Volume 57, Issue 4, April 1975
Index of content:
57(1975); http://dx.doi.org/10.1121/1.380518View Description Hide Description
In this paper are presented certain basic considerations of the dependence of noise on vibrations of surfaces. It deals with the problem of cross‐correlating vibration and noise for a given system in a semireverberant environment, taking into account the effects of multiple sources of similar character, surface‐area contributions, and reflections from the boundaries. Limitations of this approach and the standard error involved are given. Also indicated are expressions for the percentage contribution from the vibration of an individual component to the total noisepressure. The applicability of this method has been demonstrated in an investigation of structural vibration‐generated noise of a high‐powered diesel engine. It is concluded that the method can be applied successfully to investigate quantitatively the vibration‐related noise of a complex machine or structural system, even in a semireverberant acoustic field and in the presence of multiple noise sources of similar character.
Subject Classification: 20.60; 40.20; 45.40.
57(1975); http://dx.doi.org/10.1121/1.380519View Description Hide Description
This paper presents a study of the propagation of harmonic waves of plane strain in elasticcomposite materials. The compositestructure is idealized as an assembly of identical subregions, each with the displacement field represented by a finite number of generalized displacements. The resulting model possesses a periodic lattice‐type structure and its response to harmonic waves can be investigated as a problem in lattice dynamics. A set of generalized coordinates, applicable for the case of harmonic wave propagation in the discrete periodic structure, is employed to generate an algebraic eigenvalue problem, the solution of which gives the frequency spectrum for the medium. To show the accuracy of this method, examples of harmonic wave propagation in infinite isotropic and orthotropic homogeneous plates are presented, and cases of harmonic wave propagation in infinite isotropic and orthotropic media. The method is used to generate the frequency spectra for both a fiber‐reinforced composite plate and an infinite composite medium to clearly indicate the dispersive effects which exist in periodic media when the half wavelength–lattice dimension ratio approaches unity. These results are compared with several well‐known theories for composite materials.
Subject Classification: 20.15.
Three‐dimensional acoustic wave scattering and diffraction by an open‐ended vertical soft cylinder in a half‐space57(1975); http://dx.doi.org/10.1121/1.380520View Description Hide Description
The formal solutions to the three‐dimensional problem of scattering and diffraction due to an impulsive acoustic point source in a fluid half‐space, in which a semiinfinite vertical soft cylinder is embedded, have been obtained in integral forms. The early time‐displacement velocities have been evaluated (1) in the shadow region by the Residue–Cagniard method and (2) in the illuminated region by the saddle‐point–Cagniard method. In the shadow region, there are two types of diffractedwaves, i.e., the diffractedwaves without and the diffractedwaves with the reflection from the free surface. In the illuminated region, there are four types of waves: the direct wave, the reflected wave from the free surface, the reflected wave from the cylinder without reflection from the free surface, and the reflected wave from the cylinder with reflection from the free surface. Numerical results for the early time displacement velocities in the shadow region and in the illuminated region for the cases r = a, z = 5a, ϑ − ϑ0 = 0°, 90°, 120°, 150°, and 180°, and r 0 = 5a, z 0 = 10a are given.
Subject Classification: 20.30, 20.15.
57(1975); http://dx.doi.org/10.1121/1.380521View Description Hide Description
Reflection behavior is examined for an interface having periodic height variation. Upon employing the Bloch theorem, in conjunction with the extended boundary condition, exact matrix equations are obtained for surface fields, as well as transmitted and reflected wave amplitudes. Tunneling considerations then lead to new energy constraints for problems of this type, in which propagating waves are coupled with evanescent modes. In the limit of surface corrugations shallow compared with impinging wavelength, analytic results are obtained confirming both the energy constraints and early computations by Rayleigh. Numerical results demonstrate the efficiency of the method.
Subject Classification: 20.30.
57(1975); http://dx.doi.org/10.1121/1.380522View Description Hide Description
The method of multiple scales is used to derive a nonlinear Schrödinger equation for the temporal and spatial modulation of the amplitudes and the phases of waves propagating in a hard‐walled circular duct. This equation is used to show that monochromatic waves are stable and to determine the amplitude dependance of the cutoff frequencies.
Subject Classification: 25.20; 20.45.
Nonlinear oscillations of gas bubbles in liquids. Transient solutions and the connection between subharmonic signal and cavitation57(1975); http://dx.doi.org/10.1121/1.380523View Description Hide Description
The transient nonlinear oscillations of a spherical gas bubble in an incompressible, viscous liquid subject to the action of a sound field are investigated by means of an asymptotic method. Approximate analytical solutions are presented for the frequency regions of the fundamental resonance, the first and second subharmonic, and the first and second harmonic. Based on the results of this investigation, a new hypothesis to explain the connection between subharmonic signal and cavitation is put forward. It is suggested that bubbles emitting the subharmonic signal act primarily as monitors of cavitation events, and are smaller than resonance size. Finally, the free oscillations of the bubble are briefly considered.
Subject Classification: 35.10.
57(1975); http://dx.doi.org/10.1121/1.380524View Description Hide Description
Recordings of six thunder events have been analyzed in 1/3‐octave bands over the frequency range 50–500 Hz to determine the relative acoustic power spectrum. The received power spectra have been corrected for propagation loss due to viscosity,thermal conductivity, and molecular relaxation. The correction, which is strongly dependent upon atmospheric conditions that were not measured, yields spectra so nearly identical to suggest that the six thunder events have identical spectra (within 5 dB) in the frequency range considered.
Subject Classification: 28.20; 20.35.
57(1975); http://dx.doi.org/10.1121/1.380514View Description Hide Description
Recent advances in the understanding of the structure of boundary layer turbulence form the basis of a new conceptual model for the fluctuating velocity field. In this, an ’’active’’ mode of small‐scale motion is coupled to a large‐scale ’’passive’’ mode by aid of wave mechanical considerations. The small‐scale motion originates during the intermittent ’’bursting’’ in the wall layer, leading to excitation of large‐scale, damped, traveling shear waves. It is argued that the passive‐wave‐like mode gives the major contribution to the pseudosound, whereas the active bursting mode serves as the predominant source for the radiative noise. It is shown that the bursting mode gives rise to compact noise sources of both dipole and quadrupole type whose strengths are related to the turbulent shear stress production.
Subject Classification: 28.65; 50.55.
57(1975); http://dx.doi.org/10.1121/1.380515View Description Hide Description
This experiment studies the relationship between ocean movements and acoustical fluctuations southwest of Bermuda. Sound transmission over a single skip distance RSR path was maintained for a 33‐h period. During the same time interval, ocean changes were monitored both at the source and near the second turning point of the sound‐ray path. Some correlations were observed among some of these observations.
Subject Classification: 30.20; 28.60.
57(1975); http://dx.doi.org/10.1121/1.380516View Description Hide Description
The parabolic equation method for the solution of the elliptic Helmholtz equation in a waveguide is analyzed in terms of normal modes and is found to involve two approximations. The approximate treatment of mode coupling becomes exact in the limit of negligible scattering into the backward hemisphere. The approximate treatment of mode propagation becomes exact in the limit of uncoupled, single‐mode propagation. An estimate of the maximum range over which multimode propagation is accurately predicted is derived and a procedure is indicated whereby this maximum range can be increased. The result is a method, based on the parabolic equation approximation, whereby the Helmholtz equation can be solved as an initial value problem. The solution obtained approaches the exact solution in the limit of negligible backscatter. Application is considered to the problem of acoustic propagation in an ocean medium having range‐ and depth‐dependent properties.
Subject Classification: 30.20.
57(1975); http://dx.doi.org/10.1121/1.380517View Description Hide Description
Sound speed is assumed to be a function of one horizontal coordinate and depth, and the medium is taken to be time independent during a sound transmission. Rays are assumed to lie in a vertical plane and a differential equation is given for their solution. A perturbation technique is presented for determining the rays, and is applied when the horizontal sound‐speed variation is slow and much less than the vertical variation. Under appropriate assumptions, ray arcs above the SOFAR axis are found to be approximately elliptical, and a modified Snell’s law is given. The sound speed is taken to be bilinear with depth, with the upper portion pivoting with range, thereby approximating the effect of a single‐frequency internal wave. Numerical examples of SOFAR ray geometry are presented and interpreted for various internal‐wave phase angles and wavelengths. The sound speed near the source has a major effect on geometry, even at long range. However, variations in geometry along the ray suggest the importance of horizontal sound‐speed changes over the entire propagation range.
Subject Classification: 30.20; 20.25.
57(1975); http://dx.doi.org/10.1121/1.380525View Description Hide Description
In a stratified oceanmodel, in which the sound speed and density become constant as the depth coordinate becomes infinite, the pressure field can be represented as a finite sum of modes plus an integral superposition of modes. This later contribution is given by an integration around a branch cut. In this analysis the sound‐speed and density profiles are partitioned in layers such that in each layer the square of the index of refraction can be approximated by a straight line and the density by a constant. The profile is terminated in a high‐speed isovelocity half space. Using this profile, it is possible to express the depth‐dependent portion of the pressure field in terms of Airy functions. Evaluation of the modal and branch line contributions shows that the branch integral can contribute significantly to the pressure field over a range equal to at least one water depth and in some cases to many water depths.
Subject Classification: 30.20, 30.25.
57(1975); http://dx.doi.org/10.1121/1.380526View Description Hide Description
This paper presents the results of an experimental investigation of several passive sonar targets of the types used for calibration, marking, and tracking. Targets studied include spheres, spherical lenses, triplanes, icosahedrons, biconics, and some composite types designed to have specific frequency responses. It is concluded that, of the targets investigated, only the accurately made sphere and spherical lens are suitable for use as calibration standards under the condition of the target being supported by a flexible line. The various corner reflector configurations are suitable for marking, navigation, and tracking. The feasibility of designing passive targets with a specified frequency response is demonstrated.
Subject Classification: 30.30, 30.50.
57(1975); http://dx.doi.org/10.1121/1.380527View Description Hide Description
Acoustic waves are dispersed by two distinct mechanisms as they propagate through a fiber‐reinforced viscoelastic material. The first mechanism, viscoelastic dispersion, is characterized by an increase in phase velocity with an increase in frequency, and the second mechanism, geometric dispersion, is characterized as a wave‐filtering phenomenon in which periodic waves are selectively transmitted and reflected. To study the interplay between these two mechanisms, the dispersion characteristics of two fiber‐reinforced viscoelastic materials were obtained at various temperatures using a water‐bath technique. The first composite studied was a cloth‐laminate quartz phenolic (2D‐QP). Its dispersion characteristics (both phase velocity and attenuation versus frequency) were obtained at seven temperatures, ranging from 4 ° to 40 °C. The second material studied was stainless steel wires embedded in an Epon 828‐Z matrix (Epon–SST). Its dispersion characteristics (phase velocity versus frequency) were determined at five temperatures, ranging from 5 ° to 42 °C. The characteristics of these two materials at their low‐frequency limits are similar; namely, the phase velocity decreases with increasing temperature. There, the similarity ends. The relatively fine structure of the 2D‐QP is weakly dispersive below 4 MHz, and viscoelastic dispersion dominates; whereas the relatively coarse structure of the Epon–SST is highly dispersive below 2 MHz (the cutoff frequency of the first passband was found to be about 1 MHz and this composite behaves as a wave filter.
Subject Classification: 35.26, 35.50.
57(1975); http://dx.doi.org/10.1121/1.380528View Description Hide Description
The spectrum of light scattered from thermal sound waves has been studied by Brillouinspectroscopy in molten potassium nitrate to provide information about the hypersonic velocity and the absorption of thermal waves. Brillouinspectra were investigated in a temperature range of 350–600 °C for scattering angles of 40 °–140 ° to determine the variation of the phonon velocity and attenuation as a function of temperature and frequency. The measurements did not reveal any difference between the sound velocities at a scattering angle of 40 ° (3 GHz) and at 140 ° (10 GHz), but the hypersonic velocities were all higher than the ultrasonic ones. In spite of this fact, considerable decrease in attenuation was observed within the investigated frequency interval, with the value at high frequency approaching the classical limit attributed to shear viscosity. These results indicate a relaxation frequency just below the measured frequency range. The relaxation time for the bulk viscosity coefficient was determined from two independent measurements: (1) the position of the Brillouin lines and (2) the width of these lines. A relaxation theory involving a single relaxation time has been applied and agrees with the experimental results.
Subject Classification: 35.24, 35.35.
57(1975); http://dx.doi.org/10.1121/1.380529View Description Hide Description
A tone‐burst rod analogous to a fluid‐filled pulse tube has been developed for studying audible sound propagation in small solid objects. The apparatus consists of a long aluminum rod driven at one end with longitudinal tone bursts by a small loudspeaker. Instrumentation is provided for measuring the input force, the particle displacement at points along the rod, and the force propagated to the remote end. The interval between the arrival at a displacement probe of outgoing and echo tone bursts is used to determine the impedance of objects attached to the rod. Experiments show that the quality of the mechanical tone bursts is good, the longitudinal wavesound speed in aluminum is largely independent of static tension and frequency, and the acoustical energy propagated along a statically stressed rod departs from the stressed path onto unstressed branch rods.
Subject Classification: 40.85, 40.60.
Real and imaginary parts of the complex viscoelastic modulus for boron fiber reinforced plastics (BFRP)57(1975); http://dx.doi.org/10.1121/1.380530View Description Hide Description
The general viscoelastic model was chosen to represent the mechanical properties of boron fiber reinforced plastic (BFRP). The experimental configuration selected was that of a thin beam subjected to transverse vibration. The mechanical properties of the beam (in the direction x parallel to the length of the beam) then manifest themselves in the form of a viscoelastic complex modulusE* x x = E\ x x + i E\ x x . In this investigation the purposes were to measureE′ x x and E\ x x (and the loss factor) for BFRP and to compare the loss factors for BFRP with that for a metallic material such as aluminum 2024‐T4 alloy. Boronlaminates used in these studies were fabricated from NARMCO 5505 preimpregnated boron fiber epoxy tape. Values of storage modulusE′ x x and loss modulusE\ x x as a function of excitation frequency are presented for three fiber orientations, 0 ° (undirectional), ±45 ° (crossply), and 90 ° (all transverse). Also presented is the damping (or loss) factor η x x as a function of excitation frequency for the three above‐mentioned fiber orientations. The values obtained for damping factor are compared with those obtained by measuring exponential decay of BFRP beams initially excited in the free–free mode of vibration.
Subject Classification: 40.60, 40.22.
57(1975); http://dx.doi.org/10.1121/1.380531View Description Hide Description
A complete solution is obtained for nonaxisymmetric resonant vibrations of a free cylinder or disk involving infinite sums. For axisymmetric longitudinal vibrations an alternative to previous solutions is included. In principle, the solutions satisfy exactly the stress‐free boundary conditions , in contrast to the approximate bending‐mode solutions due to Pickett or approximate solutions based on a small diameter/length ratio and small shearing stresses at the ends.
Subject Classification: 40.26, 40.24; 20.40.
Utilization of a forced‐choice technique to verify statistical performance requirements for detection systems57(1975); http://dx.doi.org/10.1121/1.380532View Description Hide Description
An automated forced‐choice method of evaluating detection performance is employed instead of the familiar fixed‐threshold technique. The latter method utilizes a number of preselected, constant thresholds to estimate both detection and false‐alarm probabilities, whereas the former incorporates a variable threshold with a precise false‐alarm probability to estimate only the detection probability. The advantages of the forced‐choice technique are a predetermined false‐alarm rate, a single parameter test, less required test time, and real‐time monitoring of test results by minimizing the amount of data reduction. A comparison of both techniques is presented for two sets of statistics which are representative of those typically encountered in detection systems under test conditions. Because of the uncertainty associated with the variable threshold, the forced‐choice results are slightly pessimistic, but are within 0.3 dB of the fixed threshold results. However, the forced‐choice technique can easily be made equivalent to the fixed‐threshold procedure by incorporating a correction factor into the test procedure.
Subject Classification: 60.20, 60.30.
57(1975); http://dx.doi.org/10.1121/1.380533View Description Hide Description
An ambient narrow‐frequency‐band acoustic field is described by the power density function N (cos ϑ), with ϑ the bearing angle from a line array of sensors. This field is observed through a conventional delay‐and‐sum beamformer, with average power output B (cos φ) when steered to bearing φ. We present a method (spectrum restoration) for obtaining the (wavenumber) bandlimited version of N from observed values of B. We consider only uniformly spaced arrays, and treat two computationally distinct situations: Δ < λ/2 and Δ ? λ/2, where λ is the wavelength of the narrow‐band field incident on the array and Δ is the array element spacing. In the former case, our method is only approximate; however, it can be carried through computationally, in contrast with methods proposed earlier, which in general succeed only for the case Δ ? λ/2. Computational results are presented for a variety of simulated noise fields, indicating sharper resolution and decreased side‐lobe levels in the obtained field restoration, as compared with the beamformer response.
Subject Classification: 60.20.