摘要:

When the boundary conditions at the two endpoints of a second‐order differential system depend explicitly upon the eigenvalues such that the system becomes non‐self‐adjoint, a generalized condition of orthogonality which includes endpoint terms can be developed. The generalized orthogonality condition is used to determine modal coefficients for the expansion of arbitrary functions in series of eigenfunctions. The method is applied to the particular case of acoustic wave propagation in a rectangular duct with a uniform mean‐flow profile and walls with finite acoustic impedance. The ability of the eigenfunction expansion to converge to a plane‐wave acoustic pressure profile is demonstrated under a variety of flow, frequency, and wall‐impedance conditions.

ISSN:0001-4966    

DOI:10.1121/1.381383

出版商:Acoustical Society of America    

年代:1977

数据来源: AIP

摘要:

Two frequently employed measures of a statistical radiation field, i.e., the mutual coherence function and the acoustic‐intensity angular spectral density, are considered as they apply to deterministic beamed signals. Mathematical formulations, in the form of differential equations, that govern the propagation of these measures had previously been presented [J. J. Mcloy and M. J. Beran, J. Acoust. Soc. Am. 59, 1142–1149 (1976)]. Here, we show that solutions of these formulations suggest an interpretation of a radiation field in terms of sub‐beams. These sub‐beams are the natural extensions of the ray tubes of the geometric theory. In the Appendix we consider the relationships between the acoustic‐intensity angular spectral density and other more commonly encountered measures of a radition field.

ISSN:0001-4966    

DOI:10.1121/1.381384

出版商:Acoustical Society of America    

年代:1977

数据来源: AIP

摘要:

The reciprocity relations that apply to the scattering of plane, elastic waves that are incident upon an obstacle of finite extent are investigated. In these relations, the particle‐displacement radiation characteristics of the scattered waves occur. The elastic medium outside the obstacle is assumed to be homogeneous, isotropic, and perfectly elastic. Hence, two kinds of acoustic waves can propagate in it, viz., irrotational, compressional orPwaves and solenoidal, shear orSwaves; each of these two waves has its own radiation characteristic. It is shown that the far‐zone scattered wave due to an incident wave propagating in the direction ? and observed in the direction −? is related to the far‐zone scattered wave due to an incident wave propagating in the direction ? and observed in the direction −?. This reciprocity property is next applied to two incidentPwaves, two incidentSwaves, and an incidentPwave and an incidentSwave. The resulting reciprocity relations hold under the assumption that the scattering obstacle is linear and reciprocal in its elastic behavior.

ISSN:0001-4966    

DOI:10.1121/1.381393

出版商:Acoustical Society of America    

年代:1977

数据来源: AIP

摘要:

A distributed coupling transducer consists of an electric and an acoustic transmission line continuously and reversibly coupled to each other. The operation of this device is described by four coupled first‐order differential equations. The solution to these equations is obtained in closed form for both infinite and finite transmission‐line systems. The example of a side‐plated piezoceramic bar is considered in setting up the equations. A comparison between the complete theory and an approximation based on the infinite transmission line is given. Some aspects of the design of a high‐efficiency, broadband electroacoustic transducer with a relatively constant resistive electrical driving‐point impedance are presented.

ISSN:0001-4966    

DOI:10.1121/1.381394

出版商:Acoustical Society of America    

年代:1977

数据来源: AIP

摘要:

It is commonly observed in long‐range propagation that the phase fluctuation period is longer than that of the amplitude. A phase‐random multipath model, used previously to explain amplitude statistics [I. Dyer, J. Acoust. Soc. Am. 48, 337–345 (1970)], is now applied to the joint problem of amplitude and phase. The ratio of phase period to amplitude period is found to be proportional to a Rayleigh probability density, with a peak value of about three. This result is supported by data acquired by the Woods Hole Oceanographic Institution and analyzed by us, for a 300‐km propagation path extending approximately northeast from Eleuthera.

ISSN:0001-4966    

DOI:10.1121/1.381395

出版商:Acoustical Society of America    

年代:1977

数据来源: AIP

摘要:

Acoustic phase and amplitude fluctuations measured during two experiments, one near Eleuthera Island and one near Bermuda, are presented and interpreted in terms of the interaction of sound with internal gravity waves. Data were collected with a variety of sensors including drifting ship‐suspended hydrophones, sonobuoys (free‐floating acoustic receivers equipped with a UHF transmitter for data communication), and moored hydrophones. The phase data were corrected for hydrophone motion by means of a bottom‐moored Doppler navigation system. Oceanographic data are presented and compared with the acoustic data; these data comparisons show that internal waves are responsible for much of the acoustic fluctuations. Phase spectra obtained with moored hydrophones show a rapid spectral decay at frequencies above the highest osberved Brunt–Vaisala frequency as predicted by internal‐wave–acoustic models. Spectra obtained with drifting hydrophones are compared with a recently proposed random, multipath model based on interaction of sound with internal waves. Spectra obtained for drifting hydrophones at a depth of 1500 m agree with the multipath‐model prediction. Spectra from phones at shallower depths exhibit an order of magnitude more fluctuation energy than is predicted. Slowly drifting sonobuoys at a depth of 300 m produce spectra with a complex frequency dependence that can not be predicted by the random multipath model.

ISSN:0001-4966    

DOI:10.1121/1.381396

出版商:Acoustical Society of America    

年代:1977

数据来源: AIP

摘要:

Temporal modulation of light obtained by a diffraction device consisting of an ultrasonic beam and an optical grating has been theoretically described under the hypotheses of diffraction effects not superposed (thick‐screen treatment). In comparison with any thin‐screen theory considering spatially superposed effects, the present thick‐screen treatment is in better agreement with the experimental results.

ISSN:0001-4966    

DOI:10.1121/1.381397

出版商:Acoustical Society of America    

年代:1977

数据来源: AIP

摘要:

The stability of an elastic layer being excited by a flow field is examined. The dynamics of the elastic layer is assumed to be governed by the basic elasticity equations. On the lower surface the layer is assumed to be fixed to a rigid surface. On the upper surface, a potential flow field is assumed to provide the exciting force. A solution to the linearized set of elasticity and fluid‐mechanics equation is obtained. When all of the boundary conditions are satisfied, a compatibility equation is obtained. Complex and real eigenvalues of this equation for different Poisson’s ratio, Young’s modulus, and flow velocity have been obtained. In the limit as the fluid density goes to zero the classical Rayleigh surface waves are recovered.

ISSN:0001-4966    

DOI:10.1121/1.381398

出版商:Acoustical Society of America    

年代:1977

数据来源: AIP

摘要:

In this study, reflection and refraction of transient waves in a nonhomogeneous fluid‐filled porous body is investigated. The body involves a layer of one porous material perfectly bonded to a half‐ space of another porous material. Transient waves are generated at the top surface of the layer by a time‐dependent applied pressure. For a variety of material properties chosen for the layer and half‐space, the time variations of various physical quantities are found at two stations: one in the layer, the other in the half‐space. A study of numerical results, obtained by the method of characteristics, indicates that the rigidity of the half‐space relative to that of layer strongly affects the reflection and refraction characteristics of transient waves with regard to sign while the relative permeability of the half‐space has an influence on their dispersive characteristics.

ISSN:0001-4966    

DOI:10.1121/1.381399

出版商:Acoustical Society of America    

年代:1977

数据来源: AIP

摘要:

A characteristic equation is derived analytically for a rectangular plate with thickness varying linearly in one direction by using the trigonometric series. Boundary conditions of the plate are simply supported along two opposite sides, free along one side and simply supported or free along the remaining side. By using the results computed numerically from the characteristic equation, approximate formulas are derived for estimating accurately the fundamental natural frequency of the plate.

ISSN:0001-4966    

DOI:10.1121/1.381400

出版商:Acoustical Society of America    

年代:1977

数据来源: AIP