Feit's seminal article on radiation of sound by a vibrating plate.

The Reflections series takes a look back on historical articles from The Journal of the Acoustical Society of America that have had a significant impact on the science and practice of acoustics.

Far-field approximation for a point-excited anisotropic plate.

An analytic approximation is derived for the far-field response of a generally anisotropic plate to a time-harmonic point force acting normal to the plate. This approximation quantifies the directivity of the flexural wave field that propagates away from the force, which is expected to be useful in the design and testing of anisotropic plates. Derivation of the approximation begins with a two-dimensional Fourier transform of the flexural equation of motion. Inversion to the spatial domain is accomplished by contour integration over the radial component of wave number followed by an application of the method of stationary phase to integration over the circumferential component of wave number. The resulting approximation resembles that of an isotropic plate but involves wave numbers, wave amplitudes, and phases that depend on propagation angle. Numerical results for a plate comprised of bonded layers of a graphite-epoxy material illustrate the accuracy of the method compared to a numerical simulation based on discrete Fourier analysis. Three configurations are analyzed in which the relative angles of the layers are varied. In all cases, the agreement is quite good when the distance between force and observation point is greater than a few wavelengths.

Dictums for problem solving and approximation in mathematical acoustics: examples involving low-frequency vibration and radiation.

A sequence of dictums for mathematical acoustics is given representing opinions intended to be regarded as authoritative, but not necessarily universally agreed upon. The dictums are presented in the context of the detailed solution for a class of problems involving the forced vibration of a long cylinder protruding half-way into a half-space bounded by a compliant surface (impedance boundary) characterized by a spring constant. One limiting case corresponds to a cylinder vibrating within an infinite rigid baffle, and another limiting case corresponds to a vibrating cylinder on the compliant surface of an incompressible fluid. The second limiting case is identified as analogous to that of a floating half-submerged cylinder whose vibrations cause water waves to propagate over the surface. Attention is focused on vibrations at very low frequencies. Difficulties with insuring a causal solution are pointed out and dictums are given as to how one overcomes such difficulties. Various approximation techniques are described. The derivations involve application of the theory of complex variables and the method of matched asymptotic expansions, and the results include the apparent entrained mass in the near field of the cylinder and the radiation resistance per unit length experienced by the vibrating cylinder.

Relation of sound absorption and shallow water modal attenuation to plane wave attenuation.

Prediction of attenuation of acoustic fields in weakly absorbing media often uses the substitution of (omega/c)-->(omega/c)+ialpha(pw) into the idealized equations for constant frequency, with alpha(pw) representing the local plane wave attenuation coefficient. This assumption is flawed whenever the local absorption of sound is proportional to the square of the gradient of the acoustic pressure, as is the case when the absorption is caused by fluid velocity relaxation. A realistic analysis yields an improved weighting function over depth for determination of guided mode attenuation coefficients.

On the exponent in the power law for the attenuation at low frequencies in sandy sediments.

Shallow water transmission loss measurements yield intrinsic attenuation estimates for acoustic waves in the underlying sediment, with results that are consistent with attenuation being proportional to frequency raised to a power n, with n between 1.6 and 1.87. Plausible theory suggests that n should be identically 2. The discrepancy can be explained because the inverse analysis inferences were made with the neglect of an additional attenuation mechanism where generated lower velocity shear waves carry energy downwards out of the waveguide. The shear wave effect has a weaker dependence on frequency than the intrinsic attenuation, so the apparent exponent is shifted downward.

Low-frequency attenuation of acoustic waves in sandy/silty marine sediments.

Sandy/silty marine sediments are water saturated and consist of diverse tiny rock pebbles. The weight of higher pebbles holds lower pebbles in contact. For low-frequency acoustic disturbances, the no-slip condition and viscosity cause the local water displacement near solid surfaces to be nearly the same as that of the neighboring pebbles. Water farther from surfaces oscillates relative to solid matter because of mass density difference, and viscosity limits the oscillation amplitude. Derived dissipative wave equation predicts attenuation proportional to frequency squared, proportional to the square of the difference of the densities, and inversely proportional to viscosity.

Geoacoustic inversion by mode amplitude perturbation.

This paper introduces a perturbative inversion algorithm for determining sea floor acoustic properties, which uses modal amplitudes as input data. Perturbative inverse methods have been used in the past to estimate bottom acoustic properties in sediments, but up to this point these methods have used only the modal eigenvalues as input data. As with previous perturbative inversion methods, the one developed in this paper solves the nonlinear inverse problem using a series of approximate, linear steps. Examples of the method applied to synthetic and experimental data are provided to demonstrate the method's feasibility. Finally, it is shown that modal eigenvalue and amplitude perturbation can be combined into a single inversion algorithm that uses all of the potentially available modal data.

Higher-order acoustic diffraction by edges of finite thickness.

A cw solution of acoustic diffraction by a three-sided semi-infinite barrier or a double edge, where the width of the midplanar segment is finite and cannot be ignored, involving all orders of diffraction is presented. The solution is an extension of the asymptotic formulas for the double-edge second-order diffraction via amplitude and phase matching given by Pierce [A. D. Pierce, J. Acoust. Soc. Am. 55, 943-955 (1974)]. The model accounts for all orders of diffraction and is valid for all kw, where k is the acoustic wave number and w is the width of the midplanar segment and reduces to the solution of diffraction by a single knife edge as w-->0. The theory is incorporated into the deformed edge solution [Stanton et al., J. Acoust. Soc. Am. 122, 3167 (2007)] to model the diffraction by a disk of finite thickness, and is compared with laboratory experiments of backscattering by elastic disks of various thicknesses and by a hard strip. It is shown that the model describes the edge diffraction reasonably well in predicting the diffraction as a function of scattering angle, edge thickness, and frequency.