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It is well known that the mean force due to the Langevin radiation pressure on a sphere freely placed in a plane progressive sound field is always positive force (i.e., repulsive force). In the case of spherical diverging field, however, the situation is quite different. At very large distances from the source the radiation force obeys an inverse square law of repulsion. As the source of the field is approached, the repulsion decreases to zero and then becomes a force of attraction [T. F. W. Embleton, J. Acoust. Soc. Am., 26, 40-45 (1954)]. The present paper discusses the mechanisms for the attracting force acting on a rigid sphere placed freely in a spherical diverging sound field. The distribution of the three components of the radiation force on a sphere (i.e., kinetic energy density K, potential energy density U. and tensor term T that includes momentum flux density) is investigated and compared with the case of plane progressive sound field. In the cases of grazing incident of plane waves and spherical waves, it is shown theoretically that the contribution of the tensor term vanishes and the Lagrangean density L = K - U becomes the only cause of radiation force. In the case of incident plane waves, the effect of (L) vanishes because (K) = (U), where the symbol ( ) denotes the time-averaging operation, while attracting force arises because (K) > (U) in the case of incident spherical waves.

The frequency dependence of the acoustic radiation pressure on a solid elastic sphere placed freely in an incident plane progressive sound field in water has been investigated. In particular, the behavior of the acoustic radiation pressure at resonance frequencies of the elastic vibration of the sphere has been studied theoretically by taking into account the three components of the radiation pressure, namely, kinetic energy, potential energy, and tensor term. It has shown that the contribution of potential energy to radiation pressure is the largest and it has a positive value, that which of kinetic energy is rather small and has a negative value, and that which of tensor term is so small as to be negligible in the cases far from resonance frequencies. At resonance frequencies, potential energy falls off rapidly, while the softer the material are, the greater positive values kinetic energy and tensor term are increased up to, with a few exceptions. As a result, there takes place, in general, a series of maxima in the frequency characteristic curves of radiation pressure for relatively soft materials such as lead, and a series of minima for relatively hard materials such as iron at the resonance frequencies, because the increase in kinetic energy and in tensor term overcome the decrease in the potential energy for relatively soft materials. Materials of intermediate hardness such as brass have the frequency characteristic curves mixed by maxima and minima.

Each of all the existing theories of the acoustic radiation pressure has, of course, peculiar excellent advantages.It is also the fact, however, that there are more or less ambiguities, leaps in logic, and unnecessary assumptions in many existing theories.The purpose of the present paper is to develop a general theory that covers both the Rayleigh and Langevin radiation pressures, and is simple and easy to understand, with merits of existing theories incorporated as far as possible.We distinguish between the Rayleigh and Langevin radiation pressures according as the force acting on an obstacle depends on a fractional change in static pressure or not.Since it is a matter of the experimental conditions whether one observes the Rayleigh radiation force or the Langevin radiation force, both radiation forces should be treated theoretically from a common physical point of view.The emphasis is placed on pointing out that the tensor properties cannot be disregarded in the Rayleigh radiation pressure as well as in the Langevin radiation pressure, by showing where the tensor term originates in.A brief review is given for a few of existing theories at the end of the chapter.

Interactions between nonlinear media and an object in it are studied theoretically and numerically using dynamical models. The KdV soliton is incidented to the object by numerical simulation and the generation of solitons are detected. The measured amplitudes coincide very well with the theoretical results.

The present paper deals with the Rayleigh radiation pressure which is defined as the time-averaged force per unit area of the wall of a closed vessel when an acoustic field is applied. Previous theories on the Rayleigh radiation pressure are examined critically and erroneous results are noted and rectified. A new theory of radiation pressure on a partially reflecting plate is developed as a function of the linear reflection coefficient and transmission coefficient of the plate. It is shown that the time-averaged Lagrangian pressure does not depend on the Lagrangian coordinate and that the effects of acoustic straining cannot be disregarded even in the presence of reflected waves in a closed tube. The present theory is applicable to various types of reflectors. The principal conclusion of this work is that the Rayleigh radiation pressure on a perfectly absorbing plate and that on a perfectly reflecting plate are both given by (γ+1)‹E›/4, where γ is the ratio of specific heats of the medium and ‹E› is the time-averaged energy density.

Scattering of the nonlinear Schrodinger (NLS) solitons in discontinuous media is studied numerically. As a physical model, one-dimensional anharmonic lattice which has a discontinuity in its mass distribution, is analized. After the collision of the incident NLS soliton against the mass interface, we detect the amplitude of the reflected and transmitted solitons. They coincide very well with those of the theoretcal ones (T. Iizuka and M. Wadati, J. Phys. Soc. Jpn. 61 (1992) 3077), which is based on the inverse scattering method.

The scattering of nonlinear Schrodinger solitons due to an impurity in anharmonic lattices is studied numerically. At most one soliton is generated in both reflected and transmitted waves. Their amplitudes coincide very well with those of the theoretical result, which has been obtained through the inverse scattering method.

The reflection of active waves in a reaction-diffusion equation with spatial inhomogeneity is analyzed by use of the eikonal equation. The counterpart of the Rankine-Hugoniot relation, i.e. the shock condition, is derived for the transition layer in reaction-diffusion systems. In the case that the curvature effect of a wavefront is negligible, we show that the time evolution of a front is well described by Whitham's shock-ray coordinate theory. It is shown that total internal reflection is possible for the speed of a wavefront increasing along a ray.

In the complex impedance representation, we observed either one or two semicircles strongly dependent on x, and a transition from one semicircle to two semicircles at x=0.4. Ultrasonic velocity showed an anomaly at x=0.4. Owing to this fact, we observed the bulk conduction and grain boundary diffusion.

The acoustic radiation pressure resulting from a plane wave incident on spherical shells and cylindrical shells immersed in a fluid is investigated theoretically in relation to the thickness of the shell and the contents of the hollow region. The results for the frequency dependence of acoustic radiation pressure computed on the basis of the theory are demonstrated for stainless shells with the hollow region filled water or air. Significant differences in acoustic radiation pressure occur when the interior region is changed from water to air.

The acoustic radiation force exerted on a rigid sphere whose time‐averaged center is at any specified point on the axis of a circular piston vibrator was investigated theoretically including points in the near zone of the radiation with a view to applying it to the absolute measurement of ultrasonic intensity. The velocity potential of incident waves in the near field was expressed in the form of an infinite series of spherical surface harmonics, thereby allowing the use of the conventional scattering theory to calculate the radiation force. The theoretical framework has the advantages that it includes neither approximations nor numerical integrations, and that it is applicable to elastic or compressible sphere cases with slight modifications of the boundary conditions.

The propagation of active waves in a reaction-diffusion system with spatial inhomogeneity is examined using the geometrical shock dynamics method. The refraction or diffraction of active waves is found for the case that the diffusivity of the system changes with a spatial variable.

We studied the electrical impedance as a function of frequency ranging from 75 kHz–20 MHz at temperature ranging from 30–253°C, and the ultrasonic velocity dependence on x at room temperature in order to investigate ionic conduction mechanisms of Na1+2 x Zr2- x Mn x (PO4)3 with a bottle-neck structure. In the complex impedance representation, we observed either one or two semicircles strongly dependent on x, and a transition from single semicircle to double semicircles at x=0.5. Ultrasonic velocity showed an anomaly at x=0.5. Based on these results, we concluded that we observed the bulk conduction and grain boundary diffusion of the sodium ion.

The electrical impedance of Na2Zr1.5Mg0.5(PO4)3-Al2O3 composite has been studied as a function of frequency ranging from 120 Hz-20 MHz at temperatures ranging from 30-253°C. In the complex impedance representation, we observed either one or two semicircles strongly dependent on Al2O3 concentration, and a transition from two semicircles to one semicircle at 10 mol% Al2O3. Ultrasonic velocity showed an anomaly at 10 mol% Al2O3. Due to the dependence of both electrical impedance and elastic data on Al2O3 concentration, we observed the bulk conduction and grain boundary diffusion of the sodium ion in Na2Zr1.5Mg0.5(PO4)3.

Recoil process of adatoms by ion beam bombardment has been studied by computer simulation. Owing to the focusing effect, the intensity of adatom recoil depends strongly on both the angle of incidence and the angular position of the detector. When the detector is arranged in a backward direction with respect to the direction of the primary ion beam, structural information on surface hydrogen and other light elements can be obtained efficiently.

The ultrasonic absorption coefficient α has been measured in a critical binary mixture of nitrobenzene/n-hexane over the ultrasonic frequency f of 0.2–3 MHz. The temperature dependence of α/f 2 in a binary mixture is remarkably larger at low frequency than that at high frequency. Frequency dependence of critical absorption at critical temperature T c has been measured and discussed by the theory of Ferrell and Bhattacharjee (FB). The absorption relative to critical absorption at T c has been plotted as a function of the reduced frequency and also compared with the scaling function by the theory of FB.

The acoustic radiation force on a solid sphere in a wave field in an inviscid fluid has been investigated theoretically and numerically taking into account the effects of elasticity of the sphere material for the following three cases: (I) the wave field is stationary, (II) the wave field is quasistationary, (III) the sound absorption in the sphere material is taken into account in each case above. The results show several features quite different from the rigid sphere solution.

The advantages of using fused silica spheres as the target in the radiation force method of acoustic intensity determination are considered. Experimental determination of the radiation force function, for fused silica spheres in water in the range of k a 2–24, was carried out. The experimentally obtained values of the radiation force function agree within 2% of those calculated from the theory of the radiation force on solid elastic spheres. This makes possible determination of ultrasonic intensity and calibration of acoustic probes with uncertainties

The rigorous expansion developed by the present authors for the velocity potential of a circular piston source [J. Acoust. Soc. Am. 74, 1044–1047 (1983)] is extended to include the space average pressure in the nearfield and the Fresnel diffraction of incident plane waves by an infinitely thin rigid disk. The present theoretical framework has the remarkable advantage that it includes neither approximations nor numerical integrations.

The acoustic radiation force on a sphere in quasistationary waves has been investigated experimentally. The radiation forces measured with fused silica spheres have been compared with a previous theory by the present author which takes into account the elasticity of the sphere material. Good agreement has been found. It has been demonstrated that the acoustic radiation forces on fused silica spheres show much deviation from the conventional theory for rigid spheres for ka larger than approximately four.

The theory of the acoustic radiation pressure on an elastic sphere, placed freely in an inviscid fluid in a field of plane progressive sound waves, is modified to include the effect of a hysteresis type of absorption of shear and compressional waves in the solid material of the sphere. This type of absorption is typical of some types of polymer materials. Calculated results are presented for polymethylmethacrylate lucite and polyethylene spheres in water for ka values between 0 and 24. The results are of interest in view of the use of radiation pressure measurements to determine sound intensity.

This paper presents a new method for calculating the velocity potential in the nearfield of a circular concave piston source in an infinite plane baffle for both the case where the vibration is normal to the piston surface and where it is parallel to the axis. The solution is given in the form of an infinite series of spherical surface harmonics in the spherical coordinate system, taking the origin at the center of curvature. The theoretical framework has the advantage that it includes neither approximations nor numerical integrations.

An analysis has been made of the acoustic radiation pressure acting on a rigid sphere in a spherical sound field for the purpose of completing the work of Embleton [J. Acoust. Soc. Am. 26, 40–45 (1954)] from the angle of practical application. His presentation has been simplified mathematically and improved into a more general form. Numerical calculations have been made with particular emphasis on the difference from the results for incident plane progressive waves as a function of the density of the sphere, the size parameter, and the distance of the sphere from the sound source.

The acoustic radiation force experienced by a solid cylinder suspended freely in a plane progressive sound field is calculated, taking into account the elasticity of the cylinder. The results of numerical calculations are presented, indicating the ways in which the form of the frequency dependence of the radiation force function YP for cylindrical targets is affected by variations in the material parameters of the cylinder. The results are compared with those for solid spherical targets.

In the case of boundary value problems such as the sound scattering from a sphere placed in the nearfield of a plane piston source, it is sometimes essential to express the velocity potentials in terms of the orthogonal expansion. It is demonstrated in the present work that the Rayleigh surface integral, giving the velocity potential for a plane piston source surrounded by an infinite rigid flange, reduces to a rigorous expansion of the simplest form for a circular piston as series of spherical surface harmonics. The resulting equation is valid for any field points even on the piston surface. Sample calculations made with a microcomputer are presented with three‐dimensional and contour plots.

The expression obtained by Hasegawa and Yosioka [J. Acoust. Soc. Am. 46, 1139–1143 (1969)] for the acoustic radiation pressure on a solid elastic sphere in a plane progressive sound field is reformed into a simpler form, in which the acoustic‐radiation‐pressure function is represented only in terms of scattering coefficients and the size parameter ka. On the other hand, the extension of the Maidanik calculation [J. Acoust. Soc. Am. 29, 936–940 (1957)] for a fluid sphere to solid elastic spheres is attempted. The result is compared with the former. It is demonstrated that the computational differences are commensurate with the same result.

The acoustic radiation force on a homogeneous solid sphere placed freely in a spherical sound field in an inviscid fluid is calculated; the effect of the elasticity of the sphere material is studied. Calculated results are presented for a variety of solid spheres in water. Quite distinctive resonance departures from the rigid sphere solution are found.

A special technique is developed to find the cycle‐for‐cycle matching between the two pulses using two transducers. The one‐way travel time of ultrasound is determined with an accuracy of several percent of the period of quartz transducer resonance. The results of the technique show the accuracy of the absolute sound velocity of about 1 m/s, in a highly attenuating liquid using 3‐MHz transducers separated by 65 mm.

The acoustic radiation force on a solid sphere suspended freely in a plane progressive sound field is calculated taking into account the elasticity of the sphere. The radiation force versus ka curve, ka being the radius times the wavenumber in the surrounding medium, shows sharp maximums or minimums corresponding to resonance in every normal mode of free vibration of the sphere. The measurements made in our laboratory are in good agreement with the theory. The accuracy of absolute acoustic‐intensity determination by the radiation‐force method will be improved by the use of the present theory instead of King's.

The acoustic radiation force on a fused silica sphere of the size parameter ka up to 100 is investigated experimentally with a view to complete a previous work [T. Hasegawa and K. Yosioka, J. Acoust. Soc. Am. 58, 581–585 (1975)] and to develop an accurate method for determining the acoustic intensity in the high megahertz range. It is shown that the radiation force function Yp for a fused silica sphere in water is regarded as substantially equal to 0.90±0.04 over a wide range of ka greater than 30.

The exact theory for the radiation of a circular concave piston surrounded by an infinite rigid baffle is presented. The Rayleigh surface integral, giving the velocity potential for a circular concave piston source, reduces to an infinite series of the simplest form when the origin of a system of spherical coordinates is taken at an arbitrary point on the acoustic axis. The theoretical framework has the advantages that it includes neither approximations nor numerical integrations and that it has application in solving other boundary‐value problems such as the sound scattering by a sphere whose center coincides with the origin in the field of a concave piston source.

A discrepancy in the recent paper ’’Monostatic reflection of a plane wave from an absorbing sphere’’ [F.H. Vogt et al., J. Acoust. Soc. Am. 57, 558–561 (1975)] is investigated. Calculations are made by means of a modified method for lucite and polyethylene spheres in water. A serious disagreement between Vogt et al. and us is demonstrated in the case where no absorption is included.

This article presents a nonconventional way using the ring‐function method for the analysis of the nearfield of a circular piston in an infinite baffle for the case where the velocity distribution across the face of the piston has a parabolic profile.

A new acoustical method for measuring the virtual mass is described in this paper. The fundamental frequency f 0 of a rectangular tube with both ends closed is reduced to f 0-f by the introduction of a cylinder at the center of the tube; the cylinder is inserted in the tube perpendicularly through a wall of the tube and reaches the opposite wall. A theoretical formula for the inertia coefficient (the ratio of the additionally induced mass to the mass of air displaced by the cylinder) is obtained as L=(f/f 0)/(S/S 0)-1, where S and S 0 are the areas of the cross sections of the cylinder and the tube, respectively, and two-dimensional motion of the air is assumed. Experiments were made using a tube of f 0=247 Hz and several circular and elliptic cylinders of f=0.6 ∼2.5 Hz. The values of L thus obtained are in good agreement (within 10%) with the theoretical values which are well known in hydrodynamics.

A new method for measuring the phase velocity at MHz frequencies is presented. Two quartz transducers are separately placed; the time difference between the ac-voltage pulse (tone burst) applied to the transmitting transducer and the out-put-voltage pulse of the receiving transducer is measured with an accuracy of several percent of the period of resonant vibration of the transducers. A special technique is used in order to find the cycle-for-cycle matching between the two pulses. The measurement is easily performed even with a liquid of 40 dB absorption between the two transducers.