Volume 52, Issue 1B, July 1972

Measurements of Ultrasonic Velocities Using a Digital Averaging Technique
View Description Hide DescriptionA new pulse‐echo technique using real‐time digital averaging is described for measuring the phase velocity in solids up to 50 MHz. The technique can measure the transit time between any two echoes to an absolute accuracy of 0.1 nsec and measure small changes in transit time to a sensitivity of 20 psec. Experimental examples are given based upon ultrasonic velocitymeasurements in a single crystalsuperconductor.

Generation of Ultrasound by a Dielectric Transducer
View Description Hide DescriptionIn this paper we report the generation of ultrasonic waves in solids, at frequencies varying from 10 to 200 MHz, using a dielectrictransducer. It is shown that the dominant process involved is the effect of electrostatic forces acting directly on the propagation medium, and not piezoelectricity or electrostriction of the central dielectric.

Nonlinear Acoustical Parameters of Piezoelectric Crystals
View Description Hide DescriptionThe wave equation for elastic waves in piezoelectric crystals is found, including the third‐order terms in the expansion of the thermodynamic potential in the strain and electric field. The effective nonlinear parameters for a general crystal are obtained. In the general case these parameters depend on the second‐order and third‐order coefficients: nonlinear piezoelectric, electrostrictive, and linear electro‐optic. These coefficients are considered for piezoelectric and nonpiezoelectric crystals. Some estimates are given of the values of the nonlinear coefficients.

Scattering of Elastic Waves by Moving Objects
View Description Hide DescriptionIt is shown that simple elastic media in motion exhibit new properties, owing to the effective compressional and shear wavevelocities produced by the motion. Presently, we consider scattering of a compressional plane wave by (1) a half‐space moving parallel to the interface and (2) a cylinder moving along its axis. In both cases the assumed boundary conditions correspond to good contact at the interface. Computational results are given for the scattering amplitudes as a function of velocity and angle of incidence.

Multipole Expansion of Sound Radiation from Moving Rigid Bodies
View Description Hide DescriptionThe solution of the wave equation with a source term extended in space and moving as a rigid body with translation and rotation is expanded about an interior point in terms of point multipoles, which are expressed as spatial derivatives of the Liénard‐Wiechert solution for a monopole. An application to sound radiation from moving rigid bodies is given using the theory of Ffowcs‐Williams and Hawkings. As examples, the radiation fields of a rotating ellipsoid and a sphere in accelerated rectilinear motion are estimated.

Transmission of Sound in Ducts with Thin Shear Layers—Convergence to the Uniform Flow Case
View Description Hide DescriptionThe problem of the transmission of sound in a duct with very thin shear layers at the walls is treated by an inner expansion method. The results show that the formulation of the problem of the transmission of sound in a duct with a shear layer at the wall converges, in the case of a vanishingly thin shear layer, to the formulation of the same problem when uniform flow is assumed and the wall boundary condition is that of continuity of particle displacement.

Transient Acoustical Sources in an Idealized Jet
View Description Hide DescriptionThe transmission of acoustic disturbances from the interior of the jet through the mean velocity profile and into the farfield is studied in detail. The noisegenerator is taken to be a sequence of transient acoustical point sources traveling with the local fluid in the idealized jet. The idealized jet is two‐dimensional, and extends to infinity upstream and downstream with velocity profile independent of streamwise position. For the limited set of examples considered the following conclusions apply: (1) Velocity profile has a large effect on the magnitude of the noise radiated to the farfield. (2) Much of the farfield noise, especially at low Strouhal numbers, originates not as true waves but in the form of acoustical disturbances within the jet which are not radiating energy. (3) At subsonic velocities, the characteristic lobes appearing in a polar plot of farfield mean‐square pressure approach the downstream axis as frequency decreases. This somewhat resembles experimental trends, but many other factors must be considered before a valid comparison can be made.

Theoretical Analysis of Rough‐Surface Shadowing from Point‐Source Radiation
View Description Hide DescriptionThe shadowing function, defined as the probability that a point on a rough surface will be illuminated by radiation from a source at fixed height above the surface, is considered. An exact expression for this probability is derived and evaluated approximately when the surface elevation is a normal random process. The effect of surface correlation is considered and shown to be appreciable. Several numerical computations of the shadowing function are presented.

Separation and Analysis of the Acoustic Field Scattered by a Rigid Sphere
View Description Hide DescriptionThe scattered field calculated when a plane acoustic wave is incident upon an ideally rigid sphere is considered as a composite and resolved into two parts. One part, which includes the specularly reflected contribution to the field, arises out of scattering by the bright hemisphere—the scattering sphere being divided into two regions by the boundary of the geometrical shadow. The second part, owing to scattering by the shadow side of the sphere, includes the major part of the radiation due to creeping waves. This separation is consimilar with the separation of the scattered field that is made in the creeping‐wave formulation of scattering theory. The separation is made here, however, by treating the scattering sphere as a spherical radiator and solving a pair of boundary‐value problems by classical means. Each of the boundary‐value problems is related to one part of the scattered field. Both parts are found to yield scattering components that are related to “image pulses” such as are predicted when scattering problems involving transient signals are analyzed using theory based on the Kirchhoff approximation. It is found, however, that the image‐pulse‐type returns, which arise out of the exact classical theory, cancel when the two separate parts of the scattered field are added together, so that, in the complete scattered field, no image‐pulse‐type return is detectable. It is also found that a secondary creeping‐wave component originates in the scattering from the bright side of the sphere. This result indicates that the generation of creeping waves may not be a phenomenon taking place solely at the geometrical shadow boundary. Moreover, it is found that the part of the scattered field which yields the specularly reflected return can be very closely approximated by the scattered field that would be predicted by calculations incorporating the Kirchhoff approximation. Interference between the various components, identified as a result of the separation, explain a number of features of the scattering behavior observed when long pulses are incident on the sphere.

Theory of Acoustical Wave Propagation in Porous Media
View Description Hide DescriptionA theory is developed to describe the propagation of sound waves in a rigid isotropic and homogeneous porous medium filled with a compressible fluid, including both the effect of viscous dissipation and the effect of thermal conduction. An expression for the conductance as a function of the frequency is derived by assuming a capillaric model. A comparison is made with independent experimental results, and close agreement with the theoretical results is obtained. A discussion of the structural parameters, including a description of a method for determining their values at a given frequency, is also made.

Impact of a Spherical Tool against a Sonic Transmission Line
View Description Hide DescriptionThe impact of a tool against a sonic transmission line is a subprocess of the impact coupling method of sonic power transfer. This process is modeled and the nonlinear governing equation developed in this paper. A probability density function is derived that enables the average rebound velocity of the impacting tool to be established. Numerical results are obtained, for selected material‐geometry parameters, on the stress pulses resulting from several conditions of impact, for the rebound velocity as a function of phase angle of impact and for the average rebound velocity. Future work will consider the entire impact coupling process and tools of more complex shape.

Vibrations of Circular Elastic Plates due to Sonic Boom
View Description Hide DescriptionThe problem of transient axisymmetric vibrations of thin circular elastic plates due to sonic boom excitation is investigated. The equation of motion for a solid circular plate is solved by applying the modified finite Hankel transform and the Laplace transform, and the numerical results are obtained with the help of the digital computer. From the analysis of the data, obtained for the dynamic deflections of the plates for the boom duration, it is concluded that for a normal flight the boom duration has a significant effect on the vibrations of plates as compared to the overpressure of the boom.

Transient Analysis of Lumped and Distributed Parameter Systems Using an Approximate Z‐Transform Technique
View Description Hide DescriptionAn approximate Z‐transform approach is presented to compute at discrete time intervals the time responses of lumped or distributed parameter systems which exhibit wave propagation or time delay effects. The approach was previously developed by Boxer and Thaler [R. Boxer and S. Thaler, Proc. IRE 44, 89–101 (1956)] as a numerical method of solving linear and nonlinear equations and is an extension of the more familiar Laplace transform technique which is used for the analysis of continuous linear systems. Rather than directly utilizing the inverse Laplace transformation to obtain the time function, a mapping of the Laplace transform of the function from the s domain to the z domain is performed via the transformation z = e^{sT} , where T is the desired sampling interval of the time function. Unlike the inverse Laplace transformation, which requires the pole‐zero structure of the transform to obtain the continuous time function, the sampled time function is then obtained from its z domain representation without using the theory of residues. Numerical solutions to several problems are presented to illustrate the advantages of the approximate Z‐transform approach.

The Ray Sweep‐Out Method
View Description Hide DescriptionTo calculate the ray intensity field at a point (a receiver point) in range and depth, all significant ray paths from the source to the receiver must be found. When there are a large number of receiver points, it is desirable to use a method in which all receiver points are considered as the rays are tested to find those that travel from the source to a receiver. This paper describes a simple method for finding all ray arrivals during a single sweep out of the source beam pattern and at the same time calculating the total ray intensity field at the receiver points.

Coherent Reflection by the Rough Sea Surface of the Acoustic Field from a Source of Arbitrary Directivity
View Description Hide DescriptionThe angular plane‐wave spectrum representation of the acoustic field due to a source of arbitrary directivity is used to formulate the problem of scattering by a rough sea surface. An approximate solution is obtained by applying Kirchhoff‐type boundary condition at the surface. The solution suggests a straightforward modification of current ray‐tracing techniques in order to estimate the coherent part of the reflected field.

Velocity of Transient Cavities in an Acoustic Stationary Wave
View Description Hide DescriptionThis paper concerns the high‐speed motion of transient cavities generated in an acoustic stationary wave in a cylinder filled with water. Time‐exposure photographs are presented of the cavities illuminated by a high‐speed stroboscope showing multiple exposures of an individual cavity as it was propelled outward from a region of large acoustic pressure amplitude. The photographs show several interesting details of the cavitation event. Velocities obtained by the cavities were on the order of 1 m/sec, pressure amplitudes on the order of 5 bars, and cavity lifetimes on the order of 10 msec. A theoretical analysis of the cavity motion is obtained by considering the cavity as a spherical inhomogeneity in an acoustic stationary wave. Comparison of theory and experiment show good agreement provided that a velocity‐squared drag law is used with a drag coefficient of 0.77.

The Sea Surface as a Random Filter for Underwater Sound Waves
View Description Hide DescriptionWhen underwater soundwaves propagate from a transmitter to a receiver, part of the energy reaches the receiver after reflection and scattering from the sea surface. This boundary effect can be called the impulse response of the sea surface if the incident sound field is caused by a delta pulse. In this paper the Helmholtz diffraction integral is used together with a perturbation technique for the derivation of a formula for the corresponding transfer function. The result is a random function that depends on the frequency of the incident wave, on time, and on the source‐receiver configuration. Its validity is limited by three assumptions: (1) the medium is ideal (constant velocity, no subsurface layer), (2) source and receiver depth are many times larger than the surface elevation, and (3) the bottom is infinitely far away. For very high frequencies the formula indicates specular reflection from each surface “highlight.” In the Fraunhofer domain, the transfer function reduces to specular reflection with phase fluctuations. Some results of a statistical analysis are included for that frequency domain.

Ray Propagation in a Channel with Depth‐Variable Sound Speed and Current
View Description Hide DescriptionRay geometry, travel time, and spreading loss are examined for a moving medium. The sound speed and current are both depth‐variable, and the current direction is fixed in space. For a linear sound speed and current, ray geometry is investigated and an approximate solution is obtained which leads to helical paths. For a bottom‐mounted source and receiver in the vertical plane of the current, the linear model is used to investigate ray geometry, travel time, spreading loss, and the acoustic field associated with refracted/bottom‐reflected (RBR) transmissions. It is shown that the effects of current gradients and bottom currents on the phase and amplitude of the acoustic field are important and cannot be ignored. Further, long‐term time variations in the current gradient are shown to cause much shorter‐term variations in phase and amplitude.

Sound Radiation by Resonances of Free‐Free Beams
View Description Hide DescriptionThe pressure field of nonuniform, slender, free‐free beams of circular cross section is constructed by modeling the beam as a dipole array. Using the orthogonality relation of normal modes, the farfield pressure in a plane normal to the beam axis is shown to be associated with rigid‐body translation and, under highly restrictive conditions, viz. local deviations of the effective beam density from the beam's mean density, on elastic, particularly resonant modes.

Acoustic Cavitation in Helium, Nitrogen, and Water at 10 kHz
View Description Hide DescriptionObservations of acoustic cavitation have been in helium I and II using an extensional‐mode vibrator capable of very high intensities at 10 kHz. Remote monitoring of the drive oscillatory velocity was achieved. In helium I clouds of small vapor bubbles were visible, as well as larger bubbles near the expected radial resonance size. For comparison, observations were also made using two other normal liquids—nitrogen and water—at temperatures near their boiling points. In helium II observation of acoustic streaming with emission of white noise suggested the presence of even smaller vapor bubbles. A strong subharmonic signal with low threshold excitation has not been fully explained.