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Apr 1982

Volume 71, Issue S1, pp. S1-S113

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back to top Session O. Physical Acoustics II: Nonlinear Acoustics
Contributed Papers
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Variation of B/A with 1/c for several liquids (A)

M. Paul Hagelberg

J. Acoust. Soc. Am. Volume 71, Issue S1, pp. S29-S29 (1982); (1 page)

Online Publication Date: 12 Aug 2005

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In a recent paper [B. Hartmann, J. Acoust. Soc. Am. 65, 1392ndash;1396 (1979)] a thermodynamic‐molecular model is provided for the roughly straight line relationship between the nonlinearity parameter (B/A) and the inverse sound velocity (1/c) known as Ballou's rule. When B/A is studied as a function of 1/c for a given liquid, by varying pressure and/or temperature, a straight line relationship is found in most cases. Results will be presented for several normal liquids as well as for water which, while it is anomalous as expected, proves especially interesting.
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Experimental investigation of the rise time of N waves (A)

Lori B. Orenstein and David T. Blackstock

J. Acoust. Soc. Am. Volume 71, Issue S1, pp. S29-S29 (1982); (1 page)

Online Publication Date: 12 Aug 2005

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The rise time of spark‐produced N waves in air has been measured with a condenser microphone of very wide bandwidth. The N waves had pressure amplitudes in the range 0.15 to 15 mbar, half‐durations 7.5 to 41.5 μs, and risetimes 0.5 to 6 μs. The observed rise times are in only limited agreement with standard theoretical predictions for a weak shock in a thermoviscous gas (Taylor theory of shock thickness) and in a relaxing gas. There is some question, however, about the applicability of these predictions, which are for a step wave, to our N waves, which are relatively short. Our data indicate a weak dependence of rise time on half‐duration. An alternative theoretical prediction was obtained by using a computer algorithm to predict the waveform of a propagating N wave. Included in the algorithm were finite‐amplitude distortion, spherical spreading, absorption based on the ANSI standard for still air, and dispersion appropriate for oxygen relaxation. The predicted waveforms, including amplitude, half‐duration, and rise time, were in good agreement with the measured waveforms. [Work supported by ONR.]
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Features of an underwater explosion record as function of depth (A)

David Epstein

J. Acoust. Soc. Am. Volume 71, Issue S1, pp. S29-S29 (1982); (1 page)

Online Publication Date: 12 Aug 2005

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The waveform from a deep‐fired underwater explosion bears only superficial resemblance to its shallow‐fired counterpart. The latter may be characterized as a highly nonlinear pulsation, while the former tends to look more like a linear damped oscillation. In this report, we expand upon the results given in an earlier paper. [J. Acoust. Soc. Am. Suppl. 1 69, S97 (1981)]. Calculations have been performed which yield theoretical values for features of the explosion waveform, such as the bubble pulse and first negative pulse pressure, as function of detonation depth. These calculations support the conclusion that the bubble pulse amplitude increases slowly with depth. The negative pulse, however, increases at a much more rapid rate and may even overtake the bubble pulse if the ambient pressure is sufficiently high! Estimates of the power law dependence of the features are presented.
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Numerical results for axisymmetric confined sound beams at finite amplitudes (A)

Jerry H. Ginsberg

J. Acoust. Soc. Am. Volume 71, Issue S1, pp. S30-S30 (1982); (1 page)

Online Publication Date: 12 Aug 2005

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A recent investigation [J. H. Ginsberg, “A singular perturbation analysis of axisymmetric, finite amplitude sound beams,” 9th Int. Symp. Nonlinear Acoustics, Leeds, England, 20–24 July 1981] derived an analytical expression for the pressure signal in an intense confined beam. That result consistently described the phenomena of nonlinear distortion, diffraction, and spherical spreading. The present paper develops that analytical result into an efficient computational algorithm using Gauss‐Chebyshev numerical integration. Results for assorted transducer vibratory patterns are given. The responses are displayed both as temporal waveforms, and as frequency spectra exhibiting the amplitudes and phase shifts of the fundamental and higher harmonics. [Work supported by the National Science Foundation, grant MEA‐8101106.]
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Pulsed parametric array (A)

D. H. Trivett and Peter H. Rogers

J. Acoust. Soc. Am. Volume 71, Issue S1, pp. S30-S30 (1982); (1 page)

Online Publication Date: 12 Aug 2005

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In a previous paper [J. Acoust. Soc. Am. Suppl 1 70, S89 (1981)] on the scattering of a cw plane wave by a pulse, the frequency of the scattered signal was found to be fs  =  fcw[(1 − cos θ)/(1 − cos ϕ)], where fs is the frequency of the scattered signal, fcw is the frequency of the cw plane wave, θ is the angle between the pulse wave vector and the cw wave vector, and ϕ is the observation angle with respect to the pulse wave vector. This result yields no off‐axis scattered signal when the pulse propagates in the same direction as the cw plane wave, as in the pulsed parametric array. We have extended this analysis to the case of a pulsed parametric array and found that while the interaction region has a stationary boundary (i.e., during the time the pulse exits the transducer) a sum and difference frequency signal is produced. However, once the pulse leaves the transducer (so that both boundaries are moving at the sound speed) no scattered signal is produced. The off‐axis beam pattern is the same as that obtained by Westervelt [J. Acoust. Soc. Am. 35, 535 (1963)] in his cw calculation. The received difference frequency pulse however, appears as if radiated directly from the transducer. The pulse length is independent of observation angle, identical in length to the high frequency pulse, and has the arrival time appropriate for radiation from the transducer. This would not be the case if the entire volume were radiating. Thus the high directivity of the parametric array cannot properly be considered a volume effect, as previously thought. We present experimental evidence to support these results.
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Nonlinear interaction of two sound waves in a waveguide (A)

James A. TenCate, James M. Estes, and David T. Blackstock

J. Acoust. Soc. Am. Volume 71, Issue S1, pp. S30-S30 (1982); (1 page)

Online Publication Date: 12 Aug 2005

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For collinear interaction of two sound waves (or of a single sound wave with itself) in a gas, the coefficient of nonlinearity is equal to one‐half (γ + 1), where γ is the ratio of specific heats. For interaction at an angle θ it has been proposed that β = cos θ + one‐half (γ − 1). A waveguide experiment to test this hypothesis has been designed. An intense wave of low frequency f1 travels down a rectangular waveguide (cross section a × b) in the plane wave (0,0) mode. Interacting with it is a weak wave of high frequency f2 that bounces along the guide in the (1,0) mode (angle θ = sin−1 c0/2af2). The experiment is thus a generalization of one done by Schaffer [J. Acoust. Soc. Am. Suppl. 1 57, S73 (1975)] to demonstrate the suppression of sound by sound. In our case, however, suppression is more complicated because the two waves travel at different speeds down the guide. A prediction of the null point for the high‐frequency wave has been derived. Preliminary experimental results tentatively confirm the proposed β(θ) relation. [Work supported by ONR.]
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Scattering from crossed ultrasonic beams in the presence of turbulence (A)

M. S. Korman and R. T. Beyer

J. Acoust. Soc. Am. Volume 71, Issue S1, pp. S30-S30 (1982); (1 page)

Online Publication Date: 12 Aug 2005

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Experimental results on the mutual scattering from two perpendicularly directed, continuous ultrasonic beams interacting in the presence of turbulence in water have been shown to produce a sum‐frequency component that radiates outside the interaction region. Measurements of spectral broadening and Doppler shift have been reported by the authors [10th ICA, Vol. 1, p. 164, Sydney (1980)]. An investigation of the scattering mechanisms suggests that scattering to lowest order is from the cubic quadrupole source term in the wave equation (the Reynolds stress tensor ρuiuj). This mechanism allows an excess acoustic density ρ  =  ρ1 + ρ2 to interact nonlinearly with acoustic particle velocities uiL1 + uiL1 and turbulent velocity fluctuations uiT. The theoretical results for the temporal spectrum density of the scattered sum frequency are compared with single beam scattering. The Doppler shifts of the two scattered primary waves, when added together, equal the Doppler shift of the sum frequency for each scattering angie. The prediction for the angular dependence of the sum′s broadening is Δf+  ∼  sin (θ − 45°)/2. These results are in good agreement with experiment.
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Nonlinear scattering of acoustic waves by vibrating obstacles (A)

Jean C. Piquette and A. L. Van Buren

J. Acoust. Soc. Am. Volume 71, Issue S1, pp. S30-S30 (1982); (1 page)

Online Publication Date: 12 Aug 2005

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The problem of scattering of an acoustic wave (at angular frequency ω) by an obstacle whose surface vibrates harmonically (at angular frequency Ω) was studied both theoretically and experimentally. The theoretical approach involved solving the nonlinear wave equation, subject to appropriate boundary conditions, by use of a perturbation expansion of the fields and a Green's function method. This problem was previously studied theoretically by D. Censor [(J. Sound Vib. 25, 101–110 (1972)], who used the linear wave equation together with nonlinear boundary conditions to obtain his solution. In addition to ordinary rigid‐body scattering, Censor predicted nongrowing waves at the sum and difference frequencies ω±  =  ω ± Ω. The solution to the nonlinear wave equation also yields scattered waves at frequencies ω±. However, the amplitudes of these waves tend to grow with increasing distance from the scatterer′s surface and after a very small distance dominate those predicted by Censor. Preliminary experimental results are in qualitative agreement with the theoretical results based on the nonlinear wave equation. [This work is in partial fulfillment of the requirements for the first author′s Ph.D. degree from Stevens Institute of Technology, Hoboken, NJ].
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Theory of resolution improvement in a focused acoustic imaging system using high intensities (A)

Daniel Rugar

J. Acoust. Soc. Am. Volume 71, Issue S1, pp. S30-S31 (1982); (2 pages) | Cited 1 time

Online Publication Date: 12 Aug 2005

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At the focus of a scanning acoustic microscope operating at 2.6 GHz, acoustic intensities in excess of 104 W/cm2 can be generated in a variety of liquids (e.g., water, liquid nitrogen, liquid argon). One consequence of operating at such high intensities is that the resolution of imaging is observed to significantly improve. This effect can be explained by considering the propagation of a finite amplitude focused Gaussian beam in a nonlinear medium. It is found that significant harmonic generation occurs in the converging portion of the beam and that the second harmonic beam focuses to a diffraction limited spot size which is smaller than the spot size of the fundamental beam by a factor of √2. Upon passage through the focal region, the phase relationship of the second harmonic and fundamental changes such that a significant portion of the second harmonic power is converted back to the fundamental frequency. In this way, the high resolution information sensed by the second harmonic beam is communicated to the fundamental frequency, which propagates with lower absorption. [Work supported by ONR and F.V. Hunt Postdoctoral Research Fellowship.]
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Ultransonically induced contraction of an elastically relaxing solid (A)

William P. Winfree, John H. Cantrell, Jr., and Peter Li

J. Acoust. Soc. Am. Volume 71, Issue S1, pp. S31-S31 (1982); (1 page)

Online Publication Date: 12 Aug 2005

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We previously reported the experimental verification of a static displacement induced in single crystal germanium by a propagating finite‐amplitude ultrasonic wave [J. H. Cantrell, Jr., and W. P. Winfree, Appl. Phys. Lett. 37, 785 (1980)]. The sign of the static displacement is predicted theoretically to be dependent on the sign of the ultrasonic nonlinearity parameter of the solid. The nonlinearity parameters of aluminum and fused silica have opposite signs and the equations predict an ultrasonically induced dilatation for aluminum (elastically stiffening solid) and a contraction for fused silica (elastically relaxing solid). We report experimental confirmation of these predictions.
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Acoustic streaming reversal by a finite amplitude sound wave in a non‐Newtonian fluid (A)

Robert L. Powell

J. Acoust. Soc. Am. Volume 71, Issue S1, pp. S31-S31 (1982); (1 page)

Online Publication Date: 12 Aug 2005

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Theoretical predictions are presented for the steady secondary flows (acoustic streaming) produced by the propagation of a finite amplitude planar acoustic wave in a non‐Newtonian fluid. The constitutive equation governing finite amplitude acoustic wave propagation in quiescent non‐Newtonian fluids is derived and consists of an integral expansion of the constitutive functional. Each successive term of the expansion is higher order in a small parameter related to the amplitude of the propagated wave. The linear term of the expansion governs infinitesimal wave propagation and the quadratic term governs nonlinear effects. These equations are used to study the acoustic streaming caused by the propagation of a finite amplitude planar acoustic wave in a channel which has a width greater than that of the acoustic wave. The results show that because of nonlinear viscoelastic effects, the direction of the streaming can be opposite to that found for Newtonian fluids. [Work supported by NSF.]
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Air bubble growth in guinea pig tissue by rectified diffusion (A)

Gary M. Hansen and Lawrence A. Crum

J. Acoust. Soc. Am. Volume 71, Issue S1, pp. S31-S31 (1982); (1 page)

Online Publication Date: 12 Aug 2005

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It has been previously shown [E. ter Haar and S. Daniels, Phys. Med. Biol. 26, 1145–1149 (1981)] that guinea pigs that are exposed to therapeutic ultrasound of intensities in the range of 80 mW/cm2 to 680 mW/cm2 (spatial average) develop air bubbles of observable size within the exposed tissue. We present evidence that air bubble growth in guinea pig tissue during ultrasonic irradiation is due to rectified diffusion. Through numerical integration of existing rectified diffusion equations, for the frequency and intensities used by ter Haar and Daniels in their recent work, we have found that small “undetectable” bubbles grow during irradiation to a “detectable” size. The number of bubbles growing and the final sizes predicted closely resembles the results obtained experimentally. [Work supported by the ONR and the NSF.]
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Control of vorticity by sound (A)

P. G. Vaidya

J. Acoust. Soc. Am. Volume 71, Issue S1, pp. S31-S31 (1982); (1 page)

Online Publication Date: 12 Aug 2005

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It is well known that a sound wave interacts with and modifies a vorticity wave. Usually such interactions are quite weak and, therefore, not of much practical importance. However, as the author has shown previously, under certain circumstances strong interactions are possible. In this paper these strong interactions are analyzed further. A resonance expansion technique has been used to arrive at numerical solutions to the interaction equations. Practical applications of modifying the vorticity wave to problems such as the laminar flow control are discussed.
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