Volume 121, Issue 6, June 2007
Index of content:
- GENERAL LINEAR ACOUSTICS 
121(2007); http://dx.doi.org/10.1121/1.2721878View Description Hide Description
The propagation of a normally incident plane acoustic wave through a three-dimensional rigid slab with periodically placed holes is modeled and analyzed. The spacing of the holes and , the wavelength , and the thickness of the slab are order one parameters compared to the characteristic size of the holes, which is a small quantity. Scattering matrix techniques are used to derive expressions for the transmission and reflection coefficients of the lowest mode. These expressions depend only on the transmission coefficient,, of an infinitely long slab with the same configuration. The determination of requires the solution of an infinite set of algebraic equations. These equations are approximately solved by exploiting the small parameter . Remarkably, this structure is transparent at certain frequencies and opaque for all others. Such a structure may be useful in constructing narrow-band filters and resonators.
121(2007); http://dx.doi.org/10.1121/1.2727332View Description Hide Description
A complete solution is obtained for the two-dimensional diffraction of a time-harmonic acoustic plane wave by an impenetrable elliptic cylinder in a viscous fluid. Arbitrary size, ellipticity, and angle of incidence are considered. The linearized equations of viscous flow are used to write down expressions for the dilatation and vorticity in terms of products of radially and angular dependent Mathieu functions. The no-slip condition on the rigid boundary then determines the coefficients. The resulting computations are facilitated by recently developed library routines for complex input parameters. The solution for the circular cylinder serves as a guide and a differently constructed solution for the strip is also given. Typical results in the “resonant” range of dimensionless wave number, displaying the surfacevorticity and the far-field scatteringpattern are included, with the latter allowing comparison with the inviscid case.
121(2007); http://dx.doi.org/10.1121/1.2726252View Description Hide Description
A general approach is presented for determining the acoustic fields of rectangularly symmetric, baffled, time-harmonic sources under the Fresnel approximation. This approach is applicable to a variety of separable source configurations, including uniform, exponential, Gaussian, sinusoidal, and error function surface velocity distributions, with and without focusing in either surface dimension. In each case, the radiated field is given by a formula similar to that for a uniform rectangular source, except for additional scaling of wave number and azimuthal distance parameters. The expressions presented are generalized to three different Fresnel approximations that correspond, respectively, to diffracted plane waves, diffracted spherical waves, or diffracted cylindrical waves. Numerical results, for several source geometries relevant to ultrasonic applications, show that these expressions accurately depict the radiated pressure fields, except for points very near the radiating aperture. Highest accuracy near the source is obtained by choice of the Fresnel approximation most suited to the source geometry, while the highest accuracy far from the source is obtained by the approximation corresponding to diffracted spherical waves. The methods are suitable for volumetric computations of acoustic fields including focusing, apodization, and attenuation effects.