Frequency and amplitude alterations of sound modes in a space-dependent random mass density field

Abstract

We investigate the effect of a space-dependent random mass density field on small amplitude acoustic modes that are settled in a semi-infinite medium of a temperature growing linearly with depth. Using a perturbation method, the dispersion relation is derived in the form of Hill's determinant. Numerical solutions of this equation lead to the following conclusions: (a) a weak random field (with σ eff = 0.05) essentially affects long waves which experience attenuation and a frequency reduction; (b) for a stronger random field (with σ eff = 0.1), high-order sound modes behave as sound waves as they are attenuated and their frequencies are increased; (c) for a sufficiently strong random field (with σ eff = 0.2), mode coupling occurs, as a result of which the dispersive curves cross each other, the sound modes loose their identities, and some modes are amplified. Here σ eff denotes the effective strength of a random field.

Torsional oscillations of longitudinally inhomogeneous coronal loops

“…Here we infer that in comparison to the average mass density case the wave frequency is reduced, but as a result of α 2 1 the frequency reduction is small. This is in disagreement with Fermat's law and with the results of Murawski et al (2004) who showed that sound waves experience frequency increase in a case of a spacedependent random mass density field.…”

“…(23) we find that ∆ω n > 0. This wave frequency decrease, in comparison to the case of an average mass density is now in agreement with Fermat's law and with the results of Murawski et al (2004).…”