Hongbin Yu

This study presents a systematic investigation of the 2024 International Young Physicists’ Tournament (IYPT) problem: determining the number of objects in the box solely by the sound produced while shaking the box. We conduct experiments by driving homogeneous balls within a sealed rectangular container using an orbital shaker. By acquiring and analysing acoustic signals generated from collisions, we reveal a fundamental physical characteristic: acoustic signals exhibit clear linear separability in the frequency domain as the ball count varies. Leveraging this physical insight, we developed a machine-learning-based identification algorithm that achieves over 95% accuracy. Unlike purely data-driven models, this physics-informed approach demonstrates remarkable robustness against training data reduction. Extensive experiments confirm the invariance of this linear relationship across various container materials, ball sizes, and packing densities. This work can serve as a modular experimental case for undergraduate physics education, bridging classical mechanics, statistical signal processing, and data science through a cost-effective, non-invasive monitoring solution.