Computation of modal wavenumbers using an adaptive winding-number integral method with error control

The Transfer Matrix for a Dissipative Silencer of Arbitrary Cross-Section

“…First, for a given frequency, the amount of dissipation is reduced to a minimum to gather the transverse wavenumbers along the real axis in the complex k , plane. To isolate and locate the roots approximately, the principle of arguments is then applied [20]. This will also reveal any possible degeneracy of the eigenvalues.…”

On the exponent in the power law for the attenuation at low frequencies in sandy sediments

“…A normal mode code based on Ivansson and Karasalo's study 14 was used to compute transmission loss for this case at four frequencies: 125, 250, 500, and 1000 Hz. The source and receiver depths are both 6 m. The water layer was 13 m deep with a sound speed of 1467.5 m / s. The bottom half-space has a compressional speed of 1620 m / s, a density of 1.7 gm/ cm 3 , and compressional wave attenuation ␣ i ͑f 0 ͒͑f / f 0 ͒ 2 with ␣ i ͑f 0 = 1 kHz͒ = 0.30 dB/ m͑0.49 dB/ ͒.…”

Mode Structure for Fluid–solid Media as Derived by Low-Frequency Asymptotics

“…We will use adaptive winding-number integral techniques for locating such zeros in an e$cient and reliable manner; see reference [20] for a description of our particular algorithm. It is essential, however, that the analytic functions can be evaluated e$ciently at arbitrary points.…”