Conventional vector-based memory systems rely on cosine or inner product similarity within real-valued embedding spaces. While computationally efficient, such approaches are inherently phase-insensitive and limited in their ability to capture resonance phenomena crucial for meaning representation. We propose Wave-Based Semantic Memory, a novel framework that models knowledge as wave patterns $ψ(x) = A(x) e^{iφ(x)}$ and retrieves it through resonance-based interference. This approach preserves both amplitude and phase information, enabling more expressive and robust semantic similarity. We demonstrate that resonance-based retrieval achieves higher discriminative power in cases where vector methods fail, including phase shifts, negations, and compositional queries. Our implementation, ResonanceDB, shows scalability to millions of patterns with millisecond latency, positioning wave-based memory as a viable alternative to vector stores for AGI-oriented reasoning and knowledge representation.