Volume 47, Issue 1B, January 1970

Ultrasonic‐Absorption and Sound‐Speed Data for Nine Liquids at High Pressures
View Description Hide DescriptionData for ultrasonicabsorption and sound speed are given for water, methyl alcohol, ethyl alcohol, n‐propyl alcohol, n‐butyl alcohol, eugenol, carbon tetrachloride, n‐hexane, and toluene, for pressures ranging up to about 5000 kg/cm^{2}.

Pressure Dependence of the Ultrasonic Absorption in Toluene and Hexane
View Description Hide DescriptionUltrasonicabsorption and sound speed have been measured in toluene and n‐hexane in the pressure range 1–10 000 kg/cm^{2} at 30°C. In these Kneser‐type liquids, for which the absorption may be attributed to thermal relaxational processes as well as to the dilatational and shear viscosities, various contributions to the absorption can be resolved by making specific assumptions about the ratio of the dilatational and shear viscosities. An attempt has been made to relate the thermal contribution to relevant theory.

Aperture Corrections for Sound‐Absorption Measurements with Light Scattering
View Description Hide DescriptionEven small collection angles in the receiving optics can appreciably broaden, distort, and shift Brillouin lines observed in a light‐scattering experiment, thereby causing errors in both sound absorption and sound velocity. A general expression for the observed lineshape is derived for a Lorentzian scattering line in terms of the distribution of thermal phonons and the shape of the collection aperture. Relaxational effects are also considered. For a square aperture, a closed‐form solution is obtained and discussed. Applicable correction formulas for the true linewidth and lineshift are derived. To first approximation, Brillouin line is the sum of two arctan functions.

Conical Reflection of Ultrasound from a Liquid‐Solid Interface
View Description Hide DescriptionOptical techniques are employed to investigate reradiation patterns of ultrasonic waves incident on flat liquid‐solid interfaces. It is shown that, for Rayleigh‐angle incidence, reflection takes place into a cone rather than only into the forward direction. The apex angle of the cone is found to be twice the Rayleigh angle.

Ultrasonic‐Velocity Measurements and B/A for 1‐Propanol at Pressures to 10 000 kg/cm^{2}
View Description Hide DescriptionSound‐velocity data are reported for 1‐propanol at 30°C and at pressures to 10 000 kg/cm^{2}. It is found that the sound velocity varies with pressure at the rate of 0.59 m/sec kg^{−1} cm^{−2} initially. The rate of variation decreases as the pressure is raised, with the value at 8000 kg/cm^{2} being 0.106 m/sec kg^{minus;1} cm^{−2}. The velocity at 10 000 kg/cm^{2}, 2976 m/sec, is approximately two and one‐half times that at 1 atm. From these velocity data, B/A′, the pressure‐variation term in the nonlinearity parameter, is calculated over the same pressure range. It is found that B/A′ decreases with pressure at a decreasing rate so that the value at 10 000 kg/cm^{2} is only slightly more than one‐half the atmospheric‐pressure value of 11.3. These results are compared with the corresponding results for water, for which both velocity and B/A values have previously been published. An Appendix gives values of (B/A) for mercury at high pressures.

Frequency‐Offset Method for Measuring Phase Shifts at Ultrasonic Frequencies
View Description Hide DescriptionThe frequency of a stable oscillator is periodically offset a small amount, then restored to its original value. The resulting change in phase of the oscillator output with respect to its original value can conveniently be related to the average voltage of a dc pulse generator that produces the frequency offset. For application to the ultrasonic pulse‐echo method, phase shifts for a selected echo can readily be measured by using the oscillator output as a calibrated phase reference. Two circuits for doing this are described. Several desirable features of the method are: (1) phase shift is measured at a fixed frequency; (2) phase can be varied continuously over a wide range, with essentially linear calibration; (3) application to measurements at high frequencies can be made; (4) automation of phase shift measurements with strip recorder readout can be obtained; and (5) fractional resolutions of approximately 2 in 10^{7} can be attained for low‐loss ultrasonic units. By way of illustration, experimental results are listed for measured phase shifts at 300 and 500 MHz— as required in a study of the dynamic shear properties of di‐n‐butyl phthalate.

On a Method of Generating Ultrasonic Circularly Polarized Waves
View Description Hide DescriptionIn the present paper, we suggest a device that is able to produce circularly polarized ultrasonicwaves by transposing the optical arrangement known as Fresnel's parallelepiped into the acoustic domain. A plane elastic transverse wave is propagated in an isotropic solid medium and then reflected at a plane air‐solid interface. This wave is linearly polarized at 45° to the plane of incidence and so results in two components of equal amplitude, which are in phase. After reflection at an appropriate angle, the two transverse waves are in phase quadrature and the reflected wave is circularly polarized. This result is essentially independent of frequency.

Scattering by Spherically Symmetric Inhomogeneities
View Description Hide DescriptionThe Jost‐function formulation of quantum scattering theory is applied to classical problems involving the scattering of a scalar plane wave by a medium in which the velocity is a function only of the spherical radial coordinate. This technique is used to solve the radial differential equation for scattering from a constant spherical inhomogeneity. The radial equation can be converted into an integral equation incorporating the Jost boundary conditions. The l−0 partial‐wave integral equation for a constant inhomogeneity is solved using an iteration procedure (the first two iterations are considered). The Jost function and l−0 cross section σ_{0} are plotted as a function of kR _{1}, where k is the wavenumber in the surrounding medium and R _{1} is the sphere radius. The iterative technique is good for long wavelengths (kR _{1}≪1) and any ratio of wavenumbers in the scattering and surrounding media. For shorter wavelengths and small ratio of wavenumbers (e.g., , where k _{1} is the wavenumber in the scattering medium), it gives a good approximation to σ_{0} for the entire range of kR _{1} considered . For shorter wavelengths and larger ratios of wavenumbers (e.g., , 2.0), it gives a good approximation to σ_{0} out to approximately . More general problems using this method are also discussed.

Digital Analysis of Acoustic Reflectivity in the Tyrrhenian Abyssal Plain
View Description Hide DescriptionAcoustic bottom‐reflectivity experiments with explosive sources made in the Tyrrhenian abyssal plain have been analyzed in detail using digital‐analysis techniques. The reflection losses are computed and reported as functions of both angle of incidence and frequency. The impulse response is also computed for different angles of incidence, and it shows a large number of reflections from deep interfaces. Theoretical loss and impulse response have been computed from acoustical parameters measured on cores taken in the same area, and these agree well with the experimental data.

Line Admittance of Infinite Isotropic Fluid‐Loaded Plates
View Description Hide DescriptionThe response of infinite isotropic plates submerged in a fluid and subject to spatially uniform temporally harmonic line forces and moments is obtained. The frequencies of the line loads range from f = 0 to f = f_{c} , where f _{c} is the coincidence frequency for plate waves. The power radiated into the fluid per unit length of support due to a normally incident plate wave is also obtained for (1) simple line supports, and (2) clamped supports. The effects of fluid loading on the radiated power are (1) to increase the force and moment reaction of a support to an incident plate wave, and (2) to decrease the power radiation from a line force or moment of given magnitude. The net effect of fluid loading is to decrease the radiated power, but neglect of the first effect would cause a considerable underestimation of the power radiated from supports, for f≪f_{c} . Finally, the transmission of normally incident plate waves past simple line and clamped supports is investigated.

Coupling through a Small Aperture in a Waveguide
View Description Hide DescriptionThe problem of the waveguide coupled to an external load through a small aperture is expressed in terms of an integral equation.Solution of the latter yields an equivalent circuit for the load as seen from the waveguide. Holes in terminal planes and sidewall are considered separately. Some attention is also given to multiple‐hole coupling.

Vibrations of a Dissipative Composite Lumped‐Distributed System
View Description Hide DescriptionGeneralized functions and Laplace transformation are employed to obtain a solution for the vibrations of a composite lumped‐distributed dissipative system consisting of a cantilever beam with a mass‐spring‐dashpot attached at some point along its length. The solution obtained contains the steady‐state solution in closed form. The natural modes of vibration comprising the transient solution are found to be periodically self‐similar and orthogonal in the sense that motion started in a given mode will be confined to that mode. Except for special cases, the natural modes will have no nodes. Curves are presented showing the behavior of the natural frequencies and decay constants as functions of the various parameters as well as the shapes of some associated modes. When the lumped elements are attached at the end of the beam, it is found that, for large values of the spring constant, increasing the dashpot strength may cause an increase in the natural frequency.

Driving‐Point Impedances of Cantilever Beams—Comparison of Measurement and Theory
View Description Hide DescriptionThe driving‐point impedances and natural frequencies of small, rigidly terminated, metal cantilever beams in bending vibration have been measured at low strain amplitudes. The results show excellent agreement with the predictions of the Timoshenko theory, which has been extended to account for the internal damping of the beams in addition to the effects of rotary inertia and shear displacement. Values of impedance measured at the free end of a magnesium alloy beam have a maximum dynamic range of 6×10^{6}; the lowest measured value of impedance was 4.1×10^{−5} lb‐sec/in. Attempts to avoid the excitation of the third beam mode by driving the beam at a nodal point near its midpoint have proved both successful and straight‐forward. Driving‐point impedance has also been measured at the ends of a manganese‐copper alloy beam and an aluminumbeam coated with an unconstrained layer of damping compound. The driving‐point impedance of this damped beam has been closely matched theoretically by the impedance of an equivalent, internally damped, homogeneous beam.

General Motion of Impact Dampers
View Description Hide DescriptionThe exact solution of the general steady‐state response of a sinusoidally excited primary system provided with an impact damper is derived analytically by treating the motion of the system as a piecewise linear process. The asymptotically stable regions of the resulting multivalued solutions are determined. Experimental investigations using an electronic analog computer in addition to numerical studies on a digital computer are described, and it is shown that the predictions of the theory are verified. The effects of viscous damping, frequency ratio, mass ratio, coefficient of restitution, clearance ratio, and initial conditions on the response and stability of the system are discussed, and optimum response curves over a wide frequency band are presented. The findings of this study are significantly different, both quantitatively and qualitatively from those of a recent investigation of impact dampers.

Measurement of Power Flow in Uniform Beams and Plates
View Description Hide DescriptionA novel technique is presented for measuring the vibrational intensity (power flow per unit width of cross section) in uniform plates and beams vibrating in flexure. The intensity is obtained as a vector at a measurement point. Measurements at many points yield the pattern of power flow. Experimental results of intensities in a very reverberant plate illustrate the measurement technique and are consistent with the loss factor of the plate.

Natural Frequencies and Strain Distribution in a Ring‐Stiffened Thick Cylindrical Shell
View Description Hide DescriptionThe natural frequencies and strain distribution at resonance in a freely supported circular cylindrical shell reinforced by equally spaced thin deep ring stiffeners is presented. In this approximate solution, the basic assumption admits the existence of all the strains and, by the process of systematic elimination, it is shown to be important to retain the transverse shear strain γτθ. The analytical results are compared with the experiment, and good agreement between the two is obtained.

Errors Obtained in Spectral‐Density Analysis with Sweeping Filter and Remaining Ripple When Using Equalizer‐Analyzer System for Random‐Vibration Test
View Description Hide DescriptionThis paper deals with some problems of equalizing and analyzing the acceleration density spectrum obtained when performing a random‐vibration test with specified tolerances. A peak‐notch pair in the spectrum, as obtained from a single‐degree‐of‐freedom resonance within the specimen or fixture, is considered as being the most severe part of the spectrum to equalize or analyze. This pair is characterized in the error estimation with parameters for the peak‐notch amplitude ratio and the peak‐notch frequency ratio. The influence of the analyzing filter shape outside the passband is such that an equivalent bandwidth‐increase factor can, within certain limits, be expressed as a linear function of the 12‐/3‐dB shape factor. Diagrams are given that show the errors due to bandwidth and shape of the filter used for the analysis as a function of the peak‐notch pair to be analyzed. In the case of the equalizing‐analyzing system, the filter shape was not found to have any evident influence on the accuracy of the equalization, only the 3‐dB bandwidth of each filter. The phase angles between adjacent filters are also of minor importance, as the filters in severe parts of the spectrum act rather independently. Diagrams are given that show the accuracy of the equalization as a function of the peak‐notch pair to be equalized. For a sweeping analyzer, the maximum sweep rate of 0.2 bandwidths per averaging time is recommended.

Doppler Characteristics of a Sonar Signal Propagating through an Anisotropic Medium Whose Index of Refraction is a Function of Time
View Description Hide DescriptionWhen a body is in motion through a water environment with a time‐varying index of refraction, the returned sonar signal will contain three independent Doppler shifts, one caused by the purely geometrical relative motion of the sonar and the target, one by the gradient distribution, and one by the anisotropiccharacteristics of the sonic refractive medium along the propagation path.

Dynamic Bulk Moduli of Several Solids Impacted by Weak Shockwaves
View Description Hide DescriptionThe bulk compressibility of several solids was measured using attenuated underwater shockwaves.Attenuation was such as to deliver an approximate sonic pulse to the test specimens. Measurements were made of the wave‐attenuation and the wave‐transit time in several metals, plastics, and chemical compounds. High‐speed smear‐camera shadowgraphs were used for the measurements.

Geometric Theory of Ray Tracing
View Description Hide DescriptionA temporal metric tensor is defined by combining the sound‐speed function with the spatial metric tensor for a Riemannian space. Fermat's principle implies that spatial rays are temporal geodesics. Ray equations generalized to Riemannian spaces are shown to be temporal geodesic equations expressed in spatial terms. This geometric derivation leads to the consideration of geodesic deviation and its relation to three‐dimensional spreading loss. Previous results [E. S. Eby, “Frenet Formulation of Three‐Dimensional Ray Tracing,” J. Acoust. Soc. Amer. 42, 1287–1297 (1967)] are generalized to Riemannian spaces, and tensor expressions are derived for ray curvature and torsion.