Index of content:
Volume 69, Issue 2, February 1981

Lens in the nearfield of a circular transducer: Gaussian–Laguerre formulation
View Description Hide DescriptionThe case of a thin lens located in the nearfield of a circular transducer is analyzed assuming circular symmetry for arbitrary transducer size and lens aperture, with or without absorption in the lens medium. Using the Fresnel approximation, the acoustic field is mathematically expressed as a series expansion of Gaussian–Laguerre functions. This technique is applied to the case of a circular‐piston–lens system and an analytical series solution of the field obtained for arbitrary positions of the lens. Numerical results are presented corresponding to several positions of the lens in the nearfield of the circular piston. It is found that the field pattern behind the lens is strongly dependent on the distance between the transducer and the lens, and the ratio of the focal length to the parameter a ^{2}/λ. Here a is the radius of the transducer and λ is the acoustic wavelength. It is also shown that the theory presented here can be applied to study the field of finite Gaussian transducers, focused and unfocused, and transducer–iris systems.

Hybrid ray‐mode fields in inhomogeneous waveguides and ducts
View Description Hide DescriptionHigh‐frequency fields radiated by sources in transversely inhomogeneous waveguides or ducts are conventionally analyzed by ray or normal‐mode techniques. When the duct width is very large, the excessive number of relevant rays or modes introduces computational difficulties. An alternative approach is provided by a hybrid representation that involves ray fields and modal fields in well‐defined combinations: With respect to the angular domain centered at the source point, the modes fill those angular intervals left vacant by rays, and vice versa, the mode angles being defined as the angles of the upgoing and downgoing modal ray congruences as seen from the source. The hybrid mix is dependent on the position of the observer, and an additional remainder field assures the smooth transition from one hybrid combination to another. The analytical formulation, involving partial Poisson summation of the formal ray series, is applied to various ducting environments that cause wave trapping by refraction, reflection from boundaries, or both. For the special case of monotonically varying refractive index in a parallel‐plane waveguide, the results from the asymptotic method are verified by rigorous Green’s function methods. Special examples, supported by numerical comparisons with exact reference solutions, are presented to demonstrate the validity and utility of the hybrid scheme.

Resonance theory of bubbly liquids
View Description Hide DescriptionHost materials containing a large number of small inhomogeneities (such as gas bubbles suspended in a liquid) may be characterized by a set of ’’effective’’ material parameters which differ from those of the host material, as well as from those of the inhomogeneity. A method proposed by Ament [U.S. Naval Research Lab. Tech. Rept. 5307 (1959)] is used here to obtain the effective densities and the (complex) effective propagation constant of sound for liquids containing spherical gas bubbles, by comparing low‐frequency sound scattering from the bubbles with scattering from a sphere of bubbly liquid. In contrast to previous treatments, some higher‐order terms in the low‐frequency expansion are retained here in order to include effects of the monopole resonance. Numerical results are obtained for air bubbles in water and the effects of surface tension, shear viscosity of the liquid, and thermal conduction in the gas, as derived by Nishi [Acustica 33, 65–74 (1975)], are included in our theory and displayed in the graphs.

Scattering of plane waves by a penetrable elliptic cylinder
View Description Hide DescriptionWe discuss here the problems of scattering of acoustic, electromagnetic, and elastic SH plane waves by a penetrable elliptic cylinder embedded in an infinite medium of different properties. Following usual Green’s function approach, the solution of each problem is reduced to that of two simultaneous Fredholm integral equations of the first kind which are solved when the wave lengths in the two media are large as compared with the distance between the two foci of elliptical coordinate systems. Approximate expressions for the external and internal fields, the farfield scattering amplitude, and the scattering cross section of the elliptic cylinder are derived.

Effects of multiple scattering and acoustic interactions among two parallel hydrophones and a planar baffle
View Description Hide DescriptionWhen acoustic energy is incident on a collection of objects, multiple scattering and interaction occur. As a specific case of interest, the acoustic scattering of a plane wave by a system of two cylindrical hydrophones and a planar baffle is investigated. To form a mathematically tractable problem, the cylinders are considered to be infinite in length, and the baffle is considered to be infinite in extent. Three different approaches are presented to predict the scattered fields and hydrophone outputs which result from a harmonic plane‐wave excitation. The approaches correspond to varying levels of analytical complexity which include multi‐order scattering, zero‐order scattering, and no scattering or interactions, respectively. Theoretical results based on the approaches are presented and discussed. The results of a limited experimental program are used to substantiate the validity of the analytical results.

Decoupling approach to modeling perforated tube muffler components
View Description Hide DescriptionA transformation is derived to decouple the two differential equations describing one‐dimensional acoustic wave propagation in the presence of mean flow, in mufflers with partitioned, perforated tubes. The following analysis leads to compact and exact expressions for the matrix parameters of crossflow elements without any concern for convergence of infinite series or segmental analysis employed in earlier studies. The present analysis is, however, based on assumptions of a uniform perforate impedance on the tube, and of equal mean flow in the two ducts. The predicted transmission loss curves agree very well with published data. The decoupled equations make transparent the connection between high‐frequency resonances of perforated elements and the axial propagation of radial velocity fluctuations through the holes, without mean flow. The resonance frequencies of a plug muffler are seen to coincide with resonance frequencies of crossflow elements, which in turn may be correlated very simply and accurately with the dimensionless group (ψl)^{2} defined in this work. This correlation bears out observed trends with variation of geometric parameters.

Diffraction of a spherical wave by a thin infinite plate
View Description Hide DescriptionA thin elastic plate extending to infinity is immersed in a perfect gas. The response of this system to a spherical harmonic sound source is studied, and an exact representation of the solution is developed. From this result, a series representation useful to calculate the farfield is established; expressions for the various mean powers are given.

Nearfield characteristics of parametric acoustic sources
View Description Hide DescriptionBecause it is often impractical to make measurements in the farfield of a parametric acoustic source, it is desirable to be able to predict the farfield from nearfield measurements. A nearfield theory applicable to saturation‐limited as well as absorption‐limited sources, previously outlined [J. Acoustic. Soc. Am. 63, 1622–1624 (1978)], has been programmed for digital computation. Growth curves for the source level and beamwidth of absorption‐limited sources are presented in generalized form. The theoretical results are compared with experimental data from several sources. Sources involving substantial difference‐frequency generation in the primary farfield have broader nearfield beam patterns and lower apparent source levels than in the farfield. On the other hand, when most of the generation occurs in the primary nearfield, the pattern is narrower and the apparent source level higher than in the farfield.

Nonlinear third harmonic resonance of flexural waves on a waveguide of thin elastic plate
View Description Hide DescriptionThe nonlinear third harmonic resonance of flexural waves on a waveguide of a thin elastic plate of infinite length is investigated based on a theory of large deflection of a plate. Two types of waveguide are treated, one having both side edges supported simply and the other having both side edges fixed. Since the nonlinearity in flexural motions of a thin plate is cubic in a deflection, a quasimonochromatic flexural wave and its third harmonic wave can interact resonantly due to the nonlinearity at such a frequency that both waves can propagate simultaneously. The resonance equations for the behavior of two complex wave amplitudes are derived by the method of multiple scales. It is found that, regardless of the edge conditions, the qualitative behavior in each waveguide is governed by the same type of equations. The stationary solutions of the resonance equations show that two wave amplitudes vary periodically to exchange their energy, including solitary waves as limiting cases. Under a special condition, an ’’algebraic solitary wave’’ is also possible.

Elastic wave propagation in fluid‐saturated porous media
View Description Hide DescriptionA new identification of the coefficients in the strain energy functional for Biot’s theory is presented. Two types of porous media are distinguished: (1) With the granular constituents fully consolidated so the porous frame acts as a cohesive unit, and (2) with the granular constituents only partially consolidated so a fraction of the solid particles compose the porous frame while the remaining particles are (essentially) suspended in the saturating fluid. For complete consolidation, an exact identification of the coefficients is found. This identification differs from the standard identification of Geertsma [Trans. AIME 210, 331 (1957)] and of Biot and Willis [J. Appl. Mech. 24, 594 (1957)] for frames whose effective elastic moduli are not related to the grain moduli by the Voigt average. For partial consolidation, an exact identification of the coefficients is not known, but the standard identification is a good approximation. A method from the theory of composites is used to estimate the frame moduli and a theoreticalmodel of the frame inertia in a fluid environment is developed. The predictions of the resulting model are compared to Plona’s [Appl. Phys. Lett. 36, 259 (1980)] recent measurements on a water‐saturated porous structure of sintered glass beads. Good agreement between the theory for a fully consolidated frame and the experiment is found. Measured fast and slow compressional wave speeds agree with the theoretical predictions within experimental error (3%) in all cases.

Underwater sound from surface waves according to the Lighthill‐Ribner theory
View Description Hide DescriptionThe acoustic source density given by Ribner’s version of the Lighthill theory is calculated for a stochastic surface gravity wavefield. A Green function gives the acoustic farfield, as a volume integral. The method eliminates some of the complications involving the moving oceansurface. For a homogeneous ocean, the farfield acoustic spectrum agrees with the spectrum of Hughes [J. Acoust. Soc. Am. 60, 1032–1039 (1976)], and at low frequencies with the spectrum of Brekhovskikh [Izv. Atmos. Ocean Phys. 2, 582–587 (1966)], after certain corrections are applied to their results. At high frequencies, the Brekhovskikh spectrum is larger by a factor (5/4)^{2}.

New formulation for ray theory range derivatives
View Description Hide DescriptionRay theory range derivatives (with respect to ray parameter) are needed in the evaluation of acoustic pressure and corrections for ray theory caustics. A new general formulation for the nth derivative is developed which is recursive in nature, i.e., involves a summation over previous derivatives plus a remainder term. This remainder term is expressed as an integral but can often be determined recursively. Summation over multilayered profiles are simplified with the new method. Specific examples are presented for four commonly used mathematical models of the sound speed profile.

Mode interactions in an ocean with sound speed a linear function of range
View Description Hide DescriptionPierce’s method is used to calculate mode interactions in a ’’Pekeris ocean,’’ modified so that the sound speed in the water layer, although independent of depth, changes linearly and slowly with range. This variation causes mutual perturbations of the normal modes. Simplifying restrictions are (a) two dimensions (depth and range), (b) calculations only for the lowest two modes of several, and (c) approximation of the transcendental eigenvalue equation by an algebraic form. Dissipative effects are neglected. Analytical expressions are derived for the interaction contributions of mode 2 to mode 1 and of mode 1 to mode 2. In first‐order perturbation, all contributions to any one mode are additive. Each interaction produces a forward‐scattered component and a much weaker back‐scattered one. Both are proportional to the gradient of sound speed and, approximately, to H/δ^{2} (H, water depth; δ, ratio of the density of the bottom material to that of water). The back component is also proportional to λ^{2}/H ^{2} (λ, acoustic wavelength). Results are compared with those of an earlier calculation in which the perturbing influence was a linear variation, with range, of water depth.

Laser‐generated ultrasonic pulses at free metal surfaces
View Description Hide DescriptionLongitudinal, shear, and surface acoustic pulses have been generated by irradiation of free metal surfaces with a Q‐switched Nd:YAG laser. Laser energies as low as 3 mJ are sufficient to generate ultrasonic pulses, in various metals, that are readily detected by conventional piezoelectric transducers, without the need for laser focusing. The generation efficiency of longitudinal, shear, and Rayleigh modes has been studied in both the presence and absence of a plasma. Experimental data in graphical form highlight several features of the acoustic source, from which a qualitative model is proposed.

Laser speckle method for the analysis of steady state vibration of plates
View Description Hide DescriptionA laser speckle method is described whereby time‐average slope contours are obtained from vibrating plates. It has an advantage over deflection contouring methods in that only first‐order differentiation of experimental data is needed for stress calculations.

Contaminating effect of probe noise on jet pressure correlations
View Description Hide DescriptionWhen a fast‐responding static pressure probe is inserted into a flow, there are several possible mechanisms for the generation of extraneous noise. If the probe signal is cross correlated with the farfield sound, then the ’’probe noise’’ may contribute a dominant portion of the total correlatable noise from the local source region. A theoretical model is developed for predicting the distortion of ’’causality’’ correlation signatures (obtained when in‐flow probes are cross correlated with the farfield sound), due to the parasitic probe noise. The predicted correlation functions agree with experiments conducted using probes of various shapes and sizes. In practice, the contaminated portion of the causality correlation signature is expected to be displaced in time from the ’’true’’ jet pressure correlation. An unexpected result of the present experiments is the absence of any legitimate correlation between the turbulent pressurefluctuations and the farfield jet noise. This leads to the conclusion that the extent and strength of the jet pressurefluctuations as noise sources must be very weak. Therefore, any probing device inserted into the flow will generally produce a large and potentially misleading portion of the total correlation.

Community noise levels in Patras, Greece
View Description Hide DescriptionIn the city of Patras (Greece), noise measurements were made for the purposes of determining the present noise‐pollution levels and the reaction of the people to them. For the latter purpose, a social survey was conducted with the use of a relevant questionnaire which was applied to 500 citizens. Its results show that noise pollution is ranked second in order after air pollution,and that traffic was the principal noise pollutant. The mean noise levels, in 25 monitoring stations throughout the city, were found to be high and definitely unacceptable. For three representative locations, corresponding to high, medium, and low traffic volume, the various statistical noise descriptors, such as L _{eq}, L _{NP}, L _{dn} and others, were used, together with the other measurements, to estimate the noise environment of the entire city. The high degree of annoyance of the people is justified by the high values of L _{eq}, L _{NP}, L _{dn}, and TNI that were found.

Method for obtaining a nearfield inverse scattering solution to the acoustic wave equation
View Description Hide DescriptionSince the classic paper by Gelfand and Levitan [Am. Math. Soc. Transl., Ser. 2, 1, 253–304 (1955)], much has been published on the inverse scattering problem. Assuming no bound states, there are several well‐known solutions that reconstruct one‐dimensional or spherically symmetric potentials from farfield scattering information. Moses [Phys. Rev. 102, 559–567 (1956)] and Newton [Phys. Rev. Lett. 4, 541 (1979)] have generalized these procedures for three‐dimensional potentials. In this paper, we show how the work of Moses and Newton can be extended to provide a nearfield inverse scattering solution to the acoustic waveequation. In particular, we describe a procedure for obtaining a nearfield inverse scattering solution when the incident probes are arbitrary, unknown, and not necessarily reproducible.

Scattering theory approach to the identification of the Helmholtz equation: A nearfield solution
View Description Hide DescriptionExpressing the Helmholtz equation as a Schrödinger‐type equation with a frequency‐dependent potential allows one to use the techniques of inverse scattering to determine the potential from farfield scatteringinformation. These techniques were designed to accomodate farfield experimental data which was generated by a plane‐wave probe. Here, we consider the problem of finding the potential when (1) the scatteringinformation is restricted to the nearfield and (2) the incident probes are assumed to be arbitrary, unknown, and not necessarily reproducible from experiment to experiment. The basic idea is to derive the on‐shell T‐matrix elements (or scattering amplitudes), which are required by the farfield inverse scattering techniques, from nearfield scatteringinformation. Once the T matrix is known, the potential follows from the techniques of inverse scattering. [See V. A. Marchenko, Math. Rev. 17, 740 (1956) or M. Razavy, J. Acoust. Soc. Am. 58, 956–963 (1975) for the one‐dimensional case, and A. B. Weglein, W. E. Boyse, and J. E. Anderson, to be published in Geophysics (1981) or R. G. Newton, Phys. Rev. Lett. 43, 541 (1979) for the three‐dimensional case.] Recently, M. T. Silvia and A. B. Weglein [J. Acoust. Soc. Am. 69, 478–482 (1981)], presented a nearfield inverse scatteringsolution to the acoustic waveequation for the case when the probes were arbitrary, unknown, and not necessarily reproducible. There, the scattering measurements had to include both the field and its normal derivative. In this paper, a more direct approach to the nearfield inverse scattering problem is presented. Furthermore, for this new technique, we demonstrate that when the incident probe is known, only the field on a closed surface is required for a nearfield solution.

Display of the underwater sound wavefront using the theory of holographic interference
View Description Hide DescriptionUsing the theory of holographic interference and the variable properties of the refractive index of water that has been disturbed by wave motion, a method has been developed where two holograms of the underwater acoustic field are photographed successively on one film plate, before and after the introduction of a wave, which could range in frequency from subsonic to supersonic. A He–Ne laser beam is used to illuminate the film plate, and the image of the wavefront is reconstructed. This new method helps to remove the difficulty underwater acousticengineers have frequently encountered when observing the scene of an underwater wave.