Sound Waves In Gases Research Articles

Elastic Alfven waves in elastic turbulence

Speed of sound waves in gases and liquids are governed by the compressibility of the medium. There exists another type of non-dispersive wave where the wave speed depends on stress instead of elasticity of the medium. A well-known example is the Alfven wave, which propagates through plasma permeated by a magnetic field with the speed determined by magnetic tension. An elastic analogue of Alfven waves has been predicted in a flow of dilute polymer solution where the elastic stress of the stretching polymers determines the elastic wave speed. Here we present quantitative evidence of elastic Alfven waves in elastic turbulence of a viscoelastic creeping flow between two obstacles in channel flow. The key finding in the experimental proof is a nonlinear dependence of the elastic wave speed cel on the Weissenberg number Wi, which deviates from predictions based on a model of linear polymer elasticity.

Is Brenner's Modification to the Classical Navier–Stokes Equations Able to Describe Sound Propagation in Gases?

We analyse the problem concerning the propagation of sound waves in gases by using the modified hydrodynamic theory proposed recently by Brenner for single-component fluids. The modifications introduced by Brenner are based on his proposal that the translational momentum in fluid motion is not given by the mass flux. Comparison of the sound propagation results derived from Brenner's theory with available experimental data for monatomic gases shows that this modified continuum theory is unable to describe the acoustic measurements not even in the low-frequency limit, a result that from our point of view makes Brenner's proposal questionable.

Herman Medwin as observed by an interested bystander

Herman Medwin was a brilliant scientist, a complex individual, and a strong-willed advocate. Although his most significant scientific contributions were associated with acoustical oceanography, his professional creativity was not limited to this technical field. Hank’s graduate work at UCLA involved acoustic streaming in gases; in his early professional years he reported substantial work with intense sound waves in gases; he was an accomplished violinist; and his final published work involved auditorium acoustics. His contributions to the Acoustical Society of America were particularly noteworthy, from his initial service as a technical committee and Executive Council member through its presidency. His well-deserved recognition by ASA included award of the Silver Medal in Acoustical Oceanography and the Gold Medal. He spearheaded establishment of the Medwin Prize in Acoustical Oceanography, which is awarded annually by ASA to provide recognition to mid-career researchers in the field. Personal observations are given on some of these topics by an outsider (from AO), who was privileged to spend a year assisting with Hank’s research, and who closely followed his experiences with ASA through the formalities associated with creation of the prize given in his name.

Dynamic Processes of Gas in Plastic Pipes

In the article gas movement in elastic pipelines is considered. The following things are taken into account in the present model: distribution of sound waves in gas, elastic and viscous properties of elastic pipelines, and friction of gas on the pipeline wall. The elastic properties of pipeline’s material are simulated by the rheological model of Kelvin - Foight. The received system of the equations of gas movements and deformations of the pipeline is solved by a method of the characteristics. Nonlinear algebraic equations are solved by Newton method. Movement of gas (air) in pipelines made from polyvinilchloride (PVC) is considered.

Sound waves in foams

A new (film) model is proposed for the propagation of sound waves in gas–liquid foams. The model explains the effect of sound retardation in foams by foam films inertness. It qualitatively agrees with the experimental data on the velocity of sound propagation in foams of various structures. The high absorption of sound in foams is explained by hydrodynamic losses in foam films. The experimental dependence of the sound absorption coefficient on the foam expansion is explained. The calculated expansion corresponding to the absorption maximum is close to the experimental value.

SOUND ATTENUATION IN TUBES DUE TO VISCO-THERMAL EFFECTS

The propagation of periodic axial sound waves in gases contained in circular cylindrical structures is a function of four parameters: s=Rρ·ω/μ, the shear wave number or Stokes number, k=ω·R/c, known as the reduced frequency, σ=μ·Cp/λ, the square root of the Prandtl number and γ=Cp/Cv, the ratio of specific heats. The complete Kirchhoff solution of the sound propagation in tubes problem obtained in 1868 was expressed in terms of these parameters by Tijdeman [1]. In previous works [1, 2] the complex propagation constant was obtained by solving this expression. The results were presented for a limited range in reference [1] and for a broader range in reference [2] but in both cases only for a single fluid, air. In this work the results of a computer code to solve for this propagation constant are presented. The code was used to find the propagation constants (attenuation and phase-shift coefficients) in the range 5<s<5000, 0·01<k<6, 0·8<σ<1·1 and 1·0<γ<1·7. This range of conditions covers most conditions of interest. The data was then used to fit an equation to express the attenuation and phase-shift coefficients in terms of simpler polynomial-type expressions as a function of these four parameters. A set of tables to obtain the values of the attenuation and phase shift coefficients for values of these four non-dimensional parameters in the above range is also presented. Sound attenuation measurements using superheated R134a refrigerant agrees reasonably well with the computed attenuation in the plane wave region.

Wave–wave interactions in two-fluid cosmic-ray hydrodynamics

Multiple–scales perturbation methods are used to derive equations describing wave–wave interactions in two-fluid cosmic-ray hydrodynamics in one Cartesian space dimension. Two problems are considered: (a) the interaction between short-wavelength waves in a non-uniform large-scale background flow, and (b) wave interactions between long-wavelength waves propagating through a uniform background medium. The short-wavelength wave equations describe the interaction between the backward and forward thermal gas sound waves and the contact discontinuity eigenmode via ‘wave mixing’, in which the waves are reflected by gradients in the large scale background flow. The equations also contain quadratic wave interaction terms describing (i) the Burgers self-wave interaction term, (ii) mean–wave-field interaction terms in which a specific wave interacts with the mean field of the other waves, and (iii) three-wave resonant interactions that describe how a sound wave resonantly interacts with the contact discontinuity to generate a reverse sound wave. In the limit of no interaction between the cosmic rays and thermal gas, and for a uniform background state, the equations reduce to two coupled, integro-differential Burgers equations derived by Majda and Rosales for resonantly interacting waves in adiabatic gasdynamics. The short-wavelength equations also contain squeezing instability terms associated with the large-scale cosmic-ray pressure gradient, which were first investigated by Drury and Dorfi. A generalized wave-action equation, or canonical wave-energy equation, variational principles, and WKB analyses of the linearized equations are used to investigate the modification of the cosmic-ray squeezing instability by wave mixing. Coupled Burgers equations are also derived in the long-wavelength regime that describe resonant wave interactions for weak, diffusively smoothed cosmic-ray-modified shocks. In the latter equations, the cosmic-ray-modified sound waves can resonantly interact with either the contact discontinuity or the cosmic-ray pressure-balance mode to generate a reverse sound wave.

Holographic real-time imaging of standing waves in gases

Stroboscopic holographic interferometry has been developed at an advanced undergraduate level allowing real-time imaging of standing sound waves in gas filled, closed tube resonators. A heterodyne Mach–Zehnder interferometer was first built by students to show the feasibility of interferometric detection of sound waves in a small cell. In the subsequent holographic study, the laser irradiance is modulated by an acousto-optic cell at frequencies near that of the standing wave, and a video camera records the fringe motion due to sound pressure changes. Fractional fringe shifts are observed for an air filled cell, and multiple fringe shifts are imaged for the case of freon. Sound reflections from the cell ends are easily observed, with nonsinusoidal waveforms dominating at high intensities due to superposition of resonator harmonics.

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.

On wave stability in relativistic cosmic-ray hydrodynamics

Wave stability of a two-fluid hydrodynamical model describing the acceleration of cosmic rays by the first-order Fermi mechanism in relativistic, cosmic-ray-modified shocks is investigated. For a uniform background state, the short- and long-wavelength wave speeds are shown to interlace, thus assuring wave stability in this case. A JWKB analysis is performed to investigate the stability of short-wavelength thermal gas sound waves in the smooth, decelerating supersonic flow upstream of a relativistic, cosmic-ray-modified shock. The stability of the waves is assessed both in terms of the fluid velocity and density perturbations, as well as in terms of the wave action. The stability and interaction of the short-wavelength cosmic-ray coherent mode with the background flow is also studied.

Acoustic Theory Applied to the Physics of Electrical Breakdown in Dielectrics

In order to stimulate further thought and research within the science of dielectrics, this paper discusses the remarkable correlation between acoustic theory and the physics of electrical breakdown in dielectrics. Following a brief, simplified fied review of acoustic theory and the propagation and attenuation ation of soundwaves in gases, liquids and solids, three areas in dielectrics are addressed in which the breakdown mechanisms require further clarification. These are the relative electrical strengths of gases and mixtures; streamer initiation in liquid hydrocarbons; and the incubation period before treeing or breakdown own occurs within solid dielectrics. Acoustic analysis of gas breakdown clearly shows that the relative electrical strengths of gases and mixtures vary as the inverse square of sound velocity, and consequently, are closely related to both the molecular weight and specific heat ratio of the gas or mixture. For liquid hydrocarbons, an analysis of acoustic emission levels from partial discharges combined with acoustic cavitation theory, supports the hypothesis that cavitation (collapse) of microbubbles bubbles attached to dust particles may provide the conditions for streamer initiation. Finally, attention is drawn to the relationship between the velocity of sound within solid dielectrics and Young's modulus, Poisson's ratio and density, which suggests a potential application of acoustics for assessing the mechanical strength of dielectrics as they age. Thus, simple acoustic measurements performed on solid dielectrics may provide some information on the structural condition Qf these dielectrics before treeing and subsequent breakdown occurs.

Sound conversion phenomena at the free surface of liquid helium. II. Experimental determination of acoustic coefficients and surface absorption coefficients

The acoustic coefficients of reflection, transmission, and transformation of first-, second-, and gas sound waves incident normally on the free surface of liquid helium have been determined. The experimental results are compared with the theory developed in Part I of this paper. It is shown that equilibrium theories of boundary conditions disagree with the experiments. Nonequilibrium theories, however, which take into account that mass and energy transport processes occur at the liquid-vapor interface of helium II, lead to a very good description of the experimental data below 2 K. Within experimental accuracy the measurements fully confirm several kinetic models of evaporation and energy transport processes. Near the λ point, deviations from the theory have been found which might be attributed to influences of critical phenomena. The surface absorption coefficients of first-, second-, and gas sound waves could be deduced from the experimental data on the acoustic coefficients, and it is shown that, in agreement with the theory, appreciable energy dissipation occurs at the free surface of helium II when a second-sound or a gas sound wave is incident.

Sound conversion phenomena at the free surface of liquid helium. I. Calculation of the coefficients of reflection, transmission, and transformation of sound waves incident on the liquid-vapor interface of helium

On the basis of a set of boundary conditions describing quite generally mass and energy transport processes across the free surface of helium II, the acoustic coefficients of reflection, transmission, and transformation of first sound, second sound, and the sound wave propagating in the vapor are calculated in the case of perpendicular incidence of sound waves against the liquid-vapor phase boundary. Considering rigorously the influences of the Onsager surface coefficients, the isobaric thermal expansion coefficients, and the thermal conductivities of the liquid and the vapor, we derive sets of equations from which the acoustic coefficients are determined numerically. For estimations, simple explicit formulas of the acoustic coefficients are given. It is shown that the evaporation and energy transport processes occurring at the free surface of helium II due to the incidence of sound waves may be connected with appreciable energy dissipation. The surface absorption coefficients of first, second, and gas sound waves are deduced.

On the propagation of sound waves in cylindrical tubes

It is shown that the two main parameters governing the propagation of sound waves in gases contained in rigid cylindrical tubes, are the shear wave number, s = R ρ s ω / μ , and the reduced frequency, k = ωR/a 0 . It appears possible to rewrite the most significant analytical solutions for the propagation constant, Γ, as given in the literature, as simple expressions in terms of these two parameters. With the aid of these expressions the various solutions are put in perspective and their ranges of applicability are indicated. It is demonstrated that most of the analytical solutions are dependent only on the shear wave number, s , and that they are covered completely by the solution obtained for the first time by Zwikker and Kosten (1949) . The full solution of the problem has been obtained by Kirchhoff (1868) in the form of a complicated, complex transcendental equation. In the present paper this equation is rewritten in terms of the mentioned basic parameters and brought in the attractive form F =0, which is solved numerically by using the Newton-Raphson procedure. As first estimate in this procedure the value ofaccording to the solution of Zwikker and Kosten is taken. Results are presented for a wide range of s and k values.

Radiation Pressure Against Perfect Reflectors

The concept of radiation pressure exerted against a reflecting surface by electromagnetic waves and by sound waves in gases is a familiar one. The absence of radiation pressure for sound waves in a “linear medium” is becoming well known. The equations are somewhat different for the radiation pressure for these two cases where the radiation pressure is not zero. The mechanisms usually called on to explain them (nonlinearity of the equation of state of the gas, acceleration of charges in the reflector by the electromagnetic waves) are widely removed from each other. Consequently, it is not evident on the surface whether radiation pressure is a general property of waves or the capricious result of isolated physical phenomena associated with some waves. A generalized concept of radiation pressure is here developed and then applied to several kinds of waves: sound waves in various media, waves on strings and springs, electromagnetic waves. Also, a simple demonstration of radiation pressure (for waves in a ripple tray) is described.

The Theory of the Propagation of Plane Sound Waves in Tubes

The propagation of plane sound waves in gases in tubes can be divided into three main types, depending on the radius and frequency involved. These types are described as `narrow' tube, `wide' tube and `very wide' tube propagation. The phase velocity, attenuation and cross section profile of particle velocity etc. are investigated theoretically, and their inter-relation pointed out. The factors affecting the validity of Kirchhoff's formulae are considered, and the theory is applied to some recent work.

The velocity of sound in gases in tubes

The main objects of the series of experiments described in the present paper were two-fold: ( a ) to make precision measurements, over a moderate tempera­ture-range, of the velocity of sound-waves in gases contained in resonating tubes; ( b ) to investigate the applicability of the Helmholtz-Kirchhoff expression for the relation between the “tree-space” velocity and the “tube” velocity in a gas. As regards ( b ) different observers in the past have reached diverse con­clusions as to the dependence of tube-velocity on the frequency, on the roughness of the wall surface, and on the nature of the material of the tube.

Dispersion and Absorption of High Frequency Sound Waves

The absorption of sound waves in gases had been explained heretofore by friction and heat conduction. A third factor is here introduced, namely, the slow rate of exchange of energy between the translational movement and the internal degrees of freedom of the molecules. The formulas determining the absorption and dispersion of sound waves, due to these three effects, are developed. Comparison with the experimental data available shows that the new effect is either of considerable influence or even predominant. The rate of exchange can be calculated.