Prediction of broadband high-frequency acoustic reflection and transmission from subcritical membranes and elastic plates

Abstract Reflection and transmission phenomena associated with high-frequency linear wave incidence on irregular boundaries between adjacent acoustic or electromagnetic media, or upon the irregular free surface of a semi-infinite elastic solid, are studied in two dimensions. Here, an ‘irregular’ boundary is one for which small-scale undulations of an arbitrary profile are superimposed upon an underlying, smooth curve (which also has an arbitrary profile), with the length scale of the perturbation being prescribed in terms of a certain inverse power of the large wave-number of the incoming wave field. Whether or not the incident field has planar or cylindrical wave-fronts, the associated phase in both cases is linear in the wave-number, but the presence of the boundary irregularity implies the necessity of extra terms, involving fractional powers of the wave-number in the phase of the reflected and transmitted fields. It turns out that there is a unique perturbation scaling for which precisely one extra term in the phase is needed and hence for which a description in terms of a Friedlander–Keller ray expansion in the form as originally presented is appropriate, and these define a ‘distinguished’ class of perturbed boundaries and are the subject of the current paper.

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Conservative Finite-Difference Scheme for High-Frequency Acoustic Waves Propagating at an Interface Between Two Media

Communications in Computational Physics ◽

10.4208/cicp.111209.240710s ◽

2012 ◽

Vol 11 (2) ◽

pp. 351-366

Author(s):

J. Staudacher ◽

É Savin

Keyword(s):

Phase Space ◽

Acoustic Waves ◽

High Frequency ◽

Numerical Scheme ◽

Propagation Model ◽

Uniform Grid ◽

Two Dimensional ◽

Reflection And Transmission ◽

Conservative Finite Difference Scheme ◽

Homogeneous Media

AbstractThis paper is an introduction to a conservative, positive numerical scheme which takes into account the phenomena of reflection and transmission of high frequency acoustic waves at a straight interface between two homogeneous media. Explicit forms of the interpolation coefficients for reflected and transmitted wave vectors on a two-dimensional uniform grid are derived. The propagation model is a Liouville transport equation solved in phase space.

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An approximate theory for high-frequency vibrations of elastic plates

International Journal of Solids and Structures ◽

10.1016/0020-7683(72)90031-5 ◽

1972 ◽

Vol 8 (5) ◽

pp. 581-612 ◽

Cited By ~ 51

Author(s):

P.C.Y. Lee ◽

Z. Nikodem

Keyword(s):

High Frequency ◽

Approximate Theory ◽

Elastic Plates ◽

High Frequency Vibrations

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Airway area by acoustic reflections measured at the mouth

Journal of Applied Physiology ◽

10.1152/jappl.1980.48.5.749 ◽

1980 ◽

Vol 48 (5) ◽

pp. 749-758 ◽

Cited By ~ 141

Author(s):

J. J. Fredberg ◽

M. E. Wohl ◽

G. M. Glass ◽

H. L. Dorkin

Keyword(s):

High Frequency ◽

Upper Airway ◽

Local Area ◽

Cross Sectional ◽

Acoustic Reflection ◽

Acoustic Data ◽

Reflection Data ◽

Radiographic Measurements ◽

Average Coefficient ◽

Radiographic Data

We tested the hypothesis that features of upper airway and tracheal geometry can be inferred from acoustic reflection data recorded at the mouth. In six subjects we computed inferences of airway cross-sectional area vs. distance and compared them with measurements obtained from orthogonal radiographic projections of the trachea. The acoustic data show local area maxima at the uvula and hypopharynx and local minima at the oropharynx and the glottis. With subjects breathing air the inferred tracheal areas markedly exceeded the radiographic measurements. With subjects breathing 80% He-20% O2 there was good intrasubject agreement between acoustic and radiographic data in spite of large intersubject variability. The average coefficient of variation of tracheal area determinations for five trials in all subjects was 0.16. These studies suggest that features of airway geometry between the mouth and carina can be determined accurately and noninvasively in individual subjects from high-frequency reflection data measured at the mouth.

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