David T. Blackstock

Atmospheric absorption of sound: Further developments

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.

Connection between the Fay and Fubini Solutions for Plane Sound Waves of Finite Amplitude

Plane, progressive, periodic sound waves of finite amplitude are considered. The well‐known solutions of Fay and Fubini are reviewed. At first glance, the two solutions seem contradictory, but, actually, each holds in a different region of the flow, the Fubini solution close to the source and the Fay solution rather far from the source. In the intermediate, or transition, region, neither solution is valid. A more general solution is obtained by using a method commonly employed for waves containing weak shocks. For distances up to the shock‐formation point, the general solution reduces exactly to the Fubini solution. For distances greater than about 3.5 shock‐formation lengths, the general solution is practically indistinguishable from the sawtooth solution, which, in turn, is the limiting form of Fays solution for strong waves. The form of the general solution shows clearly how, in the transition region, the Fubini solution gives way to the sawtooth solution. The problem of an isolated cycle of an origin...

Time‐domain modeling of finite‐amplitude sound in relaxing fluids

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.

Parametric array in air

An experimental investigation of the parametric array in air was conducted using a circular piston transducer which produced spherically spreading, collinear, primary beams at frequencies of 18.6 and 23.6 kHz. Since source levels were not strong (about 110 dB re 0.0002 μbar at 1 ft), the 5−kHz difference frequency signal generated by the parametric array was relatively weak. Because of space limitations, all measurements were made in the nearfield of the array. Spurious difference frequency signals resulting from intermodulation distortion in the receiving system were suppressed by judicious choice of electronic components and by the addition of an acoustical filter in front of the microphone. The classic properties of the parametric array were observed. The 5−kHz beam was narrow, and no minor lobes were evident. The propagation curve first increased with increasing range, reached a broad maximum, and then gradually decreased. Theoretical predictions were based on a perturbation solution of Burgers’ equat...

Generalized Burgers equation for plane waves

Burgers’ equation, an equation for plane waves of finite amplitude in thermoviscous fluids, is generalized by replacing the thermoviscous term Aut’t’ (A is the thermoviscous coefficient, u particle velocity, and t’ retarded time) with an operator L(u). This operator represents the effect of attenuation and dispersion, even if known only empirically. Specific forms of L(u) are given for thermoviscous fluids, relaxing fluids, and fluids for which viscous and thermal boundary layers are important. A method for specifying L(u) when the attenuation and dispersion properties are known only empirically is described. A perturbation solution of the generalized Burgers equation is carried out to third order. An example is discussed for the case α2=2α1, where α1 and α2 are the small‐signal attenuation coefficients at the fundamental and second‐harmonic frequencies, respectively. The growth/decay curve of the second harmonic component is given both with and without the inclusion of dispersion. Dispersion causes a sma...

Propagation of Plane Sound Waves of Finite Amplitude in Nondissipative Fluids

An extensive theoretical treatment is presented of the problem of plane progressive sound waves (simple waves) produced by continuous, high‐amplitude motion of a piston in a lossless, semi‐infinite tube. The fluid in the tube is assumed to be nondissipative; liquids as well as perfect gases are considered. The analysis is given in both Eulerian and Lagrangian coordinates. Earnshaws exact solution in parametric form is first given for arbitrary piston motion. Special attention is then given to the case of sinusoidal piston motion. Approximate but explicit power‐ and Fourier‐series solutions for this case are derived from the exact solution. A low‐amplitude nonlinear theory of simple waves is proposed. In this theory nonlinear effects are considered in a simple yet general manner.A brief analysis of shock formation is also given. It is shown that the generally accepted formula for the distance at which the shock forms when the piston motion is sinusoidal is rigorously correct only under very special circum...

Propagation of finite amplitude sound through turbulence: Modeling with geometrical acoustics and the parabolic approximation

Sonic boom propagation can be 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. Turbulence is modeled as a set of individual realizations of a random temperature or velocity field. In the first model, linear geometrical 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 from numerical experiments that simulate the propagation of spark-produced N waves through turbulence are presented. It is observed that turbulence decreases, on average, the peak pressure of the N waves and increases the rise time. Nonlinear distortion is less when turbulence is present than without it. The effects of random vector fields are stronger than those of random temperature fields. The location of the caustics and the deformation of the wave front are also presented. These observations confirm the results from the model experiment in which spark-produced N waves are used to simulate sonic boom propagation through a turbulent atmosphere.

COMPARISON OF COMPUTER CODES FOR THE PROPAGATION OF SONIC BOOM WAVEFORMS THROUGH ISOTHERMAL ATMOSPHERES

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 l...

Model experiment to study sonic boom propagation through turbulence. Part I: General results

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: ...

Bioeffects of positive and negative acoustic pressures in vivo.

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.