Related Experiment Video
Updated: Jun 24, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Acoustic Analogy of Quantum Baldin Sum Rule for Optimal Causal Scattering
Sichao Qu1, Zixiong Yu2, Erqian Dong1
1The University of Hong Kong, Department of Mechanical Engineering, Pokfulam Road, Hong Kong, China.
Abstract:
The mass law is a cornerstone in predicting sound transmission loss, yet it neglects the constraints of causal dispersion. Current causality-based theories, such as the Rozanov limit, are applicable only to one-port reflective absorbers. Here, we derive a universal sum rule governing causal scattering in acoustic systems, establishing a rigorous analogy to the Baldin sum rule in quantum field theory. This relation reveals that the integral of the extinction cross section is fundamentally locked by the scatterer's static effective mass and stiffness, which is validated numerically using seminal examples of underwater metamaterials. Furthermore, the proposed sum rule predicts an optimal condition for an anomalously broadened transmission loss bandwidth, as experimentally observed through the spectral shaping effect of an acoustic Fano resonator. Our findings open up an unexplored avenue for enhancing the scattering bandwidth of passive metamaterials.
Related Concept Videos
The Quantum-Mechanical Model of an Atom
The de Broglie Wavelength
Interference and Diffraction
The Bohr Model
Superposition Theorem for AC Circuits
The principle of superposition stipulates that the output of a linear circuit with several concurrent inputs is equivalent to the...
Parseval's Theorem
Interestingly, Parseval's theorem also holds for the trigonometric form of the Fourier series, which expresses a...