Dynamic Frequency Optimization for Underwater Acoustic Energy Transmission: Balancing Absorption and Geometric Diffusion in Marine Environments

The transmission efficiency of underwater acoustic is doubly constrained by absorption attenuation and geometric spreading losses, with the relative interaction between these loss mechanisms exhibiting complex dynamic variations across the frequency spectrum. Achieving dynamic equilibrium between these frequency-dependent loss mechanisms is key to enhancing acoustic energy transmission performance. To address this, this paper proposes a multi-variable coupled acoustic energy transmission model that systematically integrates the cumulative effects of the propagation distance, the geometric configuration of acoustic source arrays, and the interactive influences of critical environmental factors such as the salinity, temperature, and depth to comprehensively analyze the synergistic mechanisms of absorption loss and geometric spreading loss in practical underwater environments. Based on dynamic response analysis in the frequency dimension, the model identifies and determines the optimal working frequency ranges (i.e., dynamic equilibrium points) for maximizing the efficiency of energy transmission under various propagation conditions and environmental configurations. Both theoretical derivations and numerical simulations consistently reveal a frequency band within the low-to-mid frequency range (approximately 20–100 kHz) which is associated with significantly enhanced transmission efficiency under specific parameter settings. These research findings provide a scientific basis and engineering guidance for frequency selection and the structural optimization of underwater acoustic energy systems, offering substantial theoretical value and application prospects that can strongly support the development of acoustic technologies in ocean engineering, resource exploration, and national defense security.