Volume 57, Issue 1, January 1975
Index of content:
57(1975); http://dx.doi.org/10.1121/1.380397View Description Hide Description
A T−matrix formulation of both acoustic and electromagneticscattering has been given by Waterman for the case of one homogeneous scatterer, and this formulation has subsequently been extended to the case of several such scatterers by the present authors. In the present article we show that the matrix formulation is also well suited for the treatment of acoustic scattering from scatterers consisting of an arbitrary number of consecutively enclosing homogeneous layers with different propagation constants. We also show how the earlier results on the matrix formulation of acoustic scattering can be combined with these new results so as to apply to more general types of multilayered scatterers. Some numerical applications are given.
Subject Classification: 20.30.
57(1975); http://dx.doi.org/10.1121/1.380426View Description Hide Description
Nonlinear dispersive effects on the propagation of atmospheric internal waves are investigated. The finite amplitude buoyancy oscillation is analyzed to obtain an amplitude−dependent oscillation frequency. A nonlinear dispersion relation for finite−amplitude internal waves is derived. Its relation to the nonlinear buoyancy oscillation is discussed. The nonlinesr dispersion relation is then used to study the stability of finite−amplitude modulated internal wave trains. It is found that, for certain modulations, wave trains propagating in certain directions may become unstable.
Subject Classification: 28.20.
57(1975); http://dx.doi.org/10.1121/1.380417View Description Hide Description
Radiation−driven magnetoacoustic waves are studied in an electrically conducting and thermally radiating gas confined between two plane stationary walls which are placed perpendicular to the direction of one−dimensional motion of the gas. One of the walls provides a sinusoidal input of blackbody radiation and the other wall is a perfect reflector. Two types of damped harmonic waves are excited which form a system of standing waves traveling in the positive and negative directions. One of the waves is a magnetoacoustic wave and the second has attributes basically due to radiation. The effects of magnetic field on the pressure and velocity are examined. It is seen that the pressure and velocity decrease in a warm gas, i.e., for the moderate values of Boltzmann number. However, their response increases in a hot gas, i.e., for very small values of the Boltzmann number. The contributions to pressure and velocity due to the second type of waves are insignificant in a warm gas and further decreases with the increasing strength of the magnetic field. In the case of hot gas the contributions to the pressure response are significant.
Subject Classification: 28.50; 35.60.
57(1975); http://dx.doi.org/10.1121/1.380396View Description Hide Description
The problem of noise radiated from a turbulent boundary layer is studied. It is found that the farfield noise power, spectrum, and directivity can be determined completely if the nearfield pressure cross−correlation function is known. The role of supersonic and subsonic pressure components associated with the turbulent boundary layer in relation to noise radiation is examined. By using an empirical model of wall pressure cross−correlation function, it is found that the directivity pattern of turbulent boundary layernoise differs considerably from that of a free dipole. One principal reason for this difference is the fact that the noise sources of a turbulent boundary layer are constantly in motion. The effect of mean flow outside the boundary layer on the radiated noise power and spectrum is also investigated. Numerical results indicate that this effect is very important for low frequency noise components and for a high subsonic flowMach number.
Subject Classification: 28.65; 50.55.
57(1975); http://dx.doi.org/10.1121/1.380398View Description Hide Description
A method is described for measuring the free−field radiation impedance of a single−degree−of−freedom underwater transducer. The displacement amplitude and phase of the vibrating surface in air and in water are measured with a laser interferometer and with an accelerometer. From these values and the input current, the radiation impedance may be computed. Measurements of the radiation resistance and reactance of a J9 transducer at 0.5−kHz intervals from 5.0 and 10.0 kHz are reported. The radiation resistance is also calculated from reciprocity calibrations and measurements of the directivity patterns at 5.0, 7.5, and 10.0 kHz. Excellent agreement is observed between the two methods.
Subject Classification: 30.50.
57(1975); http://dx.doi.org/10.1121/1.380399View Description Hide Description
Reflectivities are calculated as functions of sonic incidence angle, densities, and sonic velocities. The resulting sets of curves are used to determine under which conditions reflectivitymeasurements can or cannot yield information about the values of sonic velocities and density of sea ice.
Subject Classification: 30.25, 30.30.
57(1975); http://dx.doi.org/10.1121/1.380400View Description Hide Description
A unified treatment of conical ray paths, corresponding to a nonlinear sound−speed profile family, is presented. For a concave downward profile, ray arcs may be hyperbolic, and there may be two such paths. They may also be parabolic or elliptic, with vertical major axis. For a concave upward profile, ray arcs are elliptic with horizontal major axes. When a CW sound source and receiving point lie on a horizontal bottom, the number of bottom reflections, initial ray angle, travel time, and spreading loss are studied in detail for RBR (refracted/bottom−reflected) rays. In an application of our results, temperature data off the Miami coast is used to determine sound−speed profile variations as a function of time. The acoustic phase of the total RBR field is then computed at a receiver 3 NM from the source. Theoretical phase variations are shown to be in reasonably good agreement with experimental phase fluctuations.
Subject Classification: 30.20, 30.25.
Attenuation of sound by rigid spheres: measurement of the viscous and thermal components of attenuation and comparison with theory57(1975); http://dx.doi.org/10.1121/1.380401View Description Hide Description
An acoustic cavity technique has been developed to separately measure the viscous and thermal components of the attenuation of sound by rigid spheres in various gases. A rigorous quantitative test of theoretical predictions for the individual components of attenuation has been carried out for spheres of known size in argon, nitrogen, and dichlorodifluoromethane (Freon−12), gases selected to cover a wide range in the relative influence of thermal damping to viscous damping. Theory and experiment are in good agreement in regard to both qualitative and quantitative features. Qualitatively, the most striking feature observed is the sinusoidal variation of attenuation with displacement of the spheres along the cavity axis, as predicted by theory. The absolute values of the viscous and thermal damping constants agree quite well with theory. Even better agreement with theory is obtained for the difference between viscous and thermal attenuation, a measurement that does not require opening the cavity to insert or remove the spheres. In addition, the damping produced by the slender cylindrical translating rod exhibits some interesting structure which can be quantitatively explained by theory.
Subject Classification: 35.20; 20.35.
57(1975); http://dx.doi.org/10.1121/1.380402View Description Hide Description
A modulated or chopped beam from an argon ion laser, with CW power at the 1−W level, is used to generate thermoelastic waves in several liquids. The ceramic cylinder surrounding the liquids is the transducer for the acoustic waves. Output signal is measured as a function of frequency, with different laser powers and different amounts of absorption in the liquids. The analysis makes use of thermoelastic potentials in the liquid and in the ceramic cylinder, with appropriate continuity conditions between the two regions, and predicts results in good agreement with those measured. Conversion efficiency from laser power to acoustic power is extremely low at this power level, but increases directly with the laser power. Thus it is concluded that the acoustic wave generated by a modulated laser beam at the 1−W level propagating through sea water would only be detectable near the beam, but for a pulsed beam at the megawatt level, acoustic power might be detectable for several kilometers.
Subject Classification: 35.65.
57(1975); http://dx.doi.org/10.1121/1.380403View Description Hide Description
The propagation of small−amplitude sinusoidal waves in a chemically reacting mixture of nonconducting elastic materials is considered. Limiting attention to mixtures with binary reactions, we derive expressions for the phase velocity and attenuation of infinitesimal sinusoidal waves and examine the influence of the thermochemicalproperties of the mixture on the wave behavior. The general relation between small−amplitude sinusoidal waves and acceleration waves is also established.
Subject Classification: 35.26.
57(1975); http://dx.doi.org/10.1121/1.380404View Description Hide Description
A discrete−continuum theory for periodically layered composite materials is presented. Based on a two−term truncated power series expansion of the displacement field about the middle plane of each layer, two−dimensional equations of motion are obtained for the individual layers. After introducing appropriate continuity conditions at the interfaces between neighboring layers, the governing field equations for periodically layered media are derived in the form of a system of differential−difference equations. The accuracy of the theory is examined by applying it to the propagation of plane harmonic waves in an unbounded layered medium and comparing the results with those obtained from theory of elasticity. To illustrate the application of the theory, thickness−twist vibrations of laminated plates are studied. Numerical examples are included and comparison is made with exact solutions.
Subject Classification :40.24.
57(1975); http://dx.doi.org/10.1121/1.380405View Description Hide Description
Free transverse vibrations of rods which are axially constrained at ends and initially loaded with an axial force at an intermediate point are discussed. The theoretical developments are based on Timoshenko equations and explicit solutions and results have been obtained for hinged−hinged and fixed−fixed beams. Various interesting and new aspects, such as the influence of the magnitude and location of axial forces on the frequency spectrum, are evident from the numerical results.
Subject Classification: 40.22.
57(1975); http://dx.doi.org/10.1121/1.380406View Description Hide Description
A system of six two−dimensional plate equations is derived for motions of small−amplitude waves or vibrations superimposed on finite, elastic deformations due to static, initial stresses. In the stress−strain relations, the nonliner terms associated to the third−order elastic stiffness coefficients are included. These equations accomodate the coupling of the six lowest modes of vibration, i.e., the flexure, extension, face−shear, thickness−shear, thickness−twist, and thickness−stretch modes, and all their anharmonic overtones. The new equations are applied to the rotated Y cuts of quartz in studying the thickness−shear and flexural vibrations. The changes in the resonance frequencies of the fundamental thickness−shear vibrations are computed as functions of the direction of initially applied force and of the angle of rotated Y cuts. The predicted results are compared with experimental data and with existing computed results. An explicit formula is obtained for the change of fundamental thickness−shear frequencies in terms of initial deformations and the second− and third−order elastic stiffness coefficients.
Subject Classification: 40.24.
57(1975); http://dx.doi.org/10.1121/1.380419View Description Hide Description
An exact solution is presented for the steady−state motion of a sinusoidally excited single−degree−of−freedom system exhibiting bilinear hysteresis and subjected to viscous damping that may be different in the ’’elastic’’ region from the ’’yielded’’ region.
Subject Classification: 40.20.
57(1975); http://dx.doi.org/10.1121/1.380420View Description Hide Description
The paper studies free flexural vibrations in the plane of an elliptical ring of constant cross sections. The present vibrations are considered in the elliptical coordinate system and the vibration displacements are expressed in terms of the series of Mathieu functions. The nondimensional eigenfrequencies calculate numerically are tabulated for various aspect ratios. The experimental results are obtained and are found to be in good agreement with the theoretical results.
Subject Classification: 40.26.
57(1975); http://dx.doi.org/10.1121/1.380421View Description Hide Description
We have investigated the dispersion curves of free waves in free plates. We have shown that for certain conditions a simple exact solution is possible, since incident shear (SV) waves are decoupled from the transmitted longitudinal (P) wave (and vice versa). The concept of phase decoupling yields a useful description for the construction of approximate dispersion curves in terms of certain decoupled modes M 1−M 4. The validity of various approximations based on these modes is discussed. The fomulation may be readily extended to anisotropic and to active plates.
Subject Classification: 40.24.
57(1975); http://dx.doi.org/10.1121/1.380422View Description Hide Description
Measurements have been performed of the sound pressure levels of highway noise sources, including trucks, with an array of microphones in the plane perpendicular to the direction of motion. The results show that highway sources exhibit quasi−omnidirectionality, when described in terms of A−weighted levels, at angles up to 45° above the horizontal independently of the type of vehicle or of the type of exhaust. For trucks there is limited evidence of a weak distortion of the directivity pattern of the radiated noise which increases with the number of wheels at high speed. One−third−octave−band spectral analysis at angles between 6° and 45° from the horizontal do not reveal a significant variation in the spectrum from one angle to another. For the purpose of highway noise prediction, it appears reasonable to assume that the noise radiated from conventional vehicles, including trucks, is omnidirectional.
Subject Classification: 50.50, 50.25.
57(1975); http://dx.doi.org/10.1121/1.380423View Description Hide Description
Bulk sound−absorbingmaterials are not suitable for many applications involving liquids, air flow, elevated temperature, vibration, and severe space limitations. In aircraft, all of these design constraints can occur together. The simplest alternative to the bulk absorber is the single−layer absorber, comprising a permeable facing sheet over a closed compartmented air space. Single−layer absorbers meet some of the above design requirements but their impedance versus frequency characteristic is inherently inferior to that of a good bulk absorber. A wide variety of improved absorptioncharacteristics may be attained by utilizing more acoustical elements and parallel as well as series connections among the elements. The use of resistance paralleled by lumped inertance and resistance provides a facing sheet whose resistance increases with frequency while the positive reactance decreases. Dissimilar air cavities arranged compactly in parallel provide airspace reactance that remains near zero over a broad range of frequency. The cutoff characteristics of miniature acoustic horn arrays may be exploited to provide a duel−frequency range of absorption. The upper−frequency range resembles that of a single−layer absorber, whereas the low−frequency absorption occurs in a controllable region of considerable bandwidth. These novel sound−absorbing structures may provide practical solutions to such diverse problems as fan−jet engine buzzsaw noise,combustionnoise, and noise due to cooling towers and car−wash installations.
57(1975); http://dx.doi.org/10.1121/1.380424View Description Hide Description
A numerical technique based on the finite−element method has been developed for analyzing the performance of systems of acoustic elements including expansion chambers in mufflers. The theories developed are, firstly, the variational formulation of the acoustic field existing in the system and, secondly, the finite−element approximate solutions of the variational problems. The predictions of transmission loss are then made by forming the equivalent acoustic four−terminal transmission network in which the acoustic four−pole constants are calculated from the finite−element method. As used, the finite−element approach is perfectly general and may be applied to any system component with arbitrary boundary geometry provided this may be realized by an assembly of rectangular elements. The method is applied to simple expansion chamber models because the results are tractable and theoretical results from acoustic filter theory are available for comparison purposes. The comparison brings out an important fact: the accuracy of the prediction of transmission loss implies that the variational formulation and finite−element approximations are adequately applicable to a number of practical applications.
Subject Classification: 50.40; 20.40.
57(1975); http://dx.doi.org/10.1121/1.380425View Description Hide Description
Low−correlation sequences, such as ’’maximum−length’’ and Barker sequences and certain complex (magnitude one) sequences having flat power spectra, are ideally suited for designing surfaces of hard walls with highly diffuse reflections. Recent subjective−preference evaluations [M. R. Schroeder, D. Gottlob, and K. F. Siebrasse ’’Comparative Study of European Concert Halls’’, J. Acoust. Soc. Am. 56, XXX−XXX (1974)] indicate that low−loss, high−scatter surfaces may be required for better concert−hall acoustics. Surfaces shaped to give reflection coefficients according to such sequences show the expected high scatter in model experiments with microwaves.
Subject Classification: 55.20, 55.40.