Test particle dynamics and oscillatory motion around Kiselev acoustic black hole models

In this paper, we investigate the dynamics of test particles and their oscillatory behavior around Kiselev acoustic Black Hole (BH) models. We illustrate the acoustic geometry, analyze the effective potential governing particle motion, and study the conditions for the existence of Innermost Stable Circular Orbits (ISCOs). In addition, we explore harmonic oscillations as perturbations of circular orbits and derive the corresponding frequencies as measured by both local and distant observers. In this case, the periastron precession provides insight into relativistic corrections to orbital dynamics in this acoustic background. In this context, our results illustrate the structure of particle motion in Kiselev acoustic BHs and contribute to the broader understanding of BH system parameters and their influence, where acoustic spacetimes serve as laboratory models for testing gravitational phenomena.