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The first (although slightly incorrect) wave equations for finite-amplitude sound in lossless fluids were obtained independently by Euler (1759) and Lagrange (1760). Poisson (1808) provided the first major break-through with his exact solution for progressive waves of finite amplitude in a lossless gas. Although a far-reaching result, the progressive waveform distortion (and disastrous consequences) implied by his solution went unrecognized for 40 years. Challis (1848) showed that Poisson's solution is not single valued but did not understand why. Stokes (1848) provided the why. He saw that the Poisson waveform distorts as it travels, eventually threatening to become multivalued. He postulated that a discontinuity (shock) develops to avoid waveform overturning. He also proposed that viscosity (not accounted for by Poisson) would prevent true discontinuities. Earnshaw (1860) and Riemann (1860) cleaned up the theory for plane waves in lossless gases. However, how to predict propagation after shocks form? Rankine (1870) and Hugoniot (1887, 1889) provided the first solutions for propagation when thermoviscous dissipation is included. These were the first steps toward redemption. The curtain rang down on this era of nonlinear acoustics with two excellent papers in 1910, one by Rayleigh and another by Taylor, on steady shocks in a thermoviscous fluid.

Born in 1919, Edwin L. Carstensen grew up in Oakdale, Nebraska. Thinking to be a teacher or preacher, Ed attended Nebraska State Teachers College, 1938-1941. An interest in physics and music led Ed in fall 1941 to Case School of Applied Science. But World War II interrupted; when his professor Robert Shankland was tapped to head the newly formed Underwater Sound Reference Laboratory in spring 1941, Ed followed and spent the war and early postwar years at USRL’s lab in Orlando, Florida. Thus Ed’s first serious involvement in acoustics was in underwater sound. Several publications emerged after the war; the most significant was the Carstensen-Foldy study of sound propagation through bubbly water (JASA 19, 481-501 (1947)). After PhD studies at University of Pennsylvania, 1948-55, where Herman Schwann introduced Ed to biophysics, and five years at the Army Biological Laboratory, Ft. Detrich, Maryland, Ed took a faculty position in Electrical Engineering at the University of Rochester. There he remained for th...

The first (although slightly incorrect) wave equations for finite-amplitude sound in lossless fluids were obtained independently by Euler in 1759 and Lagrange in 1760. Poisson (1808) provided the first major breakthrough with his exact solution for progressive waves of finite amplitude in a lossless gas. Although a far-reaching result, the progressive waveform distortion (and disastrous consequences) implied by his solution went unrecognized for 40 years. Challis (1848) showed that the Poisson solution is not single valued but did not understand why. Stokes (1848) provided the why. He saw that the Poisson waveform distorts as the wave travels, eventually threatening to become multivalued. He postulated that a discontinuity (shock) develops to avoid waveform overturning. He also saw that viscosity (not accounted for by Poisson) would prevent true discontinuities. Earnshaw (1860) and Riemann (1860) cleaned up plane waves in lossless gases. However, how to predict propagation after shocks form? Rankine (1870) and Hugoniot (1887, 1889) provided the first solutions for propagation when dissipation is included. These were the first steps toward redemption. The curtain rang down on this era of nonlinear acoustics with the excellent papers in 1910 by Rayleigh and Taylor on steady shocks in a thermoviscous fluid.

A method to predict the effect of nonlinearity on the power spectral density of a plane wave traveling in a thermoviscous fluid is presented. As opposed to time-domain methods, the method presented here is based directly on the power spectral density of the signal, not the signal itself. The Burgers equation is employed for the mathematical description of the combined effects of nonlinearity and dissipation. The Burgers equation is transformed into an infinite set of linear equations that describe the evolution of the joint moments of the signal. A method for solving this system of equations is presented. Only a finite number of equations is appropriately selected and solved by numerical means. For the method to be applied all appropriate joint moments must be known at the source. If the source condition has Gaussian characteristics (it is a Gaussian noise signal or a Gaussian stationary and ergodic stochastic process), then all the joint moments can be computed from the power spectral density of the signal at the source. Numerical results from the presented method are shown to be in good agreement with known analytical solutions in the preshock region for two benchmark cases: (i) sinusoidal source signal and (ii) a Gaussian stochastic process as the source condition.

A variety of methods exist to help students master material in their acoustics courses. The method chosen depends a great deal on the course. In the graduate acoustics courses at UT Austin the methods include system identification and design projects in the course on acoustical transducers, measurements, and data analysis in the courses on architectural acoustics and ultrasonics, development of computer codes based on the sonar equation in the course on underwater acoustics, and a project usually requiring literature review in the course on nonlinear acoustics. Homework problems is the method of choice for the two-semester basic course on physical acoustics, because mastery of the fundamental principles of acoustics requires students to immerse themselves in the details specific to each particular topic. Learning basic acoustics is a lot like learning calculus: one learns by doing. This presentation discusses the philosophy behind creation of the homework problems that appear in the textbook Fundamentals ...

A new method termed Directive Line Source Model (DLSM) is presented for predicting the diffracted field produced by a sound wave incident on a rigid or pressure release half plane. In the new method the edge of the half plane is modeled as an infinite set of directive point sources continuously distributed along the edge. Because DLSM is fast, simple and intuitive, it is a promising tool for the study of diffraction. It can be applied for several types of incident radiation: omnidirectional cylindrical and spherical waves, plane waves, as well as waves from directional sources. Wedges may also be treated. Finally, DLSM can handle diffraction by an arbitrarily shaped edge profile, for example, a half plane having an edge that is jagged instead of straight. Results for plane, cylindrical and spherical incident waves, as well as for arrays of line and point sources, are presented and their agreement with known analytical solutions is demonstrated. Predictions based on DLSM compare favorably with experimental data.

Diffraction by a circular aperture or disk having a ragged edge is investigated. Theory and measurements are reported. The ragged edge is modeled as N arcs, of differing radii a(i), each of which contributes a scattered signal to the edge wave on axis behind the aperture or disk. The amplitude of each scattered signal is proportional to the angle of the arc, and the corresponding time delay is square root of [(ai)2 + (s0)2/c0], where s0 is the axial distance from the aperture plane and c0 is the sound speed. Kirchhoff theory is used to make the calculation. A formula is derived for the rms pressure of the edge wave in terms of the rms pressure and autocorrelation function of the incident wave. The formula can be evaluated for incident waves that are sinusoidal, random (e.g., noise), or transient. Predictions agree reasonably well with underwater measurements made with a spark-generated pulse incident on various apertures. The main result is that making the edge ragged reduces the rms pressure of the edge wave. Indeed, an edge profile is presented that, for a given frequency and axial observation point, eliminates the edge wave completely.

The Harvard Underwater Sound Laboratory (HUSL) began in June 1941, six months before Pearl Harbor, and closed on January 31, 1946. HUSL was directed throughout its existence by (then) Assoc. Prof. Frederick V. Hunt, who incidentally coined the acronym sonar. This paper traces several contributions HUSL made to undersea warfare through exploitation of underwater acoustics. Especially significant were developments by HUSL in sonar and underwater ordnance (torpedoes). Both developments were supported by numerous subprojects on a wide range of applications such as reverberation suppression, Doppler enhancement, and torpedo transducer design. Particular attention is paid to work on air-dropped and submarine-launched acoustic homing torpedoes. HUSL’s far-reaching influence continues to be evident in today’s sonar and torpedo systems. Closure of HUSL spawned Penn State’s Ordnance Research Laboratory (now Applied Research Laboratory) and enriched sonar development at the US Navy Underwater Sound Laboratory, New London. Moreover, HUSL personnel returning to the University of Texas soon founded the Defense Research Laboratory (now Applied Research Laboratories) at Texas. We pay particular homage to living HUSL alumnus A. Wilson Nolle, who, along with our recently departed colleague, Reuben Wallace, and 12 other deceased alumni, had come to HUSL from the University of Texas.

A model experiment to study the effect of atmospheric turbulence on sonic booms is reported. The model sonic booms are N waves produced by electric sparks, and the model turbulence is created by a plane jet. Of particular interest are the changes in waveform, peak pressure, and rise time of the model N waves after they have passed through the model turbulence. A review is first given of previous experiments on the effect of turbulence on both sonic booms and model N waves. This experiment was designed so that the scale factor (approximately 10−4) relating the characteristic length scales of the model turbulence to those of atmospheric turbulence is the same as that relating the model N waves to sonic booms. Most of the results reported are for plane waves. Sets of 100 or 200 pressure waveforms were recorded, for both quiet and turbulent air, and analyzed. Sample waveforms, scatter plots of peak pressure and rise time, histograms, and cumulative probability distributions are given. Results are as follows: (1) The model experiment successfully simulates sonic boom propagation through the atmosphere. The waveform distortion of actual sonic booms is reproduced, both in scale and in character, in the laboratory study. (2) Passage through turbulence almost always causes rise time to increase; decreases are rare. (3) Average rise time is always increased by turbulence, threefold for the particular data reported here. (4) Average peak pressure is always decreased by turbulence, but the change is not as striking as that for average rise time.

An experimental investigation of the focusing of intense, airborne pressure pulses by an ellipsoidal reflector is reported. Short-duration N waves were generated by weak sparks at the near focus F1 of four different prolate ellipsoidal surfaces. Reflection then concentrated the rays at the far focus F2. Measurements were made with a wide-band microphone, primarily along the axis of the reflector. A few transverse measurements in the plane of F2 were also made. In the axial measurements the reflected (upright N wave) and edge-diffracted (inverted N wave) components of the signal are distinct at points distant from F2, approach each other as the focus is neared, and merge at the focus. At the focus the waveform is U-shaped, or cusped. Beyond F2 a “droopy” N wave emerges and, where the edge wave can be resolved, it now arrives first and is phase inverted relative to its prefocal version. The more intense reflected wave does not experience phase inversion. Some features of the observed waveforms are consisten...

Sound generally reaches the shadow zone behind a noise barrier by diffraction, or scattering, from the edge at the top of the barrier. By redirecting the incident sound into the shadow zone, the edge acts as a line source. For the traditional straight-edge barrier, the line source is coherent. Since a crooked line source is less coherent, we propose to improve barrier performance by making the edge randomly jagged. Laboratory model experiments to compare insertion loss of straight- and jagged-edge barriers are reported here. A spark was used as a point source, the barriers were thin (compared to a wavelength), and ground and meteorological effects were not important. After preliminary measurements showed that a jagged edge can produce significantly more insertion loss at high frequency, a three level full factorial experiment was done. The results led to an empirical equation for insertion loss of a jagged-edge barrier. Improvement over the straight barrier was found to increase with jaggedness. An unexplained result was the poorer performance of the jagged-edge barrier at low frequency.

In water, the inertial collapse of a bubble is more violent after expansion by a negative acoustic pressure pulse than when directly compressed by a positive pulse of equal amplitude and duration. In tissues, gas bodies may be limited in their ability to expand and, therefore, the relatively strong effectiveness of negative pressure excursions may be tempered. To determine the relative effectiveness of positive and negative pressure pulses in vivo, the mortality rate of Drosophila larvae was determined as a function of exposure to microsecond length, nearly unipolar, positive and negative pressure pulses. Air-filled tracheae in the larvae serve as biological models of small, constrained bubbles. Death from exposure to ultrasound has previously been correlated with the presence of air in the respiratory system. The degree of hemorrhage in murine lung was also compared using positive and negative pulses. The high sensitivity of lung to exposure to ultrasound also depends on its gas content. The mammalian lung is much more complex than the respiratory system of insect larvae and, at the present time, it is not clear that acoustic cavitation is the physical mechanism for hemorrhage. A spark from an electrohydraulic lithotripter was used to produce a spherically diverging positive pulse. An isolated negative pulse was generated by reflection of the lithotripter pulse from a pressure release interface. Pulse amplitudes ranging from 1 to 5 MPa were obtained by changing the proximity of the source to the biological target. For both biological effects, the positive pulse was found to be at least as damaging as the negative pulse at comparable temporal peak pressure levels. These observations may be relevant to an evaluation of the mechanical index (MI) as an exposure parameter for tissues including lung since MI currently is defined in terms of the magnitude of the negative pressure in the ultrasound field.

A numerical exercise to compare computer codes for the propagation of sonic booms through idealized atmospheres is reported. Ground waveforms are calculated using four different codes or algorithms: (1) weak shock theory, an analytical prediction; (2) SHOCKN, a mixed time and frequency domain code developed at the University of Mississippi; (3) ZEPHYRUS, another mixed time and frequency code developed at the University of Texas; and (4) THOR, a pure time domain code recently developed at the University of Texas. The codes are described and their differences noted. They are then used to calculate propagation for two different source waveforms, for both a uniform and isothermal (varying density) atmosphere, with and without the presence of molecular relaxation. In all cases the results of THOR, SHOCKN, and ZEPHYRUS are in excellent agreement. Because the weak shock theory algorithm does not include the effect of ordinary absorption, it does not predict the shock structure provided by the other codes. This leads to discrepancies particularly for an atmosphere that includes relaxation effects.

A time‐domain computer algorithm that solves an augmented Burgers equation is described. The algorithm is a modification of the time‐domain code developed by Lee and Hamilton [J. Acoust. Soc. Am. 97, 906–917 (1995)] for pulsed finite‐amplitude sound beams in homogeneous, thermoviscous fluids. In the present paper, effects of nonlinearity, absorption and dispersion (both thermoviscous and relaxational), geometrical spreading, and inhomogeneity of the medium are taken into account. The novel feature of the code is that effects of absorption and dispersion due to multiple relaxation phenomena are included with calculations performed exclusively in the time domain. Numerical results are compared with an analytic solution for a plane step shock in a monorelaxing fluid, and with frequency‐domain calculations for a plane harmonic wave in a thermoviscous, monorelaxing fluid. The algorithm is also used to solve an augmented KZK equation that accounts for nonlinearity, thermoviscous absorption, relaxation, and diffraction in directive sound beams. Calculations are presented which demonstrate the effect of relaxation on the propagation of a pulsed, diffracting, finite‐amplitude sound beam.

An underwater bubble is well known to grow in response to a strong negative acoustic pulse and then collapse because of inertial forces. Here it is shown that adding an auxiliary positive pulse after collapse begins intensifies the collapse. The negative‐then‐positive pulse sequence is produced by two ellipsoidal reflectors, each with an electrical spark at its near focus f1 and beamed so that they share a common second focus f2. The negative pulse is produced by a polyurethane (pressure release) ellipsoid, the positive by a brass (rigid) ellipsoid. A timing circuit controls the delay between the pulses. Cavitation is recorded by pitting (caused by bubble collapse) of an aluminum foil membrane, which is centered at f2 and lies coplanar with the two crossed beams. When the brass reflector is fired alone, a narrow path of ∼1‐mm diameter pits appears. Firing the polyurethane reflector alone yields more widespread, ∼0.1‐mm diameter pits. When both are fired, a pitted X pattern shows the position of the two be...

Except for a review article on radiation pressure [Am. J. Phys. (1950)], Robert T. Beyer’s earliest research in nonlinear acoustics was on the increase of absorption with intensity for water and other liquids [J. Acoust. Soc. Am. (1956) (1957), and Sov. Phys.–Acoustics (1958)]. New directions soon followed: the experimental work on the parametric array [Belli et al., J. Acoust. Soc. Am. (1960) (A)], the Keck–Beyer perturbation solution for finite‐amplitude waves in a viscous liquid [Phys. Fluids (1960)], and calculation of the parameter of nonlinearity B/A [J. Acoust. Soc. Am. (1960)]. Continuation and expansion of the latter work made Bob the foremost authority on B/A. Later interests include nonlinear effects in the field of a piston radiator [Ryan et al., J. Acoust. Soc. Am. (1962)], finite‐amplitude propagation in a relaxing fluid, self‐demodulation of a pulse [Moffett et al., J. Acoust. Soc. Am. (1970, 1971)], and various aspects of the crossed beams problem [J. Acoust. Soc. Am. (1970–1982)]. To these specific contributions must be added Beyer’s book Nonlinear Acoustics and several review articles in handbooks and journals.

Burgers’ equation is used to predict the effect of nonlinearity on the power spectral density of plane broadband noise traveling in a nondispersive thermoviscous fluid. The source signal is assumed to be stationary Gaussian noise, which, because of nonlinear propagation distortion, becomes non‐Gaussian as it travels. As opposed to time‐domain methods, the method presented here is based directly on the power spectral density of the signal, not the signal itself. The Burgers equation is transformed into an unclosed set of linear equations that describe the evolution of the joint moments of the signal. A method for solving the system of equations is presented. Only the evolution of appropriately selected joint moments needs to be calculated in order to predict the evolution of the power spectral density of the signal. The results are in good agreement with a time‐domain code [Cleveland et al., J. Acoust. Soc. Am. 98, 2865(A) (1995)]. The method can be also applied when the source condition is a stationary, e...

F. V. Hunt’s ONR-supported acoustics lab at Harvard turned out 30 PhD graduates after WW II. As one of those students in the late 1950s, I gradually became aware that Hunt had had a prewar group of graduate students as well. Leo Beranek was Hunt's first Ph.D., Dah-You Maa his second (both in 1940). Maa’s two 1939 JASA articles on room acoustics, one coauthored with Beranek and Hunt, were benchmark papers of the day. I became fascinated with Maa’s story, partly because he seemed so completely unreachable. He had returned to China during the war; afterward the Cold War intervened. I finally met my much older academic brother in 1980, at the 10th ICA in Sydney, Australia. Thus began a warm and rewarding relationship. In 1987, he began representing China on the International Commission on Acoustics, and for 7 years, we saw each other annually at Commission meetings. I learned of his work on nonlinear standing waves, a problem in which I too shared a keen interest. The high point was at the 14th ICA in Beijing...

This Letter is an extension of an earlier Letter by Bass et al., ‘‘Atmospheric absorption of sound: Update’’ [J. Acoust. Soc. Am. 88, 2019–2021 (1990)]. Errors in a formula for saturation vapor pressure are corrected, and an alternative, much simpler formula is given. The role of atmospheric pressure is emphasized by giving formulas in which the absorption, frequency, and relative humidity are all scaled with respect to atmospheric pressure. Also presented are new, more readable and useful figures showing atmospheric absorption as a function of frequency, relative humidity, and atmospheric pressure. The new figures make it possible to estimate accurately the absorption at any value of atmospheric pressure.

The International Symposia on Nonlinear Acoustics, now referred to as ISNA, have convened regularly since 1968, bringing together scientists and engineers to report and discuss the latest developments in this branch of nonlinear physics. The fact that this series of symposia is still going strong after more than four decades is testimony that nonlinear acoustics has established itself as a distinct, important, and vibrant field of research. In this paper we take a look back at the early years of ISNA to recall how it all began and trace the evolution of the symposia into their current form.

The phrase “Once nonlinear, always nonlinear” is attributed to David F. Pernet. In the 1970s he noticed that nonlinearly generated higher harmonic components (both tones and noise) don’t decay as small signals, no matter how far the wave propagates. Despite being out of step with the then widespread notion that small‐signal behavior is restored in “old age,” Pernet’s view is supported by the Burgers‐equation solutions of the early 1960s. For a plane wave from a sinusoidally vibrating source in a thermoviscous fluid, the old‐age decay of the nth harmonic is e−nαx, not e−n2αx (small‐signal expectation), where α is the absorption coefficient at the fundamental frequency f and x is propagation distance. Moreover, for spherical waves (r the distance) the harmonic diminishes as e−nαx/rn, not e−n2αx/r. While not new, these results have special application to aircraft noise propagation, since the large propagation distances of interest imply old age. The virtual source model may be used to explain the “anomalous”...

Murray Strasberg held several different offices in the Acoustical Society: Executive Council Member 1969–1972, President 1974–1975, and Secretary 1987–1990. The Society was very fortunate to have Murray at its helm in 1974–1975. Wallace Waterfall died early in Murray's term. ASA old timers remember Wallace as the man who “ran the Acoustical Society out of his hip pocket” for years and years. How were we going to get along without him? Murray led us painstakingly through the difficult reorganization. Also up was the Standards issue. ASA decided to write and publish its own acoustical standards rather than leave them to other organizations. Finally, the recent birth of INCE had sadly led to turf wars, which had to be dealt with. Several years later, long after most presidents have happily gone out to pasture, Murray again stepped up, in this case to fill the void caused by Betty Goodfriend's retirement as ASA Secretary. Murray served as ASA's last Secretary. Beyond his splendid service to the Acoustical Society, Murray was a renowned acoustical scientist and, perhaps above all, a warm and generous friend.

The most common lithotripter, a Dornier HM-3, utilizes an underwater spark to generate an acoustic pulse and a rigid ellipsoidal reflector to focus the pulse on the kidney stone to be comminuted. The pulse measured in water with a PVDF membrane hydrophone at the external focus of the ellipsoid was a 1-microsecond positive-pressure spike followed by a 3-microsecond negative-pressure trough. When we replaced the rigid reflector in our experimental lithotripter with a pressure-release reflector, the pulse was a 1.6-microsecond trough followed by a 0.6-microsecond positive spike. The waveforms are nearly time inverses (i.e., their spikes and troughs are reversed). The frequency spectra, the maximum peak positive pressures P+ (42 MPa, rigid and 43 MPa, pressure-release), and the maximum peak negative pressures P- (-12 MPa and -14 MPa) are comparable. The maximum P- occurred 20 mm closer to the reflector than did the maximum P+, for both reflectors. However, the spatial maxima of the peak pressures (P+ and P-) produced by the pressure-release reflector were located 20 mm nearer to the reflector than those produced by the rigid reflector. Qualitative explanation of the waveforms and the location of pressure maxima as well as comparison to previous theoretical and experimental results is given. The alternate waveform produced by the pressure-release reflector may be a tool in determining the role of cavitation in lithotripsy because cavitation is highly sensitive to waveform.

Dramatically different cavitation was produced by two separate acoustic pulses that had different shapes but similar duration, frequency content, and peak positive and negative pressure. Both pulses were produced by a Dornier HM-3 style lithotripter: one pulse when the ellipsoidal reflector was rigid, the other when the reflector was pressure release. The cavitation, or bubble action, generated by the conventional rigid-reflector pulse was nearly 50 times longer lived and 3-13 times stronger than that produced by the pressure-release-reflector pulse. Cavitation durations measured by passive acoustic detection and high-speed video agreed with calculations based on the Gilmore equation. Cavitation intensity, or destructive potential, was judged (1) experimentally by the size of pits in aluminum foil detectors and (2) numerically by the calculated amplitude of the shock wave emitted by a collapsing bubble. The results indicate that the trailing positive spike in the pressure-release-reflector waveform stifles bubble growth and mitigates the collapse, whereas the trough after the positive spike in the rigid-reflector waveform triggers inertially driven growth and collapse. The two reflectors therefore provide a tool to compare effects in weakly and strongly cavitating fields and thereby help assess cavitation's role in lithotripsy.

A model experiment was reported to be successful in simulating the propagation of sonic booms through a turbulent atmosphere [B. Lipkens and D. T. Blackstock, J. Acoust. Soc. Am. 103, 148–158 (1998)]. In this study the effect on N wave characteristics of turbulence intensity and propagation distance through turbulence are investigated. The main parameters of interest are the rise time and the peak pressure. The effect of turbulence intensity and propagation distance is to flatten the rise time and peak pressure distributions. Rise time and peak pressure distributions always have positive skewness after propagation through turbulence. Average rise time grows with turbulence intensity and propagation distance. The scattering of rise time data is one-sided, i.e., rise times are almost always increased by turbulence. Average peak pressure decreases slowly with turbulence intensity and propagation distance. For the reported data a threefold increase in average rise time is observed and a maximum decrease of about 20% in average peak pressure. Rise times more than ten times that of the no-turbulence value are observed. At most, the maximum peak pressure doubles after propagation through turbulence, and the minimum peak pressure values are about one-half the no-turbulence values. Rounded waveforms are always more common than peaked waveforms.

The radiation of finite-amplitude waves from the open end of a baffled, circular pipe is considered as a direct continuation of work begun by Kuhn, Blackstock, and Wright more than three decades ago [Kuhn et al., J. Acoust. Soc. Am. 63, S1, S84 (1978)]. In this paper, a 1 kHz sinusoidal pulse with initial peak pressure amplitude of nearly 1.2 kPa has been propagated down a 6.1 m pipe, whose open end (5.1 cm inner diameter) has been placed off-center in a large rectangular baffle. As the steepened or shock-like waves exit the pipe, the measured waveforms are comprised of sharp impulses that are delta function-like in nature, particularly on axis. Although linear piston theory predicts similar waveform shapes, there is also evidence that nonlinear propagation of these impulses, which exceed a peak pressure amplitude of 1.5 kPa near the pipe opening, is occurring. http://asadl.org/jasa/resource/1/jasman/v63/iS1/pS84_s5

Research on nonlinear acoustics has been performed during the 12- month period ending 30 September 1993. The following projects were completed. (1) Propagation in a periodic waveguide (2) Finite-amplitude propagation in a medium having a distribution of relaxation processes (3) Production of an isolated negative pulse in water Public communication of the research was accomplished through three theses, four oral papers, one journal article published, four journal articles submitted, and one paper in a symposium proceedings. Nonlinear acoustics, Relaxing media, Unipolar negative pulse, Generalized Burgers' equation, Bloch waves, Diffraction, Dispersion. Periodic waveguide, Temperature rise due to absorption

While graduate study in acoustics takes place in several colleges and schools at the University of Texas at Austin (UT Austin), including Communication, Fine Arts, Geosciences, and Natural Sciences, this presentation focuses on the acoustics program in Engineering. The core of this program resides in the Departments of Mechanical Engineering (ME) and Electrical and Computer Engineering (ECE). Acoustics faculty in each department supervise graduate students in both departments. One undergraduate and seven graduate acoustics courses are cross‐listed between ME and ECE. Instructors for these courses include staff at Applied Research Laboratories at UT Austin, where many of the graduate students in acoustics hold research assistantships. The undergraduate course, offered every fall, begins with basic physical acoustics and proceeds to draw examples from different areas of engineering acoustics. Three of the graduate courses are offered every year, a two‐course sequence on physical acoustics and a course on ac...

As an academic discipline at the University of Texas, acoustics began in the 1930s under C. Paul Boner in Physics and Lloyd A. Jeffress in Psychology. World War II saw Boner and many physics graduate students go to Harvard for “war work,” largely in underwater acoustics. When the war ended, Boner returned and founded the Defense Research Laboratory, later named Applied Research Laboratories. Interest in acoustics grew in Physics during the postwar years but eventually waned in the 1950s and 1960s. Acoustical activity developed in the 1960s in the College of Engineering, chiefly Electrical Engineering and Mechanical Engineering. Today physical and engineering acoustics is a strong interdisciplinary program at Texas, with faculty in several departments in Engineering and still a vestige in Physics. In addition, much work on speech, hearing, and music is done in other parts of the University. Engineering features two basic courses in physical acoustics, Acoustics I and II, and five specialty courses, which a...

Mack Breazeale received a Ph.D. degree in physics at Michigan State University in 1957. He was one of 19 doctoral students supervised by Egon A. Hiedemann, who headed a very active group in ultrasonics at Michigan State in the 1950s and 1960s. Mack’s period there, 1954–1961, is reviewed and also the history of the Hiedemann group, which was well known for its contributions to physical acoustics. A particular interest in optical measurement of ultrasonic waves led to many theses and papers in nonlinear acoustics, at that time just beginning to enjoy a renaissance. Among those who, like Mack, went on to have very active roles in the Acoustical Society of America were Laszlo Adler, Bill Cook, Logan Hargrove, and Walter Mayer.

This review covers the period from 1960 to about the mid‐1970s. Westervelt presented his theory of the parametric array at the June 1960 Acoustical Society Meeting, held at Brown Univ. In the same session, Bellin and Beyer reported experimental confirmation, primarily for the array in water. Despite the tantalizing properties of the parametric array—narrow low‐frequency beam produced with a small source, absence of sidelobes, and potentially broadband operation—the acoustical community at first paid little attention. Berktay woke us up with a series of papers in the mid‐to‐late 1960s on possible applications. Interest in underwater parametric arrays then exploded, including attempts to make parametric receiving arrays practical. Definitive experimental confirmation of the parametric array in air was finally reported in 1973. However, practical applications of the airborne array did not appear until many years later.

Considered here are three topics in atmospheric acoustics, studied by North American scientists during the 75‐year span between the Civil War and World War II. First, in 1865 Joseph Henry (1799–1878), as a member of the Light‐House Board, began to investigate fog signaling. His experiments, carried on in friendly competition with John Tyndall in England, added a great deal to our practical knowledge of atmospheric refraction. Second, the first‐ever experiments to measure the absorption of sound in the atmosphere were carried out by A. Wilbur Duff (1864–1951) in New Brunswick, Canada, in 1898 and in 1900. The failure of viscosity and heat conduction to account for the measured absorption prompted Lord Rayleigh to postulate that a relaxation mechanism in the air might be responsible for the difference. Finally, George Washington Pierce (1872–1956), who is perhaps best known for his work on piezoelectric and magnetostrictive devices, used an acoustic interferometer to measure dispersion in gases, particularly carbon dioxide. He also measured sound transmission over reflective surfaces. His results confirm the at‐first surprising result that at grazing incidence even a very hard boundary seems to act as a pressure release surface.

From 1946 to 1971, 30 Harvard Ph.D. degrees were earned in F. V. (Ted) Hunt’s Acoustics Research Laboratory. Although Hunt was on my committee, and I’ll always consider myself one of ‘‘Hunt’s boys,’’ William P. Raney was my Ph.D. (Harvard, 1960) supervisor. My direct ancestral line thus begins with Raney, who did his doctoral research at Brown University (Ph.D. 1955) under Peter J. Westervelt. The lineage going further down the tree is as follows: Westervelt (MIT, 1951), Richard H. Bolt (UCLA, 1939), Vern O. Knudsen (University of Chicago, 1922), Robert A. Millikan (Columbia, 1895), Michael I. Pupin (Berlin, 1887), Hermann von Helmholtz (Berlin, medicine, 1842). Now go up the tree. I had two Ph.D. students at the University of Rochester, Donald B. Cruikshank (1968) and James C. Lockwood (1971). My first Ph.D. graduate from the University of Texas at Austin was F. Michael Pestorius (1973); eight younger siblings followed. A bonus was being stepfather for Mark F. Hamilton (Penn State, 1983) when his Penn St...

Does the professor teach his/her students? Or do they teach the professor? While the answer to both questions is probably a qualified yes, in looking back, I see that what I know now is largely what they taught me. After a review of the research areas in which my students and I have worked, a few examples are highlighted that show that what I had expected is not how things turned out.

HIFU and harmonic imaging are hallmarks of present day biomedical ultrasound. But it wasn’t always this way. At one time linear theory ruled supreme. Although by the early 1970s nonlinear acoustics had made its way into many areas of acoustics, e.g., physical acoustics, underwater sound, and aeroacoustics, biomedical ultrasound remained a safe haven for small‐signalists. Ed Carstensen changed all that. By the mid‐1970s he realized that linear theory could not account for certain phenomena he observed. At the 1978 Allerton Conference his invited talk entitled ‘‘Nonlinear Aspects of Ultrasonic Absorption’’ may have been the first public disclosure that nonlinear effects are important in biomedical ultrasound. His first archival work appeared as two papers in 1980; Tom Muir was a coauthor for both. During the next decade Ed and a series of colleagues showed that absorption could easily be dominated by nonlinear propagation effects. In turn the increased absorption causes increased heating, an important practical application. Ed’s pioneering work paved the way for many of the well‐known applications today.

In 1950 Clayton H. Allen (1918–2004) discovered nonlinear acoustic saturation. His Penn State doctoral thesis, ‘‘Finite Amplitude Distortion in a Spherically Diverging Sound Wave in Air,’’ is about experiments on intense sound produced by a 12.2‐cm diameter baffled piston vibrating at 14.6 kHz. At r=3.8 cm (the next‐to‐last nearfield peak) the maximum SPL produced was 161 dB (re 20 μPa). The farfield began at about 50 cm. Measurements were made of the fundamental and 2nd–6th harmonics out to r=200 cm. His received level versus source level curves at r=200 cm show the now familiar plateau that is reached as nonlinear effects limit the achievable SPL for a given distance at a given frequency. Clay’s discovery is quite remarkable because (1) it was totally unexpected and (2) it came long before any theoretical predictions of the phenomenon were developed. Alas, however, the work was never published except in the Army Signal Corps report from Penn State, ‘‘Atmospheric Physics and Sound Propagation, Final Report for Period July 1, 1945 to May 20, 1950,’’ and in two papers presented orally at the Penn State ASA Meeting in June 1950. As a result, Clay’s remarkable work has gone unappreciated for many years. This presentation is dedicated to his memory.

The distinguishing feature of a shock wave is its practically instantaneous rise in pressure. Its laws of propagation are different from those for ordinary, continuous‐waveform sound waves, even when the sound wave amplitude is finite. The Rankine–Hugoniot shock relations connect the properties on either side of the shock, e.g., pressure, density, and particle velocity, with the shock velocity or Mach number. These relations are valid even for unsteady shocks, e.g., growing or decaying shocks. Weak shock theory provides a means of predicting the propagation of most steady and unsteady shocks that are encountered in acoustics, including those used in medicine. For example, in lithotripsy the focal pressure amplitude rarely exceeds 100 MPa; for such a shock the shock velocity is only ∼8% greater than the sound speed in water. Shock rise time τrise is an interesting property of shocks but often difficult to measure. For example, if the lithotripsy shock cited above was steady and in water, its rise time would be a few tens of picoseconds. When the shock is unsteady, τrise is much harder to predict.

Bradford Sturtevant (1933–2000) spent his entire academic career in the Graduate Aeronautical Labs at Caltech (GALCIT). He was a distinguished and internationally respected member of the fluid mechanics community, known particularly for his research on shock waves. Although a member of the Acoustical Society since 1974, he rarely if ever published in JASA. Nevertheless, his contributions to acoustics, mainly in what we think of as nonlinear acoustics although he probably saw them simply as part of fluid mechanics, are significant. Examples are: shock focusing, nonlinear resonance in closed‐ and open‐end tubes, sonic booms, and propagation of weak shocks through a random medium. In the late 1980s he became interested in lithotripsy. When Andrew Evan (Indiana University School of Medicine) organized a multidisciplinary consortium to solve many of the mysteries of lithotripsy, it is not surprising that Brad was picked for his expertise on shock waves and his interest in shock waves in the body. The research effort that ensued, now in its eighth year, owes much to the work of Brad and his students and to his counsel. Brad was especially concerned about the mechanism(s) by which stone breakup occurs.

A laboratory model experiment to study the effect of turbulence on waveform and rise time of sonic booms has previously been reported [B. Lipkens and D. T. Blackstock, J. Acoust. Soc. Am. 90, 2307(A) (1991)]. Electric sparks produce the N waves, which then propagate through turbulence generated by a plane jet. Downscaling of the model turbulence from atmospheric turbulence was designed to match downscaling of the model N wave (in terms of duration and rise time) from the sonic boom. Reported here are hot wire anemometry measurements of the jet, which confirm that the turbulence characteristics are indeed those of a classical plane jet. The measured values of the integral length scale, Taylor microscale, and Kolmogorov microscale show that the desired downscaling from atmospheric turbulence was achieved. Also reported are measurements that show how rise time and wave shape distortion vary with propagation distance through the jet, turbulence intensity, and peak amplitude of the N wave. [Work supported by N...

This Letter is primarily in response to the Letter to the Editor by G. M. Tarkenton entitled ‘‘Remarks on ‘On the coefficient of nonlinearity β in nonlinear acoustics’ ’’ [J. Acoust. Soc. Am. 88, XXXX–XXXX (1990)]. It is reaffirmed that for progressive plane waves, the momentum equation contributes nothing at second order to the expressions for the coefficient of nonlinearity and finite amplitude propagation speed.

Sonic boom propagation is strongly affected by atmospheric turbulence. It has been shown that turbulence affects the perceived loudness of sonic booms, mainly by changing its peak pressure and rise time. The models reported here describe the nonlinear propagation of sound through turbulence. The turbulence is modeled as a set of individual realizations of a random temperature or velocity field. In the first model, linear geometric acoustics is used to trace rays through each realization of the turbulent field. A nonlinear transport equation is then derived along each eigenray connecting the source and receiver. The transport equation is solved by a Pestorius algorithm. In the second model, the KZK equation is modified to account for the effect of a random temperature field and it is then solved numerically. Results show that, on average, turbulence decreases the mean peak pressure and increases the rise time. Nonlinear distortion is less when turbulence is present than without it. The geometric acoustics results indicated that the effects of random vectorial fields are stronger than those of random temperature fields. The location of the caustics and the deformation of the wavefront are also presented. [Work supported by a grant from NASA.]

Experimental, numerical, and analytical investigations have shown that noise barrier performance can be improved by making the top edge randomly jagged. The incident noise is a spherical N wave (produced by a spark in our model experiments). See Ho et al. [J. Acoust. Soc. Am. 101, 2669–2676 (1997)], and oral papers by (i) Menounou et al., (ii) Ohm et al., and (iii) Rosenberg et al., all in J. Acoust. Soc. Am. 101, 3075(A) (1997). In many, but not all, cases the jagged edge improves insertion loss by up to 5 dB. The most promising theoretical approach is to model the edge as a directive, crooked line source [paper (i) above]. Besides yielding predictions that agree favorably with measurements [paper (iii) above], the line source model helps in understanding the following results: (1) the jagged edge smears out the diffracted signal and makes the tail ragged, (2) insertion loss varies significantly with receiver position, and (3) the portion of the edge on the most direct path between source and receiver plays a very important role. Because the model is easy to apply, it is a promising and powerful tool for further research on jagged barriers. [Work supported by Texas Advanced Technology Program.]