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Nov 1988

Volume 84, Issue S1, pp. S2-S224

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back to top Session E. Physical Acoustics I: Nonlinear Acoustics, Part I
Invited Papers
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Nonlinearity in sound beams, with application to the scattering of sound by sound (A)

Jacqueline Naze Tjøtta and Sigve Tjøtta

J. Acoust. Soc. Am. Volume 84, Issue S1, pp. S7-S7 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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This paper addresses the fundamental theory of nonlinear acoustics in a thermoviscous fluid. Emphasis is given to the combined effects of nonlinearity, absorption, and diffraction in sound beams. An overview is presented of the various mathematical models used for the propagation of a high‐intensity sound beam, with a discussion of their range of validity. Some examples of nonlinear effects in a sound beam are shown. Nonlinear interaction between two real sound beams is also considered. The sources may possess arbitrary phase and amplitude shading, and different sizes and orientations. The obtained results are related to earlier works on the scattering of sound by sound, which are discussed. [Work supported by the IR&D program of ARL:UT, and VISTA/STATOIL, Norway.]
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New measurement techniques developed on the basis of nonlinear acoustics (A)

Takuso Sato

J. Acoust. Soc. Am. Volume 84, Issue S1, pp. S7-S7 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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When nonlinear interactions between a medium and acoustic waves are used in addition to linear interactions, two main directions can be expected in the development of new measurement techniques: (i) the extraction of new characteristics of the medium, and (ii) the construction of completely new or more compact measuring systems. In this paper, a few applications are shown of nonlinear acoustics, picked up from a method based on the use of impulsive and high‐pressure pumping waves to generate the required nonlinear effects and high‐frequency, small amplitude continuous probing waves to detect the results. The applications include (i) measurements of gas flow velocity and temperature distributions, (ii) nondestructive measurement of the stress distribution in metals, and (iii) imaging of dynamic characteristics, including the nonlinear parameter of soft tissues as a new means of medical diagnosis. The exact construction of each system and the corresponding experimental results are shown in detail.
Contributed Papers
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Theoretical approach to the virtual source based on the distortion in finite‐amplitude waves (A)

Yoshiaki Watanabe, Takao Tsuchiya, and Yasumasa Urabe

J. Acoust. Soc. Am. Volume 84, Issue S1, pp. S7-S7 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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An analytical approach is presented to derive the intensity of a virtual source from the viewpoint of the distortion in the finite‐amplitude wave. The distortion in the arbitrary waveform over a small distance is discussed in connection with the local sound velocity which depends on the local particle velocity. From the variation in the particle velocity due to the waveform distortion, the intensity of the virtual source is derived. It is dearly shown that the virtual source can be derived using only distortion in the time domain. The present analytical approach will be useful in understanding phenomena of nonlinear acoustics.
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A method of measuring the nonlinearity parameter B/A of a medium using the angle dependency of β (A)

Takao Tsuchiya, Yoshiaki Watanabe, and Yasumasa Urabe

J. Acoust. Soc. Am. Volume 84, Issue S1, pp. S7-S8 (1988); (2 pages)

Online Publication Date: 13 Aug 2005

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A new method of measuring B/A using a parametric receiving array is presented. The coefficient of nonlinearity β is treated exactly and is divided into two physically different terms. The effective value of βe (= cos θ + B/2A) is defined as the function of the crossing angle θ of two waves. The angle‐dependent pattern of βe is applied to the measurements of B/A. The following two practical methods are presented: (1) using the non interacting angle θn [= cos−1(− B/2A)] and (2) using the front‐back ratio of βe. The measurements were carried out using the two above methods for a gaseous medium and using (2) for water. The array lengths of the probing wave used were 90 mm and 40 kHz for gas, and 40 mm and 5 MHz for water, respectively. The phase modulation of the probing wave was observed and the angle dependency of β was detected. It was found that the estimated values of B/A showed good agreement with theoretical values and with the observed results presented by the other researchers.
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Measurement of the nonlinearity parameter B/A using the pulse‐echo technique (A)

Iwaki Akiyama, Masato Nakajima, and Shin'ichi Yuta

J. Acoust. Soc. Am. Volume 84, Issue S1, pp. S8-S8 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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A method for the measurement of the nonlinearity parameter B/A in biological tissues using the pulse‐echo technique was studied. Since a finite‐amplitude method is valid for the measurement of B/A in biological tissues, the values of B/A have been experimentally measured in vitro for several biological tissues. For medical applications it is necessary to have in vivo measurements, and thus it is desirable to use the pulse‐echo technique. In this study, the second harmonic component of the echo signal was analyzed, and then it is shown that the rate of increase of the second‐harmonic components with respect to time provides the value of B/A. This rate is, however, influenced by the attenuation coefficient and the reflection coefficient in biological tissues. In order to eliminate these effects, another pulse was used whose center frequency was twice as high as that of the former pulse. Also, the ratio of the second harmonic component of the echo signal of the former pulse and the fundamental component of the echo signal of the latter pulse is calculated. The value of B/A was determined by the rate of increase of the resulting quantity. The experiments were conducted to verify the feasibility of this technique, and the resulting values were in agreement with values from the literature.
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Parametric measurement of sound source directivity: Effect of the source nearfield (A)

John D. Sample

J. Acoust. Soc. Am. Volume 84, Issue S1, pp. S8-S8 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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The suggested use of a parametric receiving array to measure the directivity of a distributed sound source in a multipath environment is complicated by the disparity between the beam patterns of the difference frequency and linear sound fields. This disparity can be understood by considering the interaction volume as two independent sources: one representing the volume in the nearfield of the source and the other representing the farfield volume. The interaction volume in the farfield of the source has the same directivity as the linear radiation of the source, but the measured difference frequency directivity is contaminated by the contribution from the nearfield volume. The nature of the contamination in the case of a Gaussian‐shaded pump interacting with an approximation of a circular piston is analyzed using a previously developed computer model. The nature of the differences between linear and difference frequency directivities is described and the dependence on range and pump location is studied. The cause of these differences is identified as difference frequency sound produced in the nearfield.
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Nonlinear interaction of collinear sound beams in the nearfield (A)

Tomoo Kamakura and Yoshiro Kumamoto

J. Acoust. Soc. Am. Volume 84, Issue S1, pp. S8-S8 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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Many spectral components generated by nonlinear interaction of two collinear sound beams can be calculated using Aanonsen's method [J. Acoust. Soc. Am. 75, 749–768 (1984)]. Aanonsen's initial pressure condition is extended to the case where a radiating wave at the source consists of two adjacent harmonies. Numerical computations are performed for a nearfield of a Gaussian source in air. Propagation curves and beam patterns of the primary and secondary waves are given for various source levels. When the source intensity is increased, the higher frequency primary wave fades out more than the lower frequency wave, and the harmonics of the difference frequency increase. Parametric generation of the difference frequency and its second harmonic component for AM excitation are also considered.
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A parametric array for use as an ultrasonic proximity sensor in air (A)

Yang‐Sub Lee and Mark F. Hamilton

J. Acoust. Soc. Am. Volume 84, Issue S1, pp. S8-S8 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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An ideal ultrasonic proximity sensor has long range, high resolution, and small size. However, the absorption of sound by air makes all three characteristics difficult to achieve simultaneously with conventional acoustical designs. In this paper, the nonlinear parabolic wave equation is used to investigate the possibility of utilizing a parametric array to incorporate all three desirable characteristics. To avoid difference frequency generation at the source, one of the primary beams may be radiated from a circular (disk) source, the other from a ring source that is concentric with the disk. First, the two primary wave fields are compared, with special attention devoted to radiation from a ring source. Second, the difference frequency field is analyzed as a function of source conditions. It is concluded that, for a source with a nominal radius of 1 cm, operating in air with primary frequencies of approximately 200 kHz and on‐source sound‐pressure levels up to 140 dB (re: 20 μPa), the parametric array offers no distinct advantage over conventional ultrasonic proximity sensors. [Work supported by NSF, ONR, and the Cray Research Foundation.]
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A nonlinear, parametrically driven, variable‐reluctance electroacoustic transducer (A)

W. B. Wright and G. W. Swift

J. Acoust. Soc. Am. Volume 84, Issue S1, pp. S8-S8 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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There is a well‐known class of nonlinear acoustic drivers in which an acoustic force (or pressure) is exerted by the magnetic interaction of an electric current with itself, so that the force is proportional to the square of the current. The St. Clair driver [H. W. St. Clair, Rev. Sci. Instrum. 12, 250 (1941)] is the best‐known device of this class. Less well known is the inverse effect, the nonlinear generation of an electric current by an acoustic vibration, achieved in the same apparatus. In the present case, a resonant series LC circuit is excited by varying L (geometrically, by acoustic vibration) at twice the resonance frequency of the LC circuit. The resonance requirement and inherent overwhelming nonlinearities make this system useless as a high‐fidelity microphone. But several interesting non‐linear dynamical phenomena can be observed with this simple system; and, in addition, it is capable of highly efficient power transduction. [Work supported by DOE/BES.]
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Propagation of the difference frequency wave generated by a truncated parametric array through a water‐sediment interface (A)

Liu Wensen and Xu Zhenxia

J. Acoust. Soc. Am. Volume 84, Issue S1, pp. S8-S9 (1988); (2 pages)

Online Publication Date: 13 Aug 2005

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T. G. Muir et al. observed experimentally that the maximum of the received sound pressure in the sediment insonified by a parametric array departed significantly from the prediction of Snell's law. The wave fronts penetrated more steeply into the sediment and the attenuation with depth was less than predicted by plane‐wave theory at the postcritical incidence. It was found that, due to the variation of the length of the parametric array and the variation of the attenuation in the sediment, the maximum of the received sound pressure occurs at the line‐of‐sight between the projector and the hydrophone. It has been proved both theoretically and experimentally that Snell's law is still valid when the length of the parametric array and the attenuation in the sediment are kept constant. Due to the contribution of the secondary sources close to the boundary, the postcritical penetration of the parametric array can be deeper. The lateral wave should be considered at the postcritical incidence.
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Nonlinear interaction of an acoustic wave and mean flow at a stagnation point (model verification) (A)

Charles Thompson and Martin Manley

J. Acoust. Soc. Am. Volume 84, Issue S1, pp. S9-S9 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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A model has been developed to describe the nonlinear interaction of an acoustic disturbance and the mean flow over a bluff body near the stagnation point. The model identifies the neutral stability condition and predicts the evolution in space and time of disturbances in unstable flow. The available experimental data regarding this interaction are extremely limited. Two sets of data that do shed light are those of Hassler (1971) and Colak‐Antic (1971). These experiments concerned the effects of unsteady disturbances on a mean flow for a geometry similar to the model geometry. The flow visualizations and hot‐wire anemometer measurements of these reports illustrate some of the complex phenomena involved in the interaction. Interaction model predictions will be compared with experimental results. [Work supported by Analog Devices Professorship.]
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An exact solution for finite‐amplitude plane sound waves in a dissipative fluid (A)

Hideto Mitome

J. Acoust. Soc. Am. Volume 84, Issue S1, pp. S9-S9 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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The propagation of finite‐amplitude plane sound waves in a dissipative fluid can be described by Burger's equation, and its exact solution obtained [D. T. Blackstock, J. Acoust. Soc. Am. 36, 534–542 (1964)]. In this paper, an exact solution for sound pressure, which is suitable for the direct numerical computation of the waveform in the time domain, is derived. Numerical results show that this solution describes the whole propagation process, including shock formation and its decay. Computation is possible up to Γ = 175, where Γ is the Goldberg number indicating the importance of nonlinearity relative to dissipation, for any value of X (distance normalized by shock formation distance). Although it becomes difficult above this value (except at larger X's) because of its functional form, the solution connects smoothly with the Fubini solution at X < 1 and the Fay solution at X > 3.5. Since this solution is exact and gives the waveform at any position, it can serve as a standard solution for various approximate solutions. As an application, the saturation for the fundamental component and that for the entire wave are shown.
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Nonlinear variation in waveform and attenuation of tone‐burst sound waves with finite amplitude (A)

Akira Nakamura

J. Acoust. Soc. Am. Volume 84, Issue S1, pp. S9-S9 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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Propagation in a circular pipe of tone‐burst waves with finite amplitude was simulated by a computer. The results are compared with some experimental results [Y. Watanabe and Y. Urabe, Proc. 11th ICA, Paris, Vol. 1, pp. 337–340 (1983)]. The attenuation is separated into two parts in the time profile of the tone‐burst waveform for comparison. One is the attenuation of energy effectively corresponding to a period given by a summation of the head and tail half‐periods in the time profile. The other is the attenuation per period of the sinusoidal part located between the head and tail parts. It is found that (1) the attenuations of the head plus tail are considerably smaller than the attenuation of the sinusoidal part, and agree with the theoretical values for N waves and also with the experimental results, and that (2) the attenuations of the sinusoidal part agree with the theoretical values for repeated sawtooth waves but does not agree with experimental values, because the envelope of the profile used in the experiments had been deformed into an irregularly shaped rectangle.
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Finite‐amplitude propagation in lossless and absorptive media (A)

Clarence R. Reilly and Kevin J. Parker

J. Acoust. Soc. Am. Volume 84, Issue S1, pp. S9-S9 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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The propagation of finite‐amplitude waves in distilled water and an absorptive fluid media with acoustic characteristics similar to tissue was investigated. Axial and focal beampatterns of linear and quasilinear waves were obtained from lens focused sources of 1.75, 2.25, 2.94, and 3.38 MHz using a PYDF needle‐type hydrophone. Experimental beampatterns were compared to spherically converging and focused Gaussian beam theories. The shock parameter at the focus predicted from Gaussian theory was in general agreement with the estimate made from the relative strengths of the first four harmonics to the fundamental. Apodization provided by the lens reduced, but did not eliminate, the nearfield maxima, minima, and sidelobes associated with a piston source. Additional sidelobes predicted from the Khokhlov‐Zabolotskaya‐Kuznetsov (KZK) equation were evident in the harmonic beampatterns. Harmonic focal beamwidths decreased as n−1/2 for the lower source frequencies, in agreement with theory. Beamwidths were generally more narrow in the absorptive media than in the water. The second harmonic peak location on‐axis was distal to the fundamental, although the difference was small for higher source frequencies and propagation in the absorptive media. Higher harmonics had sharper axial focal dimensions, but the position of the axial peak was dependent on the trade‐off between propagation growth and decay caused by attenuation. The extension of the results to propagation in tissue is noted.
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