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Focusing of Finite-Amplitude Cylindrical and Spherical Sound Waves in a Viscous and Heat-Conducting Medium
The focusing of acoustic pulses is studied analytically by considering the region of study in three parts: the converging, interaction and diverging regions. First, the linear problem of a pulse of infinitesimal amplitude is studied. For the spherical case, the expected phase change as a result of focusing is verified. The nonlinear case of finite-amplitude pulses leads to the development of M-waves, as determined by applying the method of matched-asymptotic expansions to Burges equation.
Ionospheric disturbances caused by long period sound waves generated by Saturn-Apollo launches
Wavelike disturbances were observed in the ionosphere following several nuclear explosions in early 1960's. Supersonic shock waves within the atmosphere generated by large rockets can cause ionospheric electron density perturbations. A CW phase path Doppler array in the New York area was operated during the Saturn-Apollo 12 and 13 launches and recorded Doppler frequency fluctuations due to rocket launchings. Cross correlation and power spectral analyses of the phase path-path Doppler frequency variation records showed that the phase velocities of the signal arrivals were from south of the array with 700 - 800 m/sec corresponding to periods in the range of 2 to 4 minutes. Ionograms taken every 60 seconds from Wallops Islands showed clearly ionospheric disturbances due to rockets. The group velocities were estimated to be of the order of 450 m/sec 1 obtained from the earliest visible disturbances seen on CW phase path Doppler records and ionograms together with the rocket trajectory data.
Sound waves in two-dimensional ducts with sinusoidal walls
The method of multiple scales is used to analyze the wave propagation in two-dimensional hard-walled ducts with sinusoidal walls. For traveling waves, resonance occurs whenever the wall wavenumber is equal to the difference of the wavenumbers of any two duct acoustic modes. The results show that neither of these resonating modes could occur without strongly generating the other.
Sound Waves Levitate Substrates
System recently tested uses acoustic waves to levitate liquid drops, millimeter-sized glass microballoons, and other objects for coating by vapor deposition or capillary attraction. Cylindrical contactless coating/handling facility employs a cylindrical acoustic focusing radiator and a tapered reflector to generate a specially-shaped standing wave pattern. Article to be processed is captured by the acoustic force field under the reflector and moves as reflector is moved to different work stations.
Propagation of sound waves in tubes of noncircular cross section
Plane-acoustic-wave propagation in small tubes with a cross section in the shape of a flattened oval is described. Theoretical descriptions of a plane wave propagating in a tube with circular cross section and between a pair of infinite parallel plates, including viscous and thermal damping, are expressed in similar form. For a wide range of useful duct sizes, the propagation constant (whose real and imaginary parts are the amplitude attenuation rate and the wave number, respectively) is very nearly the same function of frequency for both cases if the radius of the circular tube is the same as the distance between the parallel plates. This suggests that either a circular-cross-section model or a flat-plate model can be used to calculate wave propagation in flat-oval tubing, or any other shape tubing, if its size is expressed in terms of an equivalent radius, given by g = 2 x (cross-sectional area)/(length of perimeter). Measurements of the frequency response of two sections of flat-oval tubing agree with calculations based on this idea. Flat-plate formulas are derived, the use of transmission-line matrices for calculations of plane waves in compound systems of ducts is described, and examples of computer programs written to carry out the calculations are shown.
Scattering Cross Section of Sound Waves by the Modal Element Method
#he modal element method has been employed to determine the scattered field from a plane acoustic wave impinging on a two dimensional body. In the modal element method, the scattering body is represented by finite elements, which are coupled to an eigenfunction expansion representing the acoustic pressure in the infinite computational domain surrounding the body. The present paper extends the previous work by developing the algorithm necessary to calculate the acoustics scattering cross section by the modal element method. The scattering cross section is the acoustical equivalent to the Radar Cross Section (RCS) in electromagnetic theory. Since the scattering cross section is evaluated at infinite distance from the body, an asymptotic approximation is used in conjunction with the standard modal element method. For validation, the scattering cross section of the rigid circular cylinder is computed for the frequency range 0.1 is less than or equal to ka is less than or equal to 100. Results show excellent agreement with the analytic solution.
A Variational Formulation for the Finite Element Analysis of Sound Wave Propagation in a Spherical Shell
Development of design tools to furnish optimal acoustic environments for lightweight aircraft demands the ability to simulate the acoustic system on a workstation. In order to form an effective mathematical model of the phenomena at hand, we have begun by studying the propagation of acoustic waves inside closed spherical shells. Using a fully-coupled fluid-structure interaction model based upon variational principles, we have written a finite element analysis program and are in the process of examining several test cases. Future investigations are planned to increase model accuracy by incorporating non-linear and viscous effects.
Nonlinear interactions in superfluid dynamics: Nonstationary heat transfer due to second sound shock waves
Second sound techniques were used to study superfluid helium. Second sound shock waves produced relative velocities in the bulk fluid. Maximum counterflow velocities produced in this way are found to follow the Langer-Fischer prediction for the fundamental critical velocity in its functional dependence on temperature and pressure. Comparison of successive shock and rotating experiments provides strong evidence that breakdown results in vorticity production in the flow behind the shock. Schlieren pictures have verified the planar nature of second sound shocks even after multiple reflections. The nonlinear theory of second sound was repeatedly verified in its prediction of double shocks and other nonlinear phenomena.
Robotic vision
Robotic vision, involving the use of a vision system to control a process, is discussed. Design and selection of active sensors employing radiation of radio waves, sound waves, and laser light, respectively, to light up unobservable features in the scene are considered, as are design and selection of passive sensors, which rely on external sources of illumination. The segmentation technique by which an image is separated into different collections of contiguous picture elements having such common characteristics as color, brightness, or texture is examined, with emphasis on the edge detection technique. The IMFEX (image feature extractor) system performing edge detection and thresholding at 30 frames/sec television frame rates is described. The template matching and discrimination approach to recognize objects are noted. Applications of robotic vision in industry for tasks too monotonous or too dangerous for the workers are mentioned.
Absorptive surfaces of extended reaction angle of incidence considerations
The acoustic properties of a porous absorbing surface are characterized to apply the concepts to practical situations. Propagation constants, impedance, incident pressure wave, sound waves in the air of the pores, and general acoustic behavior are presented mathematically. The design equations are applicable for highly porous bulk materials. Modified equations are appropriate for bulk liners with stiff frames or flexible frames of finite depth.
Perturbations behind thickened shock waves
Approximative sound wave scattering behind sonic boom overpressure signatures
Sound absorption in acoustically treated ducts in the presence of oblique waves
Sound absorption in acoustically treated ducts in presence of oblique waves
Contact and pressure balance structures in two-fluid cosmic-ray hydrodynamics
The role of cosmic-ray-modified contact discontinuities and pressure balance structures in two-fluid cosmic-ray hydrodynamics in one Cartesian space dimension are investigated by means of analytic and numerical solution examples, as well as by weakly nonlinear asymptotics. The fundamental wave modes of the two-fluid cosmic-ray hydrodynamic equations in the long-wavelength limit consist of the backward and forward propagating cosmic-ray-modified sound waves, with sound speed dependent on both the cosmic-ray and thermal gas pressures; the contact discontinuity; and a pressure balance mode in which the sum ofthe cosmic ray and thermal gas pressure perturbations is zero. The pressure balance mode, like the contact discontinuity is advected with the background flow. The interaction of the pressure balance mode with the contact discontinuity is investigated by means of the method of multiple scales. The thermal gas and cosmic-ray pressure perturbations satisfy a linear diffusion equation, and entropy perturbations arising from nonisentropic initial conditions for the thermal gas are frozen into the fluid. The contact discontinuity and pressure balance eigenmodes both admit nonzero perturbations in the thermal gas, whereas the cosmic-ray-modified sound waves are isentropic. The total entropy perturbation is shared between the contact discontinuity and pressure balance eigenmodes, and examples are given in which there is a transfer of entropy between the two modes. In particular, N-wave type density disturbances are obtained which arise as a result of the entropy transfer between the two modes. A weakly nonlinear geometric optics perturbation expansion is used to study the long timescale evolution of the short-wavelength entropy wave and the thermal gas sound waves in a slowly varying, large-scale background flow. The weakly nonlinear geometric optics expansion is also used to generalize previous studies of squeezing instability for short-wavelength sound waves in the two fluid model, by including a weakly nonlinear wave steepening term that leads to shock formation, as well as the effect of long time and space dependence of the background flow. Implications of cosmic-ray-modified pressure balance structures and contact discontinuities in models of the interaction of traveling interplanetary shocks and compression and rarefraction waves with the solar wind termination shock are briefly discussed.
Modulational and decay instabilities of Alfven waves - Effects of streaming He(2+)
The parametric instability of a circularly polarized Alfven wave propagating along the background magnetic field are considered, with emphasis on the effects of a second ion species, He(2+), which drifts relative to the protons. Even though its abundance is small, the He(2+) modifies the dispersion relation of the 'pump' Alfven wave and introduces a new sound wave (alpha sound) in addition to the usual sound wave carried primarily by the electrons and protons. Instabilities which are close to the He(2+) gyroresonance are found. This may provide a means of directly transferring Alfven wave energy to the alpha particles, if the alphas are able to resonantly extract energy from the unstable waves without quenching the instability altogether. Instabilities which are close to the alpha particle sound speed are also found.
Unsteady oblique interaction of a shock wave with a plane disturbance
Analysis is made of the flow field produced by oblique impingement of weak plane disturbances of arbitrary profile on a plane normal shock. Three types of disturbance are considered: (a) sound wave propagating in the gas at rest into which the shock moves; (b) sound wave overtaking the shock from behind,(The sound wave reflects as a sound wave, and a stationary vorticity wave is produced); (c) an incompressible vorticity wave stationary in the gas ahead of the shock. The incident wave refracts as a stationary vorticity wave, and either a sound wave or attenuating pressure wave is also produced. Computations are presented for the first two types of incident wave, over the range of incidence angles, for shock Mach numbers of 1, 1.5, and infinity.
Clumpy Langmuir waves in type III solar radio bursts
A model is developed for type III radio emission in the interplanetary medium based on recent data on Langmuir waves, associated with ion sound waves, density fluctuations in the interplanetary plasma, streaming electrons and radio emission. In this model, Langmuir wave growth is suppressed by refraction in field-aligned density irregularities except near density minima where clumps of Langmuir waves form. Quasi-linear relaxation limits the growth of the Langmuir waves in the clumps. The radio emission, which is attributed to coalescence of the Langmuir waves with associated ion sound waves, saturates at a brightness temperature equal to the effective temperature of the Langmuir waves, estimated to be between 10 to the 15th and 10 to the 16th K from obserrvational data. The model is consistent with all the relevant data on type III events. In particular, it accounts naturally for observed brightness temperatures of type III bursts.
Second sound shock waves and critical velocities in liquid helium 2
Large amplitude second-sound shock waves were generated and the experimental results compared to the theory of nonlinear second-sound. The structure and thickness of second-sound shock fronts are calculated and compared to experimental data. Theoretically it is shown that at T = 1.88 K, where the nonlinear wave steepening vanishes, the thickness of a very weak shock must diverge. In a region near this temperature, a finite-amplitude shock pulse evolves into an unusual double-shock configuration consisting of a front steepened, temperature raising shock followed by a temperature lowering shock. Double-shocks are experimentally verified. It is experimentally shown that very large second-sound shock waves initiate a breakdown in the superfluidity of helium 2, which is dramatically displayed as a limit to the maximum attainable shock strength. The value of the maximum shock-induced relative velocity represents a significant lower bound to the intrinsic critical velocity of helium 2.