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Journal of the Acoustical Society of America

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Dec 1968

Volume 44, Issue 6, pp. 1491-1753

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Fluctuations of Sound with Position in a Reverberant Room

David Lubman

J. Acoust. Soc. Am. Volume 44, Issue 6, pp. 1491-1502 (1968); (12 pages) | Cited 9 times

Online Publication Date: 21 Jul 2005

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Spatial fluctuations of sound in reverberant rooms are examined theoretically for the case of a fixed source and movable receiver. The approach is to describe statistics of the time‐averaged squared sound pressure, as a function of frequency. These statistics apply to reverberant rooms at high frequencies, such that the modal overlap (ratio of modal bandwidth to the average spacing between modes) is larger than about 3, and for regions sufficiently removed from the source that the reverberant field prevails. Within these bounds of frequency and space, squared sound pressure may be profitably viewed as a stochastic process over frequency. At each frequency in this range, squared sound pressure is a random variable obeying an exponential probability law over space. The family of random variables obtained by considering all frequencies in this range defines a stochastic process. The process is employed to derive formulas for the spatial variance of squared sound pressure for the cases of single tone, multitone, warbletone, and narrow‐band noise excitation. Experimental confirmation and suggested applications are given in many instances. In general, the variance is small when the product of bandwidth and reverberation time is large, as long as reverberation time is not so large as to prevent high modal overlap.

Study of Tinnitus Induced Temporarily by Noise

G. R. C. Atherley, T. I. Hempstock, and W. G. Noble

J. Acoust. Soc. Am. Volume 44, Issue 6, pp. 1503-1506 (1968); (4 pages)

Online Publication Date: 21 Jul 2005

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Subjects were exposed in one ear for 5 min to ⅓‐oct band noise centered at either 2, 3, 4, or 6 kHz at 110 dB SPL. The resulting aftersensation, called “noise‐induced short‐duration tinnitus” (NIST) was matched for pitch and loudness in the nonstimulated ear. It was found that the pitch of NIST bears a constant relation to the frequency of the stimulus and that the difference between the equivalent frequency of NIST and the frequency of maximum threshold shift was equivalent to one critical band.

Effect of Masker Spectrum Level on Masking‐Level Differences at Low Signal Frequencies

Terrence R. Dolan

J. Acoust. Soc. Am. Volume 44, Issue 6, pp. 1507-1512 (1968); (6 pages) | Cited 2 times

Online Publication Date: 21 Jul 2005

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Most, if not all, models of binaural hearing predict a dependence of the magnitude of the masking‐level difference (MLD) on signal frequency. Specifically, the size of the MLD is expected to increase as the signal frequency is decreased. The results of many experiments in which signal frequency was varied, however, do not support the above prediction. The magnitude of the MLD appears to decrease at frequencies below 300 cps. The present experiment was designed to re‐examine the decrease in the size of the MLD at low frequencies and to test a qualitative explanation of this phenomenon based on the concept of internal noise. To do so, the size of the MLD in the N0Sπ masking condition and the N0S0 masking condition was estimated relative to the NMSM masking condition at signal frequencies of 150 and 300 cps at several masker spectrum levels. The results indicated that the magnitude of the MLD at both frequencies is dependent upon spectrum level of the masker. The results further indicate that the dependence of the size of the MLD on spectrum level varies as a function of the signal frequency. The size of the MLD at 150 cps is much more sensitive to changes in masker spectrum level than is the MLD at 300 cps. Both results agree with predictions based on the internal noise hypothesis.

Frequency‐Response Characteristic of Auditory Observers Detecting Signals of a Single Frequency in Noise: The Probe‐Signal Method

Gordon Z. Greenberg and Willard D. Larkin

J. Acoust. Soc. Am. Volume 44, Issue 6, pp. 1513-1523 (1968); (11 pages) | Cited 17 times

Online Publication Date: 21 Jul 2005

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Four experiments were conducted to develop and test a method of determining the frequency‐response characteristic of the observer when he listens for single‐frequency signals presented against a continuous background of wide‐band noise. After observers were trained to detect primary signals of a single frequency, probe signals of various other frequencies were presented infrequently, in lieu of the primary signal. Primary signals and all probe signals were presented with very similar amplitudes that would be expected to render them all equally detectable if presented alone in single‐frequency experiments. Estimates of the detectability of the signals of the various frequencies were obtained concurrently in a two‐alternative forced‐choice procedure. The results from 14 observers were quite similar and show differences in detection as a function of signal frequency when the primary signal was of 1000 or of 1100 Hz. In general, the primary signal was correctly detected 75%–90% of the time while signals with frequencies at approximately 150 to 200 Hz on either side of the primary‐signal frequency were detected at the chance level, 50% correct. In as few as three experimental sessions, the observer's frequency‐response characteristic was obtained using the probe‐signal method.

Impulse Duration and Temporary Threshold Shift

Michel Loeb and John L. Fletcher

J. Acoust. Soc. Am. Volume 44, Issue 6, pp. 1524-1528 (1968); (5 pages) | Cited 1 time

Online Publication Date: 21 Jul 2005

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Subjects were exposed, on different test days, to 166‐dB (peak normal‐incidence) impulses 34, 58, 72, or 96 μsec in duration spaced 1 sec apart. For each pulse duration, the subjects were first exposed to one pulse, then the number of pulses was doubled on successive days until the temporary threshold shift (TTS) following exposure exceeded 30 dB. Intercorrelations of numbers of impulses required to reach criterion TTS at each duration were obtained; they were highest when durations were similar. At the largest pulse duration, a median of only four impulses was required to achieve criterion, some individuals exceeded criterion at one impulse, while others required hundreds. No evidence was seen of a 4‐kHz notch; maximum shift was at high frequencies (10–15 kHz) and relatively independent of impulse duration. There is reason to believe that if one exceeds allowable TTS in the speech‐range frequencies with this kind of impulse noise, there is a chance of producing permanent high‐frequency loss.

Effects of Intersignal Interval on the Human Auditory Evoked Response

David A. Nelson and Frank M. Lassman

J. Acoust. Soc. Am. Volume 44, Issue 6, pp. 1529-1532 (1968); (4 pages) | Cited 1 time

Online Publication Date: 21 Jul 2005

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Average evoked responses were recorded from human vertex in response to tone pulses presented at intersignal intervals (ISI) ranging from 0.25 through 10 sec. Tone pulses were 20 msec in duration with 20‐msec rise and decay times. Frequencies investigated were 500, 1000, and 2000 Hz. Response amplitude was found to be a linear function of log10ISI. Response latency did not change significantly with ISI, except perhaps in component N2 of the response, which appeared to increase in latency as ISI increased. These relations obtained regardless of frequency.

Mechanisms of Frequency Discrimination

Jan O. Nordmark

J. Acoust. Soc. Am. Volume 44, Issue 6, pp. 1533-1540 (1968); (8 pages) | Cited 1 time

Online Publication Date: 21 Jul 2005

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Difference limens were obtained for the discrimination of pure tones from 62.5 Hz to 12 kHz, and for short pulses from 1 to 4 kHz. In logarithmic coordinates, the data fitted straight lines with different slopes for the high‐frequency, the low‐ and medium‐frequency, and, for pulses, the very low‐frequency ranges. An analysis was made to show that the discrimination of duration and the discrimination of pitch are both based on time‐measuring processes.

Functional Changes in the Ear Produced by High‐Intensity Sound. I. 5.0‐kHz Stimulation

G. Richard Price

J. Acoust. Soc. Am. Volume 44, Issue 6, pp. 1541-1545 (1968); (5 pages)

Online Publication Date: 21 Jul 2005

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Sounds of sufficient intensity and duration can produce decrements in the cochlear microphonic (CM). It was the purpose of these experiments to determine the extent of such changes and the rate at which they occurred. Cat ears were exposed to 5.0‐kHz tones at intensities from 99 to 138 dB SPL (re 0.0002 μbar) for periods totaling 80 min. Losses in CM sensitivity (measured with a round‐window electrode) occurred for tones ranging from 0.1 to 10 kHz with the greatest losses at 3.0 or 4.0 kHz. Changes occurred at a rate that was linear in time for the lower intensities and linear in time at the higher intensities.

Submicroscopic Displacement Amplitudes of the Tympanic Membrane (Cat) Measured by a Laser Interferometer

Juergen Tonndorf and Shyam M. Khanna

J. Acoust. Soc. Am. Volume 44, Issue 6, pp. 1546-1554 (1968); (9 pages) | Cited 1 time

Online Publication Date: 21 Jul 2005

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A laser interferometer, designed and constructed in this laboratory, was evaluated with respect to its applicability to measurements of amplitudes and phases in the ear. The instrument measures continuously up to a maximal amplitude of 0.92×10−5 cm, and higher at selected points. With respect to vibrations of the tympanic membrane, measured in an open sound field, the vibration isolations of the instrument was ample. The prevailing S/N ratio made it convenient to routinely measure amplitudes of 1 × 10−7 cm in living animals. At low frequencies, this corresponds to SPL's of approximately 60 dB. In fresh cadavers, however, while there was no immediate change in the magnitude of the responses, readings were extended to 1 × 10−9 cm, owing to the absence of pulse and breathing, giving a dynamic range of 80 dB. In all experiments, repeatability was excellent, and between‐animal variations were low. The resulting transfer characteristics obtained in living animals, with the tympanic bulla closed, was generally similar to those obtained earlier, with some noted exceptions. The amplitude curve failed to show the slight hump around 1 kHz found earlier. The phase curve was much more complex than earlier ones and cannot be approximated by the assumption of simple network models.

Laser Interferometer for the Measurement of Submicroscopic Displacement Amplitudes and Their Phases in Small Biological Structures

Shyam M. Khanna, Juergen Tonndorf, and W. W. Walcott

J. Acoust. Soc. Am. Volume 44, Issue 6, pp. 1555-1565 (1968); (11 pages) | Cited 4 times

Online Publication Date: 21 Jul 2005

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An interferometer is described. It is designed for measurements of submicroscopic displacement amplitudes of small biological structures in living animals. Its output is frequency independent. The instrument may be used for measuring: (1) absolute displacement amplitudes as low as 3 × 10−10 cm between 20 and 20 000 Hz; (2) phase angles of the displacements with respect to that of the applied sound signals; (3) transient responses of the vibrating structure. Theory of operation is discussed. Fabrication of microscopic mirrors and construction details of the interferometer are given. Experiments performed with the aid of an earphone as a vibrating object are included to show the characteristics of the interferometer. Calibration is precise (within 1 dB) and repeatability is excellent, both with respect to amplitude (within 1 dB) and phase (within 5°). Experiments on living animals and cadavers, giving amplitude and phase data, will be included in a separate paper.

Generation and Detection of Acoustic Waves in Pulsed Electrical Discharges

K. J. Nygaard and G. Meltz

J. Acoust. Soc. Am. Volume 44, Issue 6, pp. 1566-1569 (1968); (4 pages) | Cited 1 time

Online Publication Date: 21 Jul 2005

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Electroacoustic resonances excited in a cylindrical plasma tube are very sensitive to minute changes in electron density and temperature and can therefore be used to detect sound waves. The principle of detection is that in the ordinary acoustic mode, the neutral particles, electrons, and ions move in phase with the same relative density changes. It is demonstrated experimentally that the acoustic transient detected at a certain distance from the negative glow of a pulsed electrical discharge is superposition of a direct pulse and a pulse that has been reflected from the cathode surface. From the perturbations of the electroacoustic resonances, relative density changes of the order of 1% in the acoustic transient are deduced.

Effect of Speaking Rate on Diphthong Formant Movements

Thomas Gay

J. Acoust. Soc. Am. Volume 44, Issue 6, pp. 1570-1573 (1968); (4 pages) | Cited 5 times

Online Publication Date: 21 Jul 2005

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Duration and formant frequency measurements of the five diphthongs, /ɔɪ,aɪ,aυ,eɪ,oɪ/, were made for three conditions of speaking rate. Results indicate that onset target position and second‐formant rate of change are fixed features of the diphthong formant movement, while offset target positions are variable across changes in duration. Other measurements show that increased diphthong duration due to the presence of a following voiced consonant is accomplished by longer steady‐state targets for /ɔɪ,aɪ,aυ/ and longer glide durations for /eɪ,oυ/. The data provide a basis for an articulatory description of diphthong production.

Primate Vocalizations and Human Linguistic Ability

Philip Lieberman

J. Acoust. Soc. Am. Volume 44, Issue 6, pp. 1574-1584 (1968); (11 pages) | Cited 8 times

Online Publication Date: 21 Jul 2005

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Some representative vocalizations of captive rhesus monkey, chimpanzee, and gorilla were recorded and analyzed by means of sound spectrograms and oscillograms. It was found that these animals' vocal mechanisms do not appear capable of producing human speech. The laryngeal output was breathy and irregular. A uniform cross section, schwalike configuration appeared to underlie all the vocalizations. These animals did not modify the shape of their supralaryngeal vocal tracts by means of tongue maneuvers during a vocalization. Formant transitions occurred in some vocalizations, but they appeared to have been generated by means of laryngeal and possibly velar or lip movements. The nonhuman primates lack a pharyngeal region like man's, where the cross‐sectional area continually changes during speech. The data suggest that speech cannot be viewed as an overlaid function that makes use of a vocal tract that has evolved solely for respiratory and deglutitious purposes; the skeletal evidence of human evolution shows a series of changes from the primate vocal tract that may have been, in part, for the purpose of generating speech. Articulate speech may not have been fully developed in some of man's ancestors. The study of the peripheral speech‐production apparatus of a fossil thus may be useful in the assessment of its phylogenetic grade.

Clipstrum Pitch Determination

A. Michael Noll

J. Acoust. Soc. Am. Volume 44, Issue 6, pp. 1585-1591 (1968); (7 pages)

Online Publication Date: 21 Jul 2005

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A new method of pitch determination similar to the cepstrum except that both the time signal and the log power spectrum are infinitely peak clipped before spectrum analysis has been simulated on a digital computer. Although this new method itself, called the “clipstrum,” is inferior to cepstrum pitch determination, the clipstrum of center‐clipped speech performs surprisingly well and sometimes is superior to the cepstrum. The clipping in the clipstrum might offer some advantages over cepstrum analysis in certain digital hardware implementations since multiplications could be replaced with additions or subtractions.

Effect of Pitch Averaging on the Quality of Natural Vowels

A. E. Rosenberg

J. Acoust. Soc. Am. Volume 44, Issue 6, pp. 1592-1595 (1968); (4 pages)

Online Publication Date: 21 Jul 2005

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A pitch synchronous analysis was carried out over the vowel portions of the CVC utterances HAYED, HOD, HODE, and the stressed vowel portions of the sentence, “FEW THIEVES ARE NEVER SENT TO THE JUG,” recorded by a male speaker. The analysis provided formant frequencies, excitation parameters, and accurate pitch‐period measurements. For each vowel, each measured period was replaced by a period obtained by averaging adjacent periods over a symmetric “window” producing a smoothed pitch contour. The speech samples were reconstituted with the vowels with smoothed pitch contours. Eight window sizes were selected for subjective evaluation, ranging from an imperceptible amount of smoothing to an amount sufficient to produce nearly monotone vowels. Subjective evaluation was carried out by means of paired‐comparison tests between utterances with different window sizes, including those with natural‐pitch contours. The results indicate that listeners are unable to discriminate between samples with natural‐pitch contours and those with an amount of smoothing sufficient to eliminate most of the period‐to‐period fine structure in the contours. In a addition, it appears that modes of discrimination with respect to pitch smoothing are distinct for the two cases of isolated vowel sounds and sentence‐imbedded vowel sounds.

Speaker Authentication and Identification: A Comparison of Spectrographic and Auditory Presentations of Speech Material

K. N. Stevens, C. E. Williams, J. R. Carbonell, and Barbara Woods

J. Acoust. Soc. Am. Volume 44, Issue 6, pp. 1596-1607 (1968); (12 pages) | Cited 1 time

Online Publication Date: 21 Jul 2005

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Speaker authentication and identification were examined for two different methods of presentation of the speech material: (1) speech samples presented aurally through headphones, and (2) speech samples presented visually as conventional intensity‐frequency‐time patterns, or spectrograms. Two kinds of experiments were carried out: (1) a series of closed tests in which there was a library of samples from eight speakers, and test utterances were known to be produced by one of the speakers; and (2) a series of open tests in which the same library of eight speakers was used, but test utterances may or may not have been produced by one of the speakers. The results for the closed tests indicate that, after about 4 h of exposure to the test situation, the percent error in identification of speakers from isolated speech samples (words or phrases) is about six percent for aural presentation and about 21% for visual presentation. These scores depend upon the talker, the subject, and the phonetic content and duration of the speech material. For the open visual tests, appreciable numbers of false acceptances (incorrect authentications) were made. The results suggest procedures that might be used to minimize error scores in practical situations.

Finite‐Amplitude Acoustic Waves in Dielectric Crystals

B. A. Richardson, R. B. Thompson, and C. D. W. Wilkinson

J. Acoust. Soc. Am. Volume 44, Issue 6, pp. 1608-1615 (1968); (8 pages) | Cited 2 times

Online Publication Date: 21 Jul 2005

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Acoustic waves at microwave frequencies show significant nonlinear effects at power densities of 10 W/cm2. These effects have been studied using Bragg diffraction of light from the harmonic components of the acoustic waves. With this technique, direct harmonic analyses of the waves have been obtained without the need for calibrated broad‐band transducers. The following effects of finite amplitude waves propagating in quartz have been observed: variation of the attenuation of the fundamental with power level; the presence of the second through fifth acoustic harmonics; the growth and decay of these harmonics as a function of the distance traveled by the acoustic wave; and the behavior of the second harmonic after reflection from a stress‐free surface. The growth of the harmonics assures that they were generated in the bulk of the solid. Similar effects have been observed in MgO and MnF2. The experimental observations have been compared with theoretical predictions and estimates of the relevant third‐order elastic constants obtained.

Generalized Boundary Condition for Multiple Scatter in Acoustic Reflection

M. A. Biot

J. Acoust. Soc. Am. Volume 44, Issue 6, pp. 1616-1622 (1968); (7 pages) | Cited 5 times

Online Publication Date: 21 Jul 2005

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A boundary condition is developed that generalizes the author's earlier results and embodies the effect of multiple scatter for acoustic reflection on a rough surface. The size of the roughness is assumed to be sufficiently small in comparison with the wavelength. Both induced radiating dipoles and radiating sources are taken into account. The results are further generalized to take into account roughness of various shapes, nonuniform distribution, and anisotropic properties. The anisotropy represented by a two‐dimensional symmetric tensor of Rank 2. Results open the way to the analysis of combined coherent and incoherent reflection including the cooperative resonance due to multiple scatter.

Farfield Radiation from an Infinite Elastic Plate Excited by a Transient Point Loading

Edward B. Magrab and Wayne T. Reader

J. Acoust. Soc. Am. Volume 44, Issue 6, pp. 1623-1627 (1968); (5 pages) | Cited 1 time

Online Publication Date: 21 Jul 2005

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An expression is obtained for the farfield pressure radiated by a thin elastic plate bounded on one side by a fluid medium when the plate is excited by a time‐varying point load. Both the fluid and the plate are considered to be infinite in extent. The solution is obtained with the use of transform theory to solve the coupled differential equations describing the transverse motion of the plate and the velocity potential in the fluid: A Hankel transform is used on the spatial coordinate and a Laplace transform on the temporal variable. The inverse Hankel transform is evaluated using the saddle‐point integration technique. The inverse Laplace transform is expressed as a convolution integral that is evaluated for the case when the point load is a short tone burst.

Free Vibration of Laminated Orthotropic Cylindrical Shells

Stanley B. Dong

J. Acoust. Soc. Am. Volume 44, Issue 6, pp. 1628-1635 (1968); (8 pages) | Cited 2 times

Online Publication Date: 21 Jul 2005

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Vibration characteristics of thin laminated orthotropic cylindrical shells are investigated. The theory, based on the Kirchhoffean hypothesis regarding deformation, can accommodate shells composed of an arbitrary number of bonded layers, each with a different thickness and different elastic orthotropic properties. Donnell‐type equations expressed in terms of the reference surface displacements are employed, and the effects of initial extensional forces in the shell are included. The frequency equation for a simply supported cylinder is derived. Next, an iterative procedure for determining the natural frequencies of a shell under an arbitrary set of homogeneous boundary conditions is described in detail. Specialization of present results to laminated orthotropic plates is indicated.

Natural Frequencies and Modes of Skew Membranes

Somayajulu Durvasula

J. Acoust. Soc. Am. Volume 44, Issue 6, pp. 1636-1646 (1968); (11 pages) | Cited 5 times

Online Publication Date: 21 Jul 2005

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Natural frequencies and mode shapes of a wide range of skew membranes are obtained by the Rayleigh‐Ritz method expressing the deflection as a double Fourier sine series in oblique coordinates. Since the eigenvalues of a polygonal simply supported plate are the squares of the eigenvalues of a polygonal membrane of the same geometry and the eigenfunctions are identical, the results of the present paper readily provide the vibration characteristics of simply supported skew plates as well. This detailed study revealed interesting features like the skew angle splitting the degenerate frequencies of rectangular membranes into distinct ones and the “frequency crossing” of some modes that belong to opposite symmetry groups of the skew membrane. With changing skew angle, the nodal patterns of some modes undergo a gradual change to other totally different patterns. Since, for some modes the diagonals happen to be the nodal lines, such modes can be interpreted as the appropriate modes of the corresponding triangular membrane and consequently, of triangular simply supported plates.

Transmission Characteristics of Conical and Cylindrical Shells under Lateral Excitation

Daniel D. Kana and William C. L. Hu

J. Acoust. Soc. Am. Volume 44, Issue 6, pp. 1647-1657 (1968); (11 pages)

Online Publication Date: 21 Jul 2005

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A theoretical and experimental study is presented for determining the steady‐state frequency response of laterally excited truncated cones and cylinders in a low to moderate frequency range. The theoretical results are formulated in terms of forward transmission matrices, although relationships are reviewed which allow application of the results for impedance or admittance formulations as well. Expressions for the 4×4 matrices of transmission for coupled bending‐shear displacements are developed by means of the membrane theory of thin shells. The results are then applied to the case of laterally excited shells that support a rigid top mass. Input and transfer coupled impedances are calculated and compared with experimental observations for 30° and 15° cones and a cylinder. Over‐all comparison of the results indicates that the membrane theory provides a reasonable approximation for determining response characteristics, but some definite deficiencies remain unexplained.

Critical Angles Associated with the Reflection‐Refraction of Elastic Waves at an Interface

H. D. McNiven and Y. Mengi

J. Acoust. Soc. Am. Volume 44, Issue 6, pp. 1658-1663 (1968); (6 pages) | Cited 1 time

Online Publication Date: 21 Jul 2005

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Goodier and Bishop established that there is a “critical” incident angle that a train of Sv waves makes with the traction‐free surface of an elastic half‐space and that as the incident angle passes through this critical value from above, the reflected P wave passes through grazing incidence and emerges as a surface wave. In this paper, study is made of the fate of a train of Sv waves on striking the plane interface between two elastic materials. It is found that there are five critical angles associated with such a wave and the emerging wave which passes through grazing incidence corresponding to each angle is transformed into a surface wave. The wave is like a Rayleigh wave in that the magnitude of motions accompanying it decay exponentially away from the interface, particle motions have an elliptical orbit, and the wave travels with a constant phase velocity. The wave is unlike a Rayleigh wave in that its velocity is not the velocity of Rayleigh waves and, in fact, depends on the incident angle. The method which is used to establish the nature of the waves that emerge probably is as important as the results. The method, which is graphical, is based on the notion of slowness surfaces developed by Synge using the solution of the field equations of elasticity. The method itself is the result of a systematic exploitation of an idea introduced by Musgrave.

Traveling Load on a Cylindrical Shell

Michael P. Mortell

J. Acoust. Soc. Am. Volume 44, Issue 6, pp. 1664-1670 (1968); (7 pages)

Online Publication Date: 21 Jul 2005

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The response of a semi‐infinite circular cylindrical shell that is subject to a constant‐pressure wave moving with constant velocity is examined, when the effects of transverse shear and rotatory inertia are included. The time dependence is suppressed by means of a Laplace transform, and the behavior of the motion near the characteristic wavefronts is examined by making an asymptotic expansion for large p, the transform variable, directly on the governing equations. The form of the solution near the load front is given and some resonant velocities are noted. By a simple yet novel technique, it is shown that the dominant long‐time disturbance travels with the bar velocity, and the behavior of the solution in this region is shown to be that of an Airy phase.

Geoacoustic Applications of Electroseismic Sources

D. M. Nash, Jr. and T. G. Barnes

J. Acoust. Soc. Am. Volume 44, Issue 6, pp. 1671-1674 (1968); (4 pages)

Online Publication Date: 21 Jul 2005

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A mobile high‐energy source for electrically producing and controlling seismic pulses is described. The source employs an electric discharge across gap in a liquid‐filled dome. Applications of this source include the detection and delineation of small anomalies in addition to conventional seismic exploration. A theoretical treatment is given to show that the high‐frequency characteristics needed for resolving the small anomalies may be obtained by shaping the pulses and by producing a train of pulses.
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