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Oct 1984

Volume 76, Issue S1, pp. S1-S95

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back to top Session K. Physical Acoustics II: Radiation and Nonlinear Effects
Contributed Papers
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An analytic description of the interaction between two acoustic transducers that are specified by their Green's functions (A)

Anthony J. Rudgers

J. Acoust. Soc. Am. Volume 76, Issue S1, pp. S23-S23 (1984); (1 page)

Online Publication Date: 12 Aug 2005

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Expressions for the self and mutual radiation impedances of two interacting transducers are analytically constructed in terms of the Green's functions of the individual transducers. One applies a symbolic iterative procedure to the expression for the pressure field of the transducers. This is best implemented by the successive application of a particular linear operator to quantities involving the Green's functions and the surface velocities on the active parts of the transducers. The radiation impedances are expressed in the form of symbolic power series in this linear operator. Individual terms of these series have simple physical interpretations. The power (i.e., index) of the operator defines the kind of interaction occurring. Thus, a term with index zero expresses the interaction of a transducer with its own field, as if the other transducer were absent; one with index unity expresses the interaction of a transducer with the field directly radiated to it by the other transducer; one with index two expresses the interaction of a transducer with its own field after this has been diffracted once by the other transducer, and so on. The iterative analytic technique can also be applied to more than two interacting transducers and in problems involving free‐space Green's functions.
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The sound field of a Gaussian transducer (A)

Gonghuan Du and M. A. Breazeale

J. Acoust. Soc. Am. Volume 76, Issue S1, pp. S23-S23 (1984); (1 page)

Online Publication Date: 12 Aug 2005

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The advantages of a Gaussian amplitude distribution at the surface of a transducer are similar to the advantages of a Gaussian amplitude distribution in a light beam: the diffraction pattern is both simpler to measure and simpler to calculate. Further, the simplification remains when one considers nonlinear terms in the wave equation. If one can achieve a truly Gaussian amplitude distribution, then comparison of experimental data with theoretical calculation also is facilitated. Previously we used electrical fringing to produce a one‐dimensional Gaussian amplitude distribution for schlieren photography. Now, we have used an electrical fringing to produce a two‐dimensional Gaussian distribution in an ultrasonic beam. The sidelobes are undetectable, and the maxima and minima in the Fresnel region have disappeared. Design and testing of the transducer are discussed. Both advantages and limitations are delineated. The mathematical description of the sound field is discussed. Analytical expressions are given for the amplitude in the nearfield (Fresnel?) as well as in the farfield (Fraunhofer?). In both cases the distribution is described by a Gaussian function. [Research supported in part by ONR.]
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Influence of baffle conditions on transient radiation (A)

Daniel Guyomar and John Powers

J. Acoust. Soc. Am. Volume 76, Issue S1, pp. S23-S23 (1984); (1 page)

Online Publication Date: 12 Aug 2005

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The influence of assumed baffle conditions (rigid, free‐space, and soft) on the transient field radiated from a planar surface are investigated. The emitter is arbitrarily shaped and a common time excitation is assumed for all points on the emitter. The technique requires that only the normal derivative of the surface excitation be known. The three baffle conditions differ in the introduction of a specific directivity factor and a convolution term. The computation of the fields is done with a time extension of the angular spectrum approach to diffraction. The spatial spectra of the fields for the three baffle conditions can be interrelated. From this model, propagation is seen to be a time‐varying low‐pass spatial filter. The method is valid for arbitrary surface shapes, arbitrary time excitations, and arbitrary propagation distances. The techniques allows time‐efficient computer solution that are rapidly convergent. Computer simulations including a circular piston, a rectangular source, and a truncated Gaussian are presented.
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Radiation from an acoustic array moving at transonic velocities (A)

Yves H. Berthelot and Ilene J. Busch‐Vishniac

J. Acoust. Soc. Am. Volume 76, Issue S1, pp. S23-S23 (1984); (1 page)

Online Publication Date: 12 Aug 2005

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According to classical acoustic theory, the Doppler shift associated with an acoustic source moving at constant velocity induces the following straining of the time coordinate: t′ = t∣1‐M cos α∣. Here t′ denotes the time coordinate in the fixed frame of reference (receiver), M is the Mach number of the source, and α is the angle between the direction of motion and the direction of observation. At transonic velocities t′ can assume a value of 0, in which case all the acoustic energy is received in an infinitesimal increment of time. This implies a transfer of infinite power so it is not physically realizable. We have used the method of characteristics to find the exact Doppler shift to a transonic source and the corresponding maximum amplitude observable at the receiver. Two cases are considered: a point source and a line source, both moving rectilinearly above a point receiver. [Work supported by the Office of Naval Research ONR.]
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Transduction efficiency for sound waves systematically pumped by controlled motion of laser beams across water surfaces (A)

Hsiao‐an Hsieh and Allan D. Pierce

J. Acoust. Soc. Am. Volume 76, Issue S1, pp. S23-S24 (1984); (2 pages)

Online Publication Date: 12 Aug 2005

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Previous analyses of laser‐generated sound predict efficiencies of the order of (β/cp)2(ωch/Lch)P/ρ, where ωch each is characteristic frequency of laser intensity modulation, Lch is characteristic length scale of energy deposition region, and P is power output of the laser. Because such efficiencies are typically extremely low, the authors have been considering [J. Acoust. Soc. Am. Suppl. 1 75, S16 (1984)] the possibility of externally controlling the temporal and spatial pattern of heat addition by moving the laser beam such as to systematically pump energy into a traveling acoustic wave. The present paper′s analysis demonstrates that doing so can yield efficiencies of the order of (β/cp)2(c2/λch3) E/ρ where λch is a characteristic wavelength of the generated sound and E is the total energy deposited in the water by the laser. The principal distinction from the previous expression is the dependence on laser energy rather than laser power; a lower power laser that operates continuously can be just as efficient a source of underwater sound as a high‐power laser. Examples that illustrate this premise include those when the laser is used to generate a periodic array (repetition distance λ) of moving (with sound speed c) slabs of heat desposition. [Work supported by ONR, Code 425 UA.]
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The nearfield directivity pattern of a thermoacoustic array (A)

Yves H. Berthelot and Ilene J. Busch‐Vishniac

J. Acoust. Soc. Am. Volume 76, Issue S1, pp. S24-S24 (1984); (1 page)

Online Publication Date: 12 Aug 2005

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A thermoacoustic array can be generated by modulating the intensity of a laser beam illuminating a liquid. The nearfield directivity pattern of a thermoacoustic array is found by taking the Fourier transform of the impulse response of the opto‐acoustic system. A simple expression in integral form has been derived for the directivity of a thermoacoustic array on a pressure release boundary such as an air/water interface. The integral is easily evaluated numerically and it clearly show the presence of side lobes in the nearfield directivity. In the limiting case of farfield radiation the directivity computed numerically reduces to the farfield directivity derived analytically. [Work supported by the Office of Naval Research ONR.]
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Evaluation of the overall sound field properties for a finite amplitude sound beam (A)

J. H. Ginsberg

J. Acoust. Soc. Am. Volume 76, Issue S1, pp. S24-S24 (1984); (1 page)

Online Publication Date: 12 Aug 2005

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The nonlinear King integral [J. H. Ginsberg, J. Acoust. Soc. Am. (to be published)] provides a general algorithm for finite amplitude axisymmetric waves radiating from a harmonically vibrating transducer. The derivation of that result was based on asymptotic analyses of the transverse wavenumber spectrum near the axis for almost planar modes and far off axis. The validity of the analysis is confirmed here by a change of variables that yields an overall measure of the associated error. Previous evaluations using the nonlinear King integral provided temporal and frequency spectrum predictions at selected locations, primarily on axis. The present paper reports on an extensive mapping of the field for a moderately high frequency in terms of amplitude and relative phase lags for the fundamental and several higher harmonics. This mapping is cross‐referenced to waveform displays that show the changing nature of the asymmetrical distortion process associated with transition from the nearfield to the farfield. [Work supported by ONR, Code 425‐UA.]
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Reflection of finite amplitude sound beams from pressure release surfaces (A)

Mark F. Hamilton, Jacqueline Naze Tjøtta, and Sigve Tjøtta

J. Acoust. Soc. Am. Volume 76, Issue S1, pp. S24-S24 (1984); (1 page)

Online Publication Date: 12 Aug 2005

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A recently described numerical procedure for solving Kuznetsov's nonlinear paraxial wave equation [S. I. Aanonsen, M. F. Hamilton, J. Naze Tjøtta, and S. Tjøtta, 10th ISNA, Kobe (1984)] is used to model finite amplitude sound beams reflected at normal incidence from both finite and infinite pressure release surfaces. The entire wave field is assumed to be progressive, with reflection simulated by multiplication of each harmonic amplitude by an appropriate coefficient. Although reflection from an infinite pressure release surface reduces finite amplitude losses incurred by the fundamental, it is shown that at some distance from the reflector even the harmonics attain higher axial levels than would occur without reflection. Following reflection from a finite surface, all spectral components exhibit a second nearfield structure characterized by the size of the reflector and the frequency of the component. As a result the axial levels of all components are ultimately higher than after reflection from an infinite surface. The present results may explain observations by Muir et al. [T. G. Muir, L. L. Mellenbruch, and J. C. Lockwood, J. Acoust. Soc. Am. 62, 271–276 (1977)]. Also considered are cases of weakly curved reflectors. [Support of MFH by F. V. Hunt Postdoctoral Research Fellowship.]
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Model study of the diffraction on an explosive transient by plane barriers (A)

Richard Raspet, Jean Ezell, and Steve Coggeshall

J. Acoust. Soc. Am. Volume 76, Issue S1, pp. S24-S24 (1984); (1 page)

Online Publication Date: 12 Aug 2005

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The results of a model study of the diffraction of transients from blasting caps over barriers are reported. A prediction technique based on Oberhettinger time domain notation was developed [J. Res. Natl. Bur. Stand. 61, 5 (1957)]. The results of this calculation are compared to the data. Finite wave effects were incorporated into the prediction and were shown to be small for the geometries and charge size employed in the model study. The finite wave effects on diffraction of transient may be important for shorter duration pulses such as N wave from sparks.
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