Sonic Bangs Research Articles

Plant Steaming Concrete Staining

Seed Scarification: Serious Taking is a light, seed, and sound installation. Few hours after the activation of the installation in an art venue, an unplanned kinetic event takes place that is marked by a sonic loud bang. At an instance creating a division in time: one segment that spans the moment before the event; the second one being the perceived change of the aftermath. A composed photo blends both moments into a fictitious here and now. This happening is discussed in this essay from a primarily experiential stance, focusing on air, atmosphere and being.

Uniform formulation of the problem of distortion of sonic booms or bangs by atmospheric turbulence

A now-classic paper relating to wave propagation through turbulence is S. C. Crow's “Distortion of sonic bangs by atmospheric turbulence” [J. Fluid Mech. 37, 529–563 (1969)]. Crow treats the linear acoustics problem of an (initially) step discontinuity in pressure (weak shock} propagating through a nominally uniform atmosphere with weak turbulence superimposed, uses a first-order perturbation theory to determine the turbulence-induced corrections to the waveform, and obtains some simple predictions concerning the variance at times somewhat later than shock onset, which have subsequently been well confirmed by field data. The singular nature of Crow's solution near the nominal time of shock onset, however, has always been somewhat disquieting to the present author, so a formulation is here given that avoids this singularity using a version of the method of strained coordinates. The recently derived approximate wave equation [Pierce, J. Acoust. Soc. Am. (in press)] for wave propagation through a fluid with inhomogeneous unsteady flow is used as a starting point. The solution for the acoustic pressure is taken in the form of a rippled wavefront (Δp)(1 + ψ)H(1 − c−1x + φ), where φ is a function of position, while ψ is a function of position and time. Here, H(t) is the Heaviside unit step function and Δp is the nominal pressure jump at the start of the boom. Linear perturbation equations governing the functions φ and ψ are developed and solved by approximate methods. [Work supported by NASA Langley Research Center and by the William E. Leonhard endowment to Pennsylvania State University.]

Sonic bangs

Abstract The article describes the phenomenon of the sonic bang by way of the answers to a series of questions, each of which seeks to uncover a little more about the phenomenon. The questions are: What causes a sonic bang? What determines how many sonic bangs one hears? Why do some observers not hear a bang? Why do some observers hear ‘super-bangs’? What is the waveform of a sonic bang in ideal situations? What is the waveform of a sonic bang in real situations?

Approximation of the perturbation equations of a quasi-linear hyperbolic system in the neighborhood of a bicharacteristic

In 1956 Whitham gave a nonlinear theory for computing the intensity of an acoustic pulse of an arbitrary shape. The theory has been used very successfully in computing the intensity of the sonic bang produced by a supersonic plane. Gubkin (1958) derived an approximate quasi-linear equation for the propagation of a short wave in a compressible medium. These two methods are essentially nonlinear approximations of the perturbation equations of the system of gas-dynamic equations in the neighborhood of a bicharacteristic curve (or rays) for weak unsteady disturbances superimposed on a given steady solution. In this paper we have derived an approximate quasi-linear equation which is an approximation of perturbation equations in the neighborhood of a bicharacteristic curve for a weak pulse governed by a general system of first order quasi-linear partial differential equations in m + 1 independent variables ( t, x 1,…, x m ) and derived Gubkin's result as a particular case when the system of equations consists of the equations of an unsteady motion of a compressible gas. We have also discussed the form of the approximate equation describing the waves propagating upsteam in an arbitrary multidimensional transonic flow.

Characteristic overpressure of a supersonic transport of given length in a homogeneous atmosphere

In recent years many investigations have been made into ways of reducing the pressure jumps across the shock waves resulting from supersonic transports. Lately Warren has stated that a quantity which typifies a sonic bang and in particular with regard to its effect on structures is the characteristic overpressure. The characteristic overpressure is the ratio of four times the running integral of the overpressure to the time interval between the first and last shock in the signature. The work on the pressure jumps across the shock waves and the resulting lower bound values have to be modified when the characteristic overpressure is considered. This note describes a preliminary investigation into methods of obtaining the lower bound values for the characteristic overpressure.

Vibrational relaxation effects in weak shock waves in air and the structure of sonic bangs

Vibrational relaxation of oxygen and nitrogen is shown to be important in determining the structure of weak shock waves in air. Of particular interest are waves with pressure jumps of 100Pa1 Pa ≡ 1 pascal = 1 N m−2. or less which are present in the atmosphere as sonic bangs. It is found that the structure of the waves depends on shock strength, ambient pressure, temperature and humidity.

An estimate of sonic boom damage to large windows

A preliminary estimate, based on statistical data, is made of the likelihood of damage to large windows due to sonic bangs. On the basis of the mean window characteristics calculated from a field survey in Reading, it seems probable that about one large window in ten thousand will be broken by a typical sonic bang. The degree of confidence held for the result obtained cannot at the moment be very high because the effects of a number of the variables are still to be included in the analysis. These variables, listed in the report, are to be evaluated in due course.

The location of the ground focus line produced by a transonically accelerating aircraft

This paper describes the theory of propagation of a sonic bang in a horizontally stratified atmosphere with wind, and the way in which this theory has been utilized to derive a computer program for finding, for an aircraft climbing and accelerating (normally along a straight line ground track), the location of the intersection of the bang wavefront with the ground. The locations of the ground focus line, along which there is a marked enhancement of the bang “overpressure” on the ground, are found for a large range of atmospheric structures. The feasibility of forecasting these locations, and the possibility of defining an area on the ground which would encompass all focus lines for a given flight plan, are also examined.

A Significant Single Quantity that Typifies a Sonic Bang

The paper introduces the concept of the characteristic overpressure, defined as 4I/T, where I is the maximum impulse, that is, the maximum value of the running integral of the overpressure with respect to time, and T is the signature interval, that is, the time interval between the onset of the first shock and the onset of the last shock in the signature. The characteristic overpressure is considered to be a significant quantity, particularly in regard to the effect of sonic bangs on structures. This is illustrated by the collapse that is achieved when the results of Crocker and Hudson are presented in a manner employing the characteristic overpressure. Finally, the characteristic overpressure is shown to lead to a particularly simple engineering formula for the dynamic magnification factor as a function of the product of the natural frequency of a structure and the signature interval.

Real-gas effects in very weak shock waves in the atmosphere and the structure of sonic bangs

An approximate expression is given for the thickness of weak fully dispersed shock waves. Using available data on the thermodynamic properties of air, it is shown that shocks of the strength expected in sonic bangs are fully dispersed. Estimated relaxation times for dry and humid air lead to wide variations in possible thickness, varying from millimetres to metres.

Recent Sonic Bang Studies in the United Kingdom

The paper summarizes the sonic bang studies that have been made in the United Kingdom since 1965, which embrace flight trials, field experiments, and laboratory studies. The main flight trial concerns the measurement of the sonic bang from the Concorde. It is shown that, when flying at 45 000 ft, the Concorde waveform at the ground has attained its fairfield N-waveshape, although this is not quite so when it is flying at 37 000 ft. The measured characteristic overpressures for these two altitudes and a Mach number of 1.3 are 110 N/m2 (2.3 lb/ft2) and 120 N/m2 (2.5 lb/ft2), respectively. The effects of sonic bangs on cathedrals is discussed, and the vibrational responses likely to be induced by the sonic bang are compared with those already arising from other environmental causes. Finally, the results of a study of the effects of simulated sonic bangs on some greenhouses are discussed, which seem to indicate that most damage can be ascribed to a triggering effect.

Recent Sonic-Bang Studies in the United Kingdom

The paper summarizes the sonic-bang studies that have been made in the United Kingdom since 1965, which embrace flight trials, field experiments, and laboratory studies. The main flight trial concerns the measurement of the sonic bang from the Concorde. It is shown that, when the Concorde is flying at 45 000 ft, the waveform at the ground has attained its farfield N-wave shape, although this is not quite so when it is flying at 37 000 ft. The measured characteristic overpressures for these two altitudes and a Mach number of 1.3 are 110 N/m2 and 120 N/m2, respectively. The effects of sonic bangs on cathedrals are discussed and the vibrational responses likely to be induced by the sonic bang are compared with those already arising from other environmental causes. Finally, the results of a study of the effects of simulated sonic bangs on some greenhouses are discussed; these results seem to indicate that most damages can be ascribed to a triggering effect.

Explosively generated air presuure waves for structural forcing

The aerial blast wave generated by a small explosion may be used to produce impulsive forcing of structures with natural periods longer than approximately 1 msec; the free response of such structures may then be determined. A technique has been developed using spatial distributions of explosive whereby it is possible to generate waves of much longer durations and of a much wider range of shapes, so that studies of the forced response of structures are made feasible. The technique has been applied to the generation of a blast waveform of the same shape as that of the sonic bang, for example, thus permitting studies of response to sonic bangs to be carried out without the necessity of flying supersonic aircraft and without recourse to scaled model experiments. Certain differences between the simulated and real sonic bang waveforms raise questions as to the adequacy of the simulant, and criteria for acceptability of simulation are discussed. To provide information relevant to these questions, the Fourier transforms of the simulant waves are compared with those of sonic bangs. The results lend support to the use of the simulants in structural response studies.

Response of Ground Structures to Sonic Loads

Within the last decade, intense low-frequency noise from large rocket boosters and sonic bangs from supersonic aircraft have become a source of significant sonic loading on building structures. Some of the basic principles of loading and response of ground structures to sonic waves are reviewed, including the effects of diffraction on three-dimensional structures, structural-acoustic wave coupling, and vibroacoustic response. Related experimental data obtained during the course of an extensive study of sonic loading on structures is also briefly reviewed for the first time. Some of the characteristics common to sonic loading by acoustic waves, sonic booms, and blast are considered.

Distortion of sonic bangs by atmospheric turbulence

Recorded pressure signatures of supersonic aircraft often show intense, spiky perturbations superimposed on a basicN-shaped pattern. A first-order scattering theory, incorporating both inertial and thermal interactions, is developed to explain the spikes. Scattering from a weak shock is studied first. The solution of the scattering equation is derived as a sum of three terms: a phase shift corresponding to the singularity found by Lighthill; a small local compression or rarefaction; a surface integral over a paraboloid of dependence, whose focus is the observation point and whose directrix is the shock. The solution is found to degenerate at the shock into the result given by ray acoustics, and the surface integral is identified with the scattered waves that make up the spikes. The solution is generalized for arbitrary wave-forms by means of a superposition integral. Eddies in the Kolmogorov inertial subrange are found to be the main source of spikes, and Kolmogorov's similarity theory is used to show that, for almost all timestafter a sonic-bang shock passes an observation point, the mean-square pressure perturbation equals$(\Delta p)^2 (t_c/t)^{\frac{7}{6}}$, where Δpis the pressure jump across the shock andtcis a critical time predicted in terms of meteorological conditions. For an idealized model of the atmospheric boundary layer,tcis calculated to be about 1 ms, a figure consistent with the qualitative data currently available. The mean-square pressure perturbation just behind the shock itself is found to be finite but enormous, according to first-order scattering theory. It is conjectured that a second-order theory might explain the shock thickening that actually occurs.

Acousto-elastic effects in the response of large windows to sonic bangs

Acousto-elastic interaction effects in the response of large windows to sonic bangs have been studied in some detail both theoretically and experimentally. If such a window is backed by a closed cavity the modification to the natural frequency of the fundamental mode, an important parameter, can be estimated with some accuracy. The point of maximum stress stays at the centre of the window, though the fundamental mode shape is considerably modified. However, the maximum stress is reduced as the acoustic stiffness of the room increases provided that resonance effects are not induced by the change in fundamental natural frequency of the system. This latter aspect can be treated separately. Movement of the point of fracture away from the window centre can probably be accounted for by departure from the basic assumption of small displacements. This is to be studied further.

Performing a visual task in the vicinity of reproduced sonic bangs

Recorded sonic bangs accompanied a fast visual task performed by subjects working indoors. The sound pressure levels of the bangs corresponded to the indoor stimulation experienced for outdoor sonic bangs of 0·80 lb/ft 2 to 2·53 lb/ft 2. Performance on the visual task was temporarily impaired when the sonic bangs were at the highest level. This was above the level of loudness set as an upper limit around airports for existing aircraft.

Sonic bang intensities in a stratified, still atmosphere

Formulas for sonic bang intensities in stratified atmospheres are obtained by a combination of geometrical acoustics and the standard procedure for modifying linear theory predictions to take account of non-linear effects. Results are obtained for an aircraft flying at constant velocity and altitude in an atmosphere where the speed of sound decreases linearly from the ground to a certain altitude and then stays constant.

A note on the spectrum analysis of transients and the loudness of sonic bangs

A computer programme has been devised to obtain the Fourier transform of a complex impulsive waveform. The method does not require data at closely or regularly-spaced time intervals, except where the complexity of the transient itself demands it. The programme has been applied to calculations of loudness of sonic bangs based on the theory of Zepler and Harel [1]. Implications of the method are discussed together with those features which specially commend its use.

Lower Bounds for Sonic Bangs in the Far Field

SummaryIn this paper lower bounds are obtained for the intensity of the sonic bang resulting from a slender aircraft flying straight and level at supersonic speeds. The lower bounds are obtained for an aircraft subject to various constraints on its total lift, volume, area distribution and centre-of-pressure position. The work described proves the results quoted in an earlier paper, corrects the results given in that paper for the general configuration, and extends the results to cover more constraints, mainly the centre-of-pressure position.