Index of content:
Volume 73, Issue 5, May 1983

A history of violin research
View Description Hide DescriptionFrom the probable origins of the violin in the early 16th century there is a long history of experimentation; first, the empirical development of the violin by the makers themselves over more than 200 years to its height of excellence in the late 17th and 18th centuries; then the scientific investigations of its vibrational characteristics which have been done since the early 19th century. These have progressed in spurts of activity associated with technological innovations, particularly the developments of increasingly sensitive measuring equipment. This paper attempts to cover briefly the work of the early mathematicians as well as that of Savart, Helmholtz, and Rayleigh as related to the violin; then considers the research of the 20th century from the pre‐electronic investigations of Raman, Miller, and Fuhr, through the spate of activity in violin research from 1930 to 1960 particularly in Germany, the USA, and Japan; and finally a brief overview of the many current developments associated with today’s electronic and optical technologies, along with the concept of the violin as a musical instrument involving research in fields as widely separated as psychoacoustics,musical composition and performance, materials research, vibration analysis, and violin making.

A finite‐difference treatment of interface conditions for the parabolic wave equation: The irregular interface
View Description Hide DescriptionA finite‐difference solution to the parabolic wave equation is extended to treat an irregular interface. Interface conditions are developed to preserve continuity of pressure and continuity of the normal component of particle velocity at the boundary between media having different sound speeds and densities. A complete mathematical treatment for the case of an irregular interface is presented. To demonstrate the method, numerical results are obtained for sound propagation from deep to shallow water.

Acoustic resonance scattering by a penetrable cylinder
View Description Hide DescriptionAlthough sound scattering by submerged elastic cylinders has been the subject of many papers, it was only recently that this and similar problems have been examined in the light of the resonancescattering theory (RST). Crucial experiments have been performed recently at Le Havre, France, in which the modal resonances contained within the cylinder’s backscattering cross section were isolated by means of a background subtraction, experimentally accomplished by a clever time‐gating technique. In the present paper we generate a variety of tailor‐made calculations and graphical displays required to thoroughly examine those experiments in the light of the RST. For the same cylinder, liquids, and frequency ranges of interest we have produced many spectral graphs displaying all the modal resonances that combine with the modal backgrounds to produce the observed and/or predicted cross sections. Our calculations: (a) display the whispering gallery and Rayleigh‐type poles in the complex frequency plane and show their connection with the target resonances they generate, which manifest themselves as circumferential w a v e s around the target, (b) explain quantitatively why some of the modal resonances were missed in the experiment, (c) establish comparisons between predicted and observed monostatic and bistatic form functions (or cross sections) in a d i r e c tscattering mode of operation, and (d) show ways to improve both the monostatic and bistatic measurements performed at Le Havre, paving the way toward the solution of i n v e r s escattering situations. Within the limits of simple shapes and compositions, and within the controlled environment of the laboratory, these favorable comparisons have satisfactorily validated many of the predictions of the RST in the field of acoustics.

Resonance reflection of acoustic waves by a perforated bilaminar rubber coating model
View Description Hide DescriptionWe construct the prediction of the resonancescattering theory (RST) for the reflection of sound waves by a bilaminar rubber configuration separating two dissimilar semi‐infinite acoustic media. The layers are further assumed to contain distributions of spherical air‐filled perforations, of various concentrations in each layer, whose behavior is governed by a simple, static, ‘‘effective parameter’’ model. We compare the direct scattering prediction of the RST to that of the exact solution in order to show the usefulness of the RST to yield clear physical interpretations of complex phenomena. The casting of the direct scattering solution in ‘‘RST‐form’’ also provides a systematic method to solve the inverse scattering problem for the composition of the bilaminar rubber configuration. The ‘‘response surface’’ and response curves of the returned echoes are shown to contain certain modulation effects, described in the text, that actually characterize the material composition of each of the layers making up the coating model. The process disentangles which resonance feature present in the reflection coefficient is caused by which one of the interacting layers. In particular, we can separate and identify the impedances and the respective thickness‐to‐speed ratios (transit times) of each of the layers, and if additionally, either the thicknesses or the speeds are known, then, the process determines the other one and also the layer densities all from the resonances in the remotely sensed acoustic reflections.

Glory‐ and rainbow‐enhanced acoustic backscattering from fluid spheres: Models for diffracted axial focusing
View Description Hide DescriptionTransmitted‐wave contributions to backscattering from large spheres are calculated. Amplitudes due to glory rays are enhanced, relative to those of axial reflections, because of focusing. The glory pressure amplitudes are proportional to a(k a)^{1} ^{/} ^{2}, where a is the sphere’s radius and k is the wavenumber. The model, though similar in form to one for optical scattering from air bubbles [D. S. Langley and P. L. Marston, Phys. Rev. Lett. 4 7, 913–916 (1981)], contains new features to facilitate the summing of amplitudes in a range of angles. An additional enhancement due to rainbow focusing is modeled for certain sound velocity ratios M; for these M the backscattered amplitude is proportional to a(k a)^{2} ^{/} ^{3}. Major features of the exact scattering are reproduced by these models when k a=1000 and (with defects) k a=100. The enhancements are not intrinsically due to resonance. Applications to the design of passive sonar targets are noted.

An examination of the composite‐roughness scattering model
View Description Hide DescriptionA perturbation technique is applied to derive a composite‐roughness theory for acoustic scattering from the sea surface. The leading term in the expansion obtained is the well‐known result obtainable using ad hoc arguments. Higher order terms are evaluated to assess their contribution to the high‐frequency monostatic backscattering strength of the sea. It is concluded that the leading term in the perturbation expansion provides an excellent approximation.

Scattering of elastic waves by a fluid inclusion
View Description Hide DescriptionThe scattering of harmonic elastic waves by a bounded fluid inclusion in an infinite elastic continuum is considered. The formalism is an extension of the T‐matrix method developed for solid inclusions and cavities in elastic media and elasticsolid inclusions in fluid media. The problem that is considered here is somewhat more complicated and shares some similarities with the case of an elastic cavity. For the fluid inclusion, however, the scattering amplitudes display resonance peaks due to interior resonances of the fluid. The convergence of the truncated series is dependent on the largest wavenumber which in the cases studied here is that in the fluid inclusion. Numerical results are presented for a prolate spheroidal inclusion.

Low‐frequency acoustic diffraction by a soft elliptic disk
View Description Hide DescriptionThe problem of the diffraction of an arbitrary incident plane sound wave by a soft‐sound elliptic disk is studied. A Fredholm integral equation of the first class is posed and solved explicitly in the low‐frequency limit up to terms of O(κ^{2}), κ being the wavenumber, though higher order terms could be found in a similar fashion without much difficulty. The solution is new and expressions for the farfield amplitude (which are also believed to be new) and the scattering cross section are obtained to the same order. The limiting values when the ellipse degenerates into a circle agree with those of a circular disk found using other methods. Also the scattering cross section agrees with expressions obtained using alternative methods.

Finite element eigenfunction method (FEEM) for elastic (SH) wave scattering
View Description Hide DescriptionA finite element eigenfunction method (FEEM) is presented for elastic (SH) wave scattering by cylinders of arbitrary cross section. The problem has been analyzed by enclosing the scatterer within an imaginary circular cylinder. The scattered field outside the circular cylinder is expanded in the usual cylindrical harmonics. The nearfield solution inside the circular cylinder is also assumed to be expanded by a series of eigenfunctions. The eigenfunctions for the nearfield are generated through the standard finite element technique by imposing suitable conditions on the circle. Then both the coefficients of the scattered field and those of the nearfield are found by means of a least‐square fit for the continuity conditions across the circle. The solution obtained thereby is considered complete in the sense that both the scattered and the nearfields are solved simultaneously. The validity of this method has been verified by comparing results with calculations from exact analysis and the T‐matrix method for (a) centered circular cylinder, (b) off‐centered circular cylinder, (c) elliptical cylinder, and (d) square cylinder.

Crosscorrelation functions for directionally distributed energy fields
View Description Hide DescriptionThis paper presents the time‐lag probability density function between two sensor outputs for several types of directionally distributed energy fields. The convolution of this density function with the inverse Fourier transform of an energy field’s frequency power density spectrum is the crosscorrelation function between the two sensor outputs.

A series expansion of the acoustic power radiated from planar sources
View Description Hide DescriptionA series expansion in ascending powers of the wavenumber k is derived for the acoustic power delivered by baffled or unbaffled planar sources. This series provides a relatively simple means of deriving expressions for the power radiated by a baffled source with a known velocity distribution and can be used for unbaffled plates when the velocity field outside the plate is also known. The terms in the series are calculated from the moments of this velocity distribution in the plane containing the source. If these moments are written as derivatives in wavenumber space, it is shown that a MacLaurin expansion of the Fourier transformedvelocity provides an easy technique for computing the first few terms of the acoustic power. Examples are provided for baffled, rectangular plates with various boundary conditions. The arbitrarily shaped plate with free boundaries is particularly interesting. It is proven that the volume flow across its surface must be zero and as a result corner and edge mode radiation cannot exist for this kind of source.

Finite amplitude method for the determination of the acoustic nonlinearity parameter B/A
View Description Hide DescriptionThe acoustic nonlinearity parameterB/A is determined using a method based on the finite amplitude distortion of a sine wave emitted by a piston. The growth of the second harmonic component of this wave is measured by a piston receiver which is coaxial with and the same size as the source. In order to determine B/A, the experimental measurements are compared to a theory which incorporates the nonlinearity parameter. The theory developed for this study accounts for the influence of both diffraction and attenuation on the experimental measurements. For this reason, the method is more accurate than previous techniques that employ plane‐wave theory for a lossless medium. To test the measurement method, experimental results for B/A in distilled water, ethylene glycol, and glycerol are compared to established values. The agreement between these values suggests that the measurement accuracy is ±4% for common liquids.

The audio spotlight: An application of nonlinear interaction of sound waves to a new type of loudspeaker design
View Description Hide DescriptionThis work was done to devise a new type of loudspeaker. The theory for sound reproduction of this loudspeaker is based on nonlinear acoustics of soundwaveinteraction in air. A finite amplitude ultrasoundwave that can be amplitude modulated by any audio signal is radiated from a transducer array into air as the primary wave. As a result, an audio signal is produced in the air because of the self‐demodulation effect of the AM soundwave due to the nonlinearity of the air. It is possible to get a flat characteristic of reproduced sound pressure by using an equalizer. In some fundamental experiments the characteristic of the reproduced sound pressure is not quite flat due to an imperfect transducer array. Improvement of the transducer makes it possible to get a flat characteristic. A special feature of this loudspeaker is its very sharp directivity pattern, which makes it possible to realize a sound spotlight.

Theoretical investigation of the response of gas‐filled micropores and cavitation nuclei to ultrasound
View Description Hide DescriptionTheory is discussed for the transverse oscillation of a small circular interface set into a rigid baffle between gas and liquid. The angular resonance frequency is given by (15πT/4ρa ^{3})^{1} ^{/} ^{2}, in which a is the radius of the interface,T is the interfacial surface tension, and ρ is the density of the liquid. Damping parameters are obtained for the radiation, viscous, and boundary‐layer mechanisms of dissipation. This model system is extended for discussion of the pulsation of gas trapped in a pit or cavity in a solid, which may simulate one type of cavitation nucleus, and straight‐through cylindrical holes or pores in a solid sheet, which is applicable to the hydrophobic membranes with gas‐trapping micropores used in studies of biological effects produced by ultrasound. Fixed and free conditions at the three‐phase line at the periphery of an interface are considered. Finally, the partially gas‐filled cavity is treated, and also the partially gas‐filled pore with two interfaces which have different mass, stiffness, and damping parameters. The results of these theoretical considerations are expected to be of value for quantitatively evaluating that specific form of stable cavitation which involves the direct activation of pre‐existing, stable bodies of gas into ultrasonic pulsation, as experimentally observed, for example, by D. Miller, J. Acoust. Soc. Am. 7 1, 471–476 (1982).

Turbulence effects on acoustic wave propagation over a smooth surface
View Description Hide DescriptionA rigorous, mathematical treatment describing refractive turbulence effects on the mean‐square pressurep̄^{2} of an isotropic acoustic source radiating above a smooth boundary is presented. The result is energy conserving, is general enough to allow the insertion of an arbitrary refractive‐index correlation function, and does not require the a d h o c introduction of arbitrary parameters. This result is compared and contrasted with earlier work by other authors.

Effect of the branch‐cut on the transformation between modes and rays
View Description Hide DescriptionIn this paper the effect of the branch‐cut on the transformation between the modes and rays is discussed. Characteristics of the bottom reflection coefficient on the ζ plane were analyzed in detail and a certain branch‐cut was taken. Once the integral path of the generalized ray is deformed to the real axis of the ζ plane, the ray representation consists of ‘‘canonical’’ generalized ray and a ‘‘lateral term.’’ The mode representation and the ray representation are given as follows: Mode representation=∑^{∞} _{ n }φ_{ n }(r,z,z _{0}) +∮_{ b }. Ray representation =∑^{∞} _{ l } B _{ l }(r,z,z _{0}) +J^{∞} _{ l }∮_{ b l }. It was found that the ‘‘canonical’’ generalized ray B _{ l } and the normal mode φ_{ n } were still connected by the Poisson summation relation strictly, as proved by our previous paper [Gao and Shang, J. Sound Vib. 8 0, 105–115 (1982)]. The sum of the ‘‘lateral term’’ of the ‘‘canonical’’ generalized ray was exactly equal to the part of the ‘‘lateral’’ wave in the mode representation:∮_{ b }=∑^{∞} _{ l }∮_{ b l }.

Modeling of long‐range acoustic transmissions through cyclonic and anticyclonic eddies
View Description Hide DescriptionAn approximate ray‐acoustic model is used to obtain general information and overall results for long‐range sound propagation through mesoscale cyclonic and anticyclonic eddies of arbitrary size and strength. Two‐dimensional ray approximations are employed, and currents and horizontal sound‐speed variations are averaged along approximate paths within an eddy. Eddy‐induced per‐ray travel‐time changes are shown to depend nearly linearly on current strength and piecewise linearly on eddy size. For transmission ranges of about 1000 km, the presence of the eddy may cause per‐ray travel time to increase (or decrease) by nearly 200 ms in the cyclonic (or anticyclonic) case. Variations in eddy current strength alone are shown to cause changes of about 100 ms in per‐ray travel time. Currents may cause travel‐time changes which are as much as those due to sound‐speed variations close to eddy edge, and which are as much as 15% of sound‐speedeffects elsewhere. This suggests that in an acoustic tomography procedure, a corresponding percentage error in predicted sound‐speed variations may arise by neglecting currents. In some total‐field examples, it is shown that variations in eddy size and strength, and in source and receiver location, can cause an increase of about 5 dB or decrease of over 10 dB in transmission loss, relative to the case when the eddy is absent. Further, it is shown that explicit inclusion of currents alone may cause an increase or decrease of over 10 dB in transmission loss.

Normal mode identification for impedance boundary conditions
View Description Hide DescriptionA prescription is presented for identifying normal modes calculated using the plane‐wave reflection coefficient (impedance condition) to represent bottom interaction. The new prescription reduces to the usual equality between mode number and number of eigenfunction zeros for a fluid layer over a homogeneous fluid bottom. For a more complex bottom composition, the mode number also has a contribution given by the number of times that, as a function of horizontal wavenumber, the reflection coefficient circles the origin in the complex plane.

Long‐range Atlantic acoustic multipath identification
View Description Hide DescriptionMultipath data from three long‐range (900 km) transmissions are examined. Two of the transmissions follow similar tracks, with one ending in the Gulf Stream at the receiving end. The third, which is substantially free of Gulf Stream influence, has been extensively studied by Spiesberger e t a l. [J. Acoust. Soc. Am. 6 7, 2011–2017 (1980)]. The path structure of the transmission crossing the Gulf Stream was characterized by low S/N and appeared to be unstable. Path identification with ray calculations was attempted for the two transmission channels exhibiting stable multipath with success for the major features of the path structures. Excessive smoothing of the sound‐speed profile which eliminates the influence of the Atlantic 18° water in the upper layers is shown to degrade the identification of early arrivals. The slight curvature of the ocean sound‐speed profile around 4 km of depth also was critical to early arrival identification. The effect of weak range dependence was small while the effect of a gradual sloping bottom near one receiver was significant.

Ray calculations with beam displacement
View Description Hide DescriptionRay theory with beam displacement is used to calculate the sound field in shallow water as a function of range. Results for the Pekeris model are compared with normal mode calculations and agreement is good even when the water depth is only a few wavelengths. The inclusion of beam displacement leads to the formation of ray caustics. Caustics are important at all ranges and occur even in isovelocity layers. Eventual failure of the ray method at short ranges and very low frequencies is traced to difficulties with the approximate evaluation of integrals by the method of stationary phase.