Sonic Band Research Articles

Sonic band structure and surface localized modes in a density-modulated system: An experimental and theoretical study

A result of the Bloch theory is that the eigenstates of an electron in a strictly periodic potential are extended and the corresponding energy levels form clustered energy bands separated by gaps. In the study reported here, a finite air-filled tube with arbitrary mass density modulation which permits the inclusion of disorder in the study of the acoustic frequency bands is theoretically considered. Since the theoretical model is finite, direct comparisons can be made with the experiment. The baffled tube is excited with a sound source at one end. The source can deliver short pulses as well as harmonic oscillations. Both normal mode analysis (NMA) and pulse analysis (PA) have been used. The spectra obtained from both methods are compared with our theoretical prediction. For the tube with evenly spaced baffles, three passing frequency bands have been found. More interestingly, some localized resonant modes are discovered whose frequencies lie in the gaps. The wave functions of these modes are confined within a few sections of divided tube at both ends.

Sonic band structure and surface localized modes in a density-modulated system: An experimental and theoretical study

As a result of the Bloch theory, the eigenstates of an electron in a strictly periodic potential are extended and the eigenenergy levels form allowed energy bands separated by forbidden gaps. In the study reported here, a finite air-filled tube with arbitrary mass density modulation is considered which allows the inclusion of the effect of disorder. Since this theoretical model is finite, it was possible to make direct comparisons with the experiment. The baffled tube is excited with the sound source emitted at one end. The source can deliver short pulses as well as harmonic oscillations. Both normal modes analysis (NMA) and pulse analysis (PA) were used. The spectra obtained from both methods are compared with the theoretical prediction. For the tube with evenly spaced baffles, three passing frequency bands were found. More interestingly, a few ‘‘surface’’ localized resonant modes whose frequencies lie in the gaps were discovered. The wave functions of the surface modes are confined within a few sections of divided tube at both ends. It was found that the acoustic intensity of higher frequency bands is drastically lower than that of the lowest band, which suggests that the baffled tube can be used as a frequency filter.

Changes in attenuation with depth in an ocean carbonate section: Ocean Drilling Program sites 806 and 807, Ontong Java Plateau

Changes of in situ seismic attenuation with depth are estimated from full waveform acoustic logs in a soft formation (rock with shear velocity less than borehole fluid velocity). The relative attenuation Qp−1 is computed from the variation with depth of the P wave amplitude spectrum of a single source receiver pair. The method is applicable when unknown source and receiver responses of the sonic tool make other methods difficult to apply. Tests with synthetic data generated by a full waveform method verify that in a soft formation the decay of the P wave amplitude spectrum depends mainly on attenuation. The method is applied to Ocean Drilling Program data from holes 806B and 807A on the Ontong Java Plateau in the western Pacific Ocean. Four attenuation logs were computed independently using data from four source receiver pairs. Agreement of the four logs at each site and agreement of results from the two sites suggest that the method is robust and practical. The attenuation logs show a maximum attenuation between 300 and 500 m below the seafloor. They agree well with compilations of high‐frequency attenuation versus porosity and frequency in marine sediments but are somewhat greater than results from seismic experiments, possibly owing to the presence of sedimentary microbeds and the three‐decade difference between the seismic and sonic frequency bands.

Giant sonic stop bands in 3‐D periodic array of liquid balloons.

Periodic binary systems can create complete acoustic bandgaps (i.e., stop bands) within which sound and vibrations are forbidden. This is of interest for applications such as acoustic filters, noise control, and improvements in transducers; as well as for pure physics concerned with the Anderson localization of sound and vibrations. The band structures for 3‐D periodic arrays of water balloons surrrounded by mercury have been computed. Complete, multiple stop bands are found for fcc, bcc, and sc lattices. It is stressed that such a simple 3‐D inhomogeneous system exhibits the widest stop bands ever reported for elastic as well as for dielectric composites. The gap/mid‐gap ratios are found to be as high as ∼1. For mercury balloons surrounded by water the gaps are found to be comparatively much smaller. Physical importance and applications of such gaps will be discussed.

Sonic bands, bandgaps, and defect states in layered structures—Theory and experiment

The propagation of sound through a one-dimensional periodic array of water and perspex plates is studied theoretically and experimentally. It is shown that the passbands and stop bands of a scatterer with a finite number of layers correspond to the bands and bandgaps of an infinite ‘‘sonic bandgap crystal.’’ The transmission coefficient of various finite structures is computed and measured as a function of frequency. The analogy with the electronic bandstructure of crystals, and the photonic bandstructure of macroscopic periodic dielectric structures, is found to be a close one. It is shown that the position and width of passbands can easily be engineered. Results are included for a finite ‘‘crystal’’ with a vacancy defect, in which a narrow passband appears in each of the stop bands.

MECHANICAL IMPULSE RESPONSE AS A MEASURE OF TOMATO FRUIT MATURITY

A mechanical impulse system for determining tomato fruit maturity and size was tested, for development of a rapid, nondestructive fruit testing instrument. Fruit were grouped into various maturity categories, ranging from immature green to red, and impulse spectra were obtained at a site over the locule at marked locations. Resistance to puncture was measured on the locular side of the pericarp wall at the same locations. A sonic resonant frequency band was weakly correlated with fruit maturity category. Stronger correlations existed with pericarp puncture resistance and fruit weight. A description of essential components and utilization of the instrument for fruit firmness determination will be presented. Supported by OCAST (Oklahoma Center for the Advancement of Science and Technology) grant AR2-069, USDA grant 92-34150-7190 and the Oklahoma Agricultural Experiment Station.

Sonic band structure in fluids with periodic density variations

In direct analogy to the electronic band structure found in semiconductors and the photonic bands for light in a medium with a periodic dielectric constant, a periodic density variation in a fluid can give rise to sonic frequency passbands and band gaps. Hence, a fluid medium can be constructed that prohibits sound propagation at certain frequencies while allowing practically free propagation at others. The effect of a sonic band medium on a monopole acoustic source is discussed in a simple one-dimensional model. In particular, the complete quenching of radiated power is seen for a harmonic radiator at a frequency that corresponds to a band gap—in analogy with a similar effect that is predicted for the atomic emission of electromagnetic waves in a photonic band structure. The ability to construct a medium that selectively prohibits sound propagation and emission in a certain range of frequencies, while allowing transmission and enhanced radiation rates at others, could have interesting practical applications.

An accurate and efficient scheme for wave propagation in linear viscoelastic media

The problem of wave propagation in a linear viscoelastic medium can be described mathematically as an exponential evolution operator of the form [Formula: see text] acting on a vector representing the initial conditions, where [Formula: see text] is a spatial operator matrix and t is the time variable. Techniques like finite difference, for instance, are based on a Taylor expansion of this evolution operator. We propose an optimal polynomial approximation of [Formula: see text] based on the powerful method of interpolation in the complex plane, in a domain which includes the eigenvalues of the matrix [Formula: see text]. The new time‐integration technique is implemented to solve the isotropic viscoacoustic equation of motion. The algorithm is tested for the problem of wave propagation in a homogeneous medium and compared with second‐order temporal differencing and the spectral Chebychev method. The algorithm solves efficiently, and with machine accuracy, the problem of seismic wave propagation with a dissipation mechanism in the sonic band, a characteristic of sedimentary rocks. The computational effort in forward modeling based on the new technique is half compared to that of temporal differencing when two‐digit precision is required. Accuracy is very important, particularly for propagating distances of several wavelengths, since the anelastic effects should not be confused with nonphysical phenomena, such as numerical dispersion in time‐stepping methods. Finally, we compute the seismic response to a single shot in a realistic geologic model which includes a gas‐cap zone in an anticlinal fold. The results clearly show the importance of the attenuation and dispersion effects for an appropriate interpretation of the seismic data. In particular, the gas‐cap response (a bright spot) suffers significant variations in amplitude, phase, and arrival time compared to the purely acoustic case.

The linear stability of viscous compressible plane Couette flow

The structure of normal modes in viscous compressible plane Couette flow is investigated. The spectrum is found to consist of two types of modes: the viscous modes, which obtain finite phase velocities by the mechanism of mode pairing; and the sonic modes, whose phase velocity becomes distorted in the supersonic regime. This leads to mode crossings which unfold, depending on the type of crossing modes, either into purely sonic or viscous-sonic instability bands. The latter provide a new example for viscous instability. Both mode pairing of viscous modes and distortion of the phase velocity of sonic modes is caused by the shear. Critical Reynolds numbers for the instabilities are derived.

Pore fluids and frequency‐dependent wave propagation in rocks

Attenuation is the anelastic process which dissipates seismic energy by conversion to heat, thus decreasing the amplitude and modifying the frequency and phase content of a propagating wavelet. Laboratory measurements show seismic phase velocity and attenuation are dependent upon the fluid saturation and the product of frequency and pore‐fluid viscosity, with a peak in attenuation between the seismic and sonic bands. The dominant mechanism by which seismic energy is dissipated in the upper crust is local viscous fluid flow in pores of small aspect ratio. Phenomenologically, this behavior is modeled as a series of linear viscoelastic elements with a narrow distribution of relaxation times, where velocity and attenuation are related through the Hilbert transform. This model may be generalized to include constant-Q behavior, as observed in dry rocks. Solutions to the wave equation may be generated for an arbitrary frequency dependence of phase velocity and Q. When Q is nearly independent of frequency, the impulse response is asymmetric and the power spectrum is a straight line with slope proportional to Q. When Q is roughly proportional or inversely proportional to frequency, the impulse response is nearly symmetrical and the power spectrum is nonlinear. These results indicate that the frequency content, phase spectrum, and velocity may be strong indicators of the type of pore fluid in a formation. Alternatively, if the type of pore fluid is known, these attributes could be used to monitor temperature changes of a formation.

Identification of the N-ethylmaleimide reactive protein of the mitochondrial phosphate transporter

The mitochondrial phosphate carrier is inhibited by the SH reagents p-(hydroxymercuri)benzoate and N-ethylmaleimide. Based on an analysis utilizing dodecyl sulfate-polyacrylamide gels, an SH-containing 32 000-dalton protein has been identified as a component of the phosphate carrier system. Two other N-[3H]ethylmaleimide-labeled proteins of the inner mitochondrial membrane have been eliminated from this role [Wholrab, H., & Greaney, J., Jr. (1978) Biochim. Biophys. Acta 503, 425] on the basis that band IV (45,000 daltons) is absent from heart sonic submitochondrial particles and band VII (6 500 daltons) does not react with p-(hydroxymercuri)benzoate. The mobility of the 32 000-dalton protein (0.43) is lower than that of the gamma subunit of the mitochondrial ATPase (0.46) and the carboxyatractyloside binding protein (0.48) on 12.5% dodecyl sulfate-polyacrylamide gels. In these flight muscle mitochondria, 0.87 nmol of N-[3H]ethylmaleimide per nmol of cytochrome a is bound to the 32,000-dalton protein.