Acoustic wave theory

In this chapter we will deal with those parts of acoustic wave theory which are relevant to chemists in the understanding of how they may best apply ultrasound to their reaction system. Such discussions tvill of necessity involve the use of mathematical concepts to support the qualitative arguments. Wherever possible the rigour necessary for the derivation of the basic mathematical equations has been kept to a minimum within the text. An expanded treatment of some of the derivations of key equations is provided in the appendices. For those readers who would like to delve more deeply into the physics and mathematics of acoustic cavitation numerous texts are available dealing with bubble dynamics [1-3]. Others have combined an extensive treatment of theory with the chemical and physical effects of cavitation [4-6]. 

Rosenbaum, J. F. Bulk Acoustic Wave Theory and Devices, Artech Boston, Sect. 

Rosenbaum JF (1988) Bulk acoustic wave theory and devices. Artech, Boston... 

Macrocyclic Compounds in Analytical Chemistry. Edited by Yury A. Zolotov Surface-Launched Acoustic Wave Sensors Chemical Sensing and Thin-Film Characterization. By Michael Thompson and David Stone Modern Isotope Ratio Mass Spectrometry. Edited by T. J. Platzner High Performance Capillary Electrophoresis Theory, Techniques, and Applications. Edited by Morteza G. Khaledi... 

Bnlk wave devices have different tolerances and recently Capelle, Zarka and co-workers have studied bulk waves in qnartz resonators and used stroboscopy to identify unwanted modes associated with defects. They have also performed tine section topography in stroboscopic mode to identify if the interaction between a dislocation and the acoustic wave could be described by simple linear piezoelectric theory. Using simulation of the section topographs to analyse the data, they conclnded that a non-Unear interaction was present near to the dislocation line, linear theory working satisfactorily in the region far from the defect. Etch channels appeared to have more inflnence on the acoustic wave than individnal dislocations. 

Ann. Occup. Hyg. Ballantine DS. Acoustic wave sensors theory, design, and physico-chemical applications. San Diego, CA Academic Press, 1997. 

The basic differences between spherical and cylindrical symmetry are in the propagation equations for the water and expln products, the equations of state and the shock front conditions remaining unchanged. Thus, even for acoustic waves, pressure for cylindrical waves varies as r-1/2 F(t—r/c0) where F is an undetermined function, as compared with r 1 F(t—r/c0), valid at any distance for acoustic spherical waves. The development of a finite amplitude theory will not therefore be as simply related to the actual state of affairs, and errors incurred in approximations used will be larger than for spherical waves... 

One strength of the theory is that it stimulates new questions and permits a more precise statement of new problems. The thermoelastic mechanism is apparently adequate to characterize the acoustic effect occurring in heads of humans and animals exposed to pulsed microwaves. The precise location in the head (scalp, skull or brain) microwave pulses are transformed into the acoustic wave of pressure however is at present not specifiable. Several speculations can be advanced, but there is little direct physiological data that would identify the possible gross tissue structures involved. Clearly, this is an area still requiring study. 

By means of method of visualization with the help of acoustic waves [1,2] we could get the microstructure images of steel samples on different depths from the surface. The analysis of acoustic images gave the possibility to calculate the dimensions of grains, to observe their transformation in the period of time or under external influences. In accordance with the theory of Hall - Peach there were defined the strength characteristics, for example flow limit ( Go,2) of the materials under study. The significance obtained o0 2 is in proper correspondence with values that are table one for the type of steel under consideration. 

THE PHYSICS OF WAVES, William C. Elmore and Mark A. Heald. Unique overview of classical wave theory. Acoustics, optics, electromagnetic radiation, more. Ideal as classroom text or for self-study. Problems. 477pp. 5b 8b. 

Figure 3.51 Pumping with flexural-wave device. Data velocity measured from video recorded motion of polystyrene spheres vs amplitude of wave motion. Solid line theoretical values based on acoustic streaming theory. (Reprimed with permission. See Ref. [74). 1989...

The second problem facing the researcher, and the one which is the subject of this paper, is to determine which, if any, effective modulus theory accurately predicts the acoustic wave velocity and attenuation in a microscopically or macroscopically inhomogeneous material. 

Dynamic Theories, Dynamic theories take into account the scattering of acoustic waves from individual inclusions and generally include contributions from at least the monopole, dipole, and quadrupole resonance terms. The simpler theories model only spherical inclusions in a dilute solution and thus do not consider multiple scattering. To obtain useful algebraic expressions from the theories, the low concentration and the low frequency limit is usually taken. In this limit, the various theories may be readily compared. 

However, the length of the sample, if it is comparable to the length of the acoustic waves can cause wave interference effects to arise at the sample-water interface and these must be taken into account in a theoretical description. The mathematical treatment of these effects can be found in the literature of transmission line theory which provides the following expression for the impedance of a length 1 of material... 

If it is accepted that a spinning mode of propagation exists, then an acoustic theory may be applied to predict the spin frequency, the slope of the helical path on the tube wall, and other characteristics of spinning detonations [75]-[76]. For a planar Chapman-Jouguet wave in an infinitely long tube and in a frame of reference in which the burnt gas is at rest, the circumferential velocity of a traveling tangential acoustic wave at the wall... 

The shear and compressional acoustic wave velocities for the inner core are the direct output parameters from seismological observations. In order to make a direct comparison between the seismic data and measured physical properties, measurements of the acoustic velocities for iron at core pressures are required. Only very recently has it become possible to measure the elastic constants of s-Fe at high pressures and room temperature (Mao etal., 1999 Lubbers etal., 2000 Fiquet et al., 2001 Anderson et at, 2001). Recent advances in theory and computational methods have also provided new tools for computing the elastic constants of s-Fe at core pressures (Stixrude and Cohen, 1995 Soderhnd et al., 1996 Cohen et al., 1997 Steinle-Neumann and Stixrude, 1999) and core conditions (Laio et al., 2000 Steinle-Neumann et al, 2001 Alfe et al., 2001). There is considerable disagreement on the elastic constants of s-Fe between experimental results and theoretical calculations. The dilferences in the aggregate shear (FJ and compressional (Vp) wave velocities are smaller (Hemley and Mao, 2001 Steinle-Neumann et ai, 2001). Further improvement of theory and experiment is required to resolve the discrepancies. 

Green s functions appear as the solutions of seismic field equations (acoustic wave equation or equations of dynamic elasticity theory) in cases where the right-hand side of those equations represents the point pulse source. These solutions are often referred to as fundamental solutions. For example, in the case of the scalar wave equation (13.54), the density of the distribution of point pulse forces is given as a product,... 

DNA-acoustic wave biosensors have been employed to study the duplex formation at the sensor surface and for monitoring a wide variety of processes involving nucleic acid chemistry at the soUd-liquid interface without the need of labels such as radiochemical or fluorescent agents. The theory and applications of acoustic wave technology were reviewed by Thompson [50,51], Ziegler [52] and co-workers. 

---