On Infrasound Waveguides and Dispersion

Waveguides are structures that provide for efficient propagation of waves. One of the earliest applications of a waveguide is the speaking tube, which was used on ships. Propagation in some waveguides leads to dispersion, a phenomenon in which the phase velocity depends on the frequency. Dispersion of elastic and sound waves in solids and liquids has been observed and treated in the scientific literature for a long time (Worzel and Ewing 1948; Pekeris 1948; Ewing et al. 1957). However, in the sub-audible acoustic domain, usually referred to as infrasound (frequencies below 20 Hz), dispersion was recognized only recently (Herrin et al. 2006). There are reports of dispersed signals recorded on infrasound sensors on the passing of surface waves of large earthquakes (Donn and Posmentier 1964; Cook 1971), but the signals in those instances were the result of ground to air coupling, and the dispersion was not related to sound propagation. In the current paper we derive the dispersion equation of an acoustic waveguide and relate it to infrasound observations. Infrasound propagation is controlled by effective sound speed, which relates the effect of temperature (as a consequence of ideal gas law) and wind strength and direction: \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \[V\_{eff}=V\_{T}+n{\cdot}{\nu},\] \end{document} where Veff is the effective sound speed, \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \(V_{T}{\oplus}20\sqrt{T}\) \end{document}; T is the Kelvin temperature; and the dot product n ·ν is the component of wind strength in the direction of the propagation. Throughout the paper when we use the term sound velocity (or sound speed) we actually mean effective sound speed, which will have the wind component in it. The following discussion follows that of Garland (1979). Consider a medium composed of a layer overlain by a half space (Figure 1), separated by an interface, with α′ > α, where α and α′ are the sound velocities in the layer and half …