquid medium disturbed by the ultrasound is considered to act as an optical phase grating. By evaluating the diffraction integral for the light amplitude, expressions for the Doppler shift, the time dependent, and the time average light intensities are found for the diffraction spectrum. Experimental measurements using two adjacent ultrasonic waves progressing in opposite directions to simulate the desired optical phase grating indicate that the theory is valid.

Photographic Verification of Ultrasonic Plane Wave Scattering by Cylinders

The ability to photograph the ultrasonic field around a model may obviate the need for extensive mathematical analysis of ultrasonic or analogous field problems. In this paper a method of photographing an instantaneous field invariant in one direction is described. Through use of a parallel-beamed light pulse of very short duration photographs were made of the ultrasonic field of continuous 3-Mc traveling sound waves in water impinging perpendicularly upon the side of a cylindrical tube. Shadowgraphs thus obtained verified the wave shapes predicted by IBM 704 computation of the mathematical analysis.

Diffraction of Light by Ultrasonic Waves of Various Standing Wave Ratios

The theory for the diffraction of light by plane ultrasonic waves of various standing wave ratios is derived. The medium disturbed by the ultrasound is considered to act as an optical phase grating. By evaluating the diffraction integral for the light amplitude. expressions for the time dependent and time average light intensities are found for the diffraction spectrum. Experimental measurements of these intensities indicate the theory is valid. (This work was supported by the Office of Ordnance Research, U. S. Army.)

Composite Piezoelectric Resonator

Various types of composite resonators and their uses are summarized. The general equations are given for the transducer for plane ultrasonic waves, consisting of a crystal assembly with back and front plates. Applications are made to several simple cases, and expressions are tabulated for the amplitude of vibration for various combinations of half- and quarter-wave components. Consideration is given to the effect of the acoustic load on the frequency for maximal amplitude. Theoretical formulas are compared with experimental results for rods of aluminum and fused quartz excited in vibration by piezoelectric crystals.

Composite Piezoelectric Resonator

Various types of composite resonators and their uses are summarized. The general equations are given for the transducer for plane ultrasonic waves, consisting of a crystal assembly with back and front plates. Applications are made to several simple cases, and expressions are tabulated for the amplitude of vibration for various combinations of half- and quarter-wave components. Consideration is given to the effect of the acoustic load on the frequency for maximal amplitude. Theoretical formulas are compared with experimental results for rods of aluminum and fused quartz excited in vibration by piezoelectric crystals.

The Scattering of Underwater Plane Ultrasonic Waves by Liquid Cylindrical Obstacles

An experimental investigation of sound scattering from liquid cylindrical obstacles was performed by Tamarkin following on the work of Bauer and others. A series of scattering patterns, confined to the region about the extended axis of the incident beam and on the opposite side of the obstacle from the source, were determined for ten liquids. The special kia values chosen (ki; = 2π/λi, λi = wavelength of the sound in the medium of the obstacle, a = radius of the cylindrical obstacle) lie in the range 26.0<kia<41.0 and are below and above the corresponding value for the water medium surrounding the obstacle. On the assumption of a plane incident wave, a series solution was found for the total scattered wave and numerical calculations were carried out for conditions approximating those of the actual experiments. The results of this theoretical investigation confirm the experimental findings that scattering of an underwater ultrasonic beam, from the special liquid cylindrical obstacles examined, lies in the zone between the geometrical region and the region of Rayleigh scattering. In this zone, diffraction predominates and the diffraction patterns based on theory agree quantitatively quite well with the positions of the experimental maxima and minima. A rather detailed and extended theoretical study of the resonance curve found experimentally was made and the plotted theoretical resonance curve shows a similar oscillating behavior with amplitude decreasing with increasing kia.

Scattering of Underwater Plane Ultrasonic Waves by Liquid Cylindrical Obstacles

This paper is a report of a theoretical investigation of sound scattering from liquid cylindrical obstacles immersed in water following closely the conditions prevailing in the previous experimental work of Tamarkin, Bauer, and others. An incident plane wave being assumed, series solution was found for the total scattered wave. Numerical calculations were carried out using parameters approximating those of Tamarkin's experiments (radius of obstacle, 0.635 cm; sound frequency, 1.145 mc/sec; wavelength, 0.13 cm). A series of scattering patterns, confined principally to the forward direction for an angular spread of about 14° (with the obstacle at the vertex) were calculated for eight liquids, chosen to give a spread of kia values (ki the wave parameter inside the liquid and a the radius) between 26.0 and 41.0. The results of this theoretical investigation confirm the experimental findings that for the liquids examined the scattering is diffractive and lies in the zone between the geometrical region and the region of Rayleigh scattering. Quantitative comparisons are made between the theoretical and experimentally plotted results with special emphasis on the experimental resonance curve and its theoretically computed counterpart.

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.