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Nov 1981

Volume 70, Issue S1, pp. S1-S109

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back to top Session OO. Physical Acoustics VI: Nonlinear Phenomena and Relaxation
Invited Papers
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Subharmonics, bifurcations. chaos and all that jazz (A)

Isadore Rudnick and Robert Keolian

J. Acoust. Soc. Am. Volume 70, Issue S1, pp. S89-S89 (1981); (1 page)

Online Publication Date: 12 Aug 2005

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In this, the sesquicentennial of the publication of Faraday's landmark experimental observation [M. Faraday, Philos. Trans. R. Soc. (London) 299 (1831), Sec. 103; Lord Rayleigh, The Theory of Sound (Dover, New York, 1945), Sec.68b] of the subharmonic, f/2, in the crispations generated on a flat horizontal plate wet with water when it is oscillated vertically at a frequency f, we report on the results of a version of this experiment where we observe subharmonics of frequency f/m where m, at this writing, has been observed to have the values 2, 4, 12, 14, 16, 18, 20, 24, 28, 30, 32, 34, 35. Moreover harmonics of these subharmonics occur in profusion so that the frequencies which appear in an FFT graph are given by pf/m, where p is an integer which can reach values as high and higher than 2 m. The transition to a chaotic [Physics Today 34, 17 (March 1981)] or turbulent state is observed.
Contributed Papers
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Combinations of the TOE constants of the fluoroperovskites CsCdF3 and KZnF3 measured as a function of temperature (A)

Jacob Philip and M. A. Breazeale

J. Acoust. Soc. Am. Volume 70, Issue S1, pp. S89-S89 (1981); (1 page)

Online Publication Date: 12 Aug 2005

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We have examined the nonlinear behavior of the fluoroperovskites CsCdF3 and KZnF3 which are known to exhibit similar linear elastic behavior. The temperature variation of some combinations of the third‐order elastic (TOE) constants have been measured as a function of temperature using the ultrasonic harmonic generation technique. Measurements have been made from room temperature to 77°K. It is observed that the constant C111 shows a higher temperature variation than it does in other cubic crystals such as copper or silicon. Between 300° and 77°C, C111 changes by 8.5% for CsCdF3 and 23.5% for KZnF3. The combination (C112 + 4C166) does not vary much with temperature, whereas the combination (C123 + 6C144 + 8C456) has a very high (negative) value and a peculiar temperature dependence, showing that these compounds are far away from being solids for which a central, nearest‐neighbors model would be appropriate. [Research sponsored by the Office of Naval Research.]
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Scattering of a cw plane wave by a pulse (A)

D. H. Trivett and Peter H. Rogers

J. Acoust. Soc. Am. Volume 70, Issue S1, pp. S89-S89 (1981); (1 page)

Online Publication Date: 12 Aug 2005

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An examination of the scattering of sound by sound indicates that the boundary of the interaction region is very important in determining not only the level of the scattered sound but also the frequency of the scattered sound. In the case of a pulse propagating through a cw plane wave (where the boundary of the interaction region is propagating at the sound speed) the frequency of the farfield scattered radiation at a fixed angle is the cw frequency, Doppler shifted i.e., fs(θ,ϕ)  =  fcw[(1‐cos θ)/(1‐cos ϕ)], where ϕ is the angle between the cw wave vector and the pulse wave vector and ϕ is the observation angle with respect to the pulse wave vector in the interaction plane. The scattered signal has a strong maximum at the Doppler angie ϕd, where the scattered signal is equal to the sum frequency. The scattered signal at ϕd observed at a finite distance from the interaction region thus appears as a pulse whose frequency sweeps from a value somewhat above the sum frequency to a value somewhat below the sum frequency. Previous detection of sum frequency in a crossed beam experiment has been attributed by Westervelt [J. Acoust. Soc. Am. 29, 199 (1957)] to “pseudo‐sound,” the interaction of the primary beam′s side lobes at the face of the transducer. Positive results from a pulse‐cw experiment exhibiting the predicted frequency dependence would unambiguously demonstrate the existence of scattering of sound by sound.
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Dynamic tension in water induced by the reflection of shock waves (A)

Glenn L. Pullen and Philip L. Marston

J. Acoust. Soc. Am. Volume 70, Issue S1, pp. S89-S89 (1981); (1 page)

Online Publication Date: 12 Aug 2005

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Negative pressures were produced in distilled water by reflecting a 70‐bar shock pulse off a quasi‐free water‐Mylar‐air interface. The incident pulses, created by symmetric impact of a projectile onto a buffer, had durations of 1–2 μs. A displacement inter‐ferometer measured the velocity u of the Mylar. After the pulse's trailing edge reaches the Mylar, u would tend to vanish in the absence of cavitation. If the region of tension cavitates abruptly when a tensile strength S is exceeded, the downward transition in u is terminated. The transition was observed to be terminated when u changed by Δu ≈ −4 m/s. Assuming the flow remains uniaxial, S  ≈  −p0 − ρcΔu/2, where ρ, c, and p0 = 1 bar are the water′s initial density, sound speed, and pressure [P. L. Marston and G. L. Pullen, Proc. of the 1981 APS Conference on Shock Waves in Condensed Matter, edited by W. J. Nellis (to be published)]. It appears that the Mylar separated from the water during pullback and the data places only a lower limit (28 bars) on S. [Work supported by ONR and the WSU Research and Arts Committee. P. Marston is an Alfred P. Sloan Research Fellow.]
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Characterization of molecular binding from ultrasonic non‐linearity parameters (A)

John H. Cantrell, Jr.

J. Acoust. Soc. Am. Volume 70, Issue S1, pp. S89-S90 (1981); (2 pages)

Online Publication Date: 12 Aug 2005

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The description of antharmonic properties of solids involves generalized Grüneisen parameters which describe the strain dependence of the lattice vibrational frequencies. A quantitative measure of solid anharmonicity, the ultrasonic nonlinearity parameter, is obtained directly from ultrasonic harmonic generation experiments and has been shown to be linearly related to the isentropic generalized Grüneisen parameter [John H. Cantrell, Jr., Phys. Rev. B 21, 4191 (1980)]. Although solid nonlinearity parameters have been measured in relatively few materials they can be calculated for many solids from published measurements of the pressure derivatives of second‐order elastic coefficients. We have used these data to calculate the ultrasonic nonlinearity parameters and the corresponding isentropic Grüneisen parameters for a number of crystalline solids of cubic symmetry. The calculations indicate a strong correlation between the value of the isentropic mode Grüneisen parameter and the type of crystalline binding. For example, the [100] mode Grüneisen parameters cluster around 7.3 for ionic crystals, 1.1 for covalent crystals, 3.0 for fcc metals, and 11.5 for bcc metals. The implications of these results are discussed.
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Interfacial tension between water and superheated liquids (A)

Chaur‐Jian Hsu and Robert E. Apfel

J. Acoust. Soc. Am. Volume 70, Issue S1, pp. S90-S90 (1981); (1 page)

Online Publication Date: 12 Aug 2005

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We have measured the interfacial tension between water and superheated liquids by using a technique similar to that described by Marston and Apfel [J. Acoust. Soc. Am. 67, 27–37 (1980)] in which the interfacial tension can be deduced from the quadrupole resonance properties of a liquid drop immersed in an immiscible host liquid. Several aspects of this technique are advantageous for studying the properties of superheated liquids. In particular, the host liquid provides a smooth and clean container for the levitated sample drop. Moreover, the shape oscillation is excited by modulating the acoustic radiation pressure on the drop, thereby avoiding contact with solid surfaces which would trigger drop vaporization. The deformation of mm‐radius drops was detected optically using a method similar to Trinh, Zwern, and Wang [to be published]. We shall discuss some of the modifications of the measurement techniques from those of previous investigators. Preliminary results will be presented and are compared with other available data. [Work supported by ONR, Physics Program.]
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A nonuniformly heated resonant chamber for levitation studies in air (A)

E. Trinh, T. G. Wang, and J. Robey

J. Acoust. Soc. Am. Volume 70, Issue S1, pp. S90-S90 (1981); (1 page)

Online Publication Date: 12 Aug 2005

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The resonance conditions of an elongated vertical chamber with a square cross section and a significant temperature gradient along its main axis obtained by heating its upper part, have been experimentally determined in the course of the development of a dual temperature levitation apparatus. Under the present conditions, the cavity can be roughly divided into three main regions: the bottom and top portions arc at a relatively uniform low and high temperature, respectively, and the middle region is a transition zone with a sharp temperature gradient. The spectrum of resonance for modes with wave vectors both parallel and perpendicular to the direction of the thermal gradient has been determined with sensors in the cool as well as the hot regions. Conditions appropriate for levitation have been found in both these portions, and revealed that the required modes having wave vectors perpendicular to the temperature gradient are determined to a large extent by the local conditions, while the modes with wave vectors parallel are dependent upon the overall temperature distribution within the chamber. Levitation of low density solid objects has been achieved with the upper part at 300°C and the lower part at 40°C. Further work is being performed in order to increase this temperature differential. [Work supported by NASA.].
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Sound absorption in a 0.02 M MgSO4 solution and in a 0.02 M MgSO4‐0.6 M NaCl mixture at 25°C and pressures up to 307 arm (A)

C. C. Hsu and F. H. Fisher

J. Acoust. Soc. Am. Volume 70, Issue S1, pp. S90-S90 (1981); (1 page)

Online Publication Date: 12 Aug 2005

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Sound absorption from 30 to 300 kHz in a 0.02 M MgSO4 aqueous solution and in a 0.02 M MgSO4−0.6 M NaCl aqueous mixture were measured at pressures of 1 and 307 atm and 25°C with a 100‐liter titanium spherical resonator. Assuming a single relaxation process for both solutions, measured data were analyzed for the values of the maximum absorption per wavelength, (αλ)m, and of the relaxation frequency, fr. The fr values are 149 kHz for the pure solution and 162 kHz for the mixture. Slight decreases of fr values with pressure were shown in both solutions. (αλ)m values decrease linearly with pressure according to the equation of (αλ)m(P) + (αλ)m(o)(1‐aP), where P is in atmg and a = 6.4 × 10−4/atmg for pure solution and 6.5 × 10−4/atmg for mixture. These pressure coefficients are nearly the same as that in the sound absorption‐equation for seawater for Schulkin and Marsh [J. Acoust. Soc. Am. 34, 864 (1962)] but 21% smaller than that measured in Lyman and Fleming seawater [Hsu and Fisher, J. Acoust. Soc. Am. Suppl. 1 69, S48(1981)] and 38% smaller than that in 0.5 M magnesium sulfate solution [Fisher and Simmons, J. Acoust. Soc. Am. 62, 558 (1977)]. [This research was supported by ONR, NSF and ARPA.]
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Acoustic absorption in aqueous the mixtures at 25°C (A)

S. Rajagopalan and Surendra A. Tiwari

J. Acoust. Soc. Am. Volume 70, Issue S1, pp. S90-S90 (1981); (1 page)

Online Publication Date: 12 Aug 2005

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We report the ultrasonic absorption in aqueous mixtures of tetrahydrofuran at 25°C in the frequency range 0.27–561 MHz. The results are analyzed by the single and double relaxation model approach. Variation with concentration of the relaxation parameters is discussed in the light of molecular interactions present. It is found that the double relaxation model is more adequate to explain the observed absorption behavior than the single relaxation. The concentration, at which the peak absorption occurs, is found to be drifting from 0.3 at lower frequencies to 0.5 at higher frequencies.
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Measurement of vibrational relaxation time of oxygen between 475° and 675°K using an acoustic resonant technique (A)

I‐an Feng and Mark C. Lee

J. Acoust. Soc. Am. Volume 70, Issue S1, pp. S90-S90 (1981); (1 page)

Online Publication Date: 12 Aug 2005

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Vibrational relaxation times of O2‐He, O2‐CO2, and O2‐H2 mixtures have been measured using a resonant chamber method between 475° and 675°K. Data for pure O2 were obtained by extrapolating that of mixtures of zero impurity concentrations. Our data agree with previous acoustic results at 473° and 573°K and shock tube results at 700°K. The temperature dependence of the vibrational relaxation time for pure O2 was compared to theories of Landau‐Teller, SSH, and Parker. The simple Landau‐Teller theory has shown better agreements with experimental data than that of SSH and Parker′s for the case of O2‐O2, O2‐He, and O2‐H2 collisions. [Work supported by NASA.]
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