This survey provides a comprehensive overview of the emerging field of world models grounded in the foundation of acoustic physical information. It examines the theoretical underpinnings, essential methodological frameworks, and recent technological advancements in leveraging acoustic signals for high-fidelity environmental perception, causal physical reasoning, and predictive simulation of dynamic events. The survey explains how acoustic signals, as direct carriers of mechanical wave energy from physical events, encode rich, latent information about material properties, internal geometric structures, and complex interaction dynamics. Specifically, this survey establishes the theoretical foundation by explaining how fundamental physical laws govern the encoding of physical information within acoustic signals. It then reviews the core methodological pillars, including Physics-Informed Neural Networks (PINNs), generative models, and self-supervised multimodal learning frameworks. Furthermore, the survey details the significant applications of acoustic world models in robotics, autonomous driving, healthcare, and finance. Finally, it systematically outlines the important technical and ethical challenges while proposing a concrete roadmap for future research directions toward robust, causal, uncertainty-aware, and responsible acoustic intelligence. These elements collectively point to a research pathway towards embodied active acoustic intelligence, empowering AI systems to construct an internal "intuitive physics" engine through sound.