Optical Theorem for Measuring the Acoustic Extinction Cross Section of Helmholtz Resonators

Abstract

The optical theorem is a powerful tool of scattering theory that directly relates the extinction cross section of a scatterer to its forward scattering amplitude. While widely used in electromagnetism and optics, its application in acoustics has remained limited, primarily due to experimental challenges. These include the finite size of practical sound sources and the stringent requirements for detecting weak scattered signals. In this work, we analyze these limitations and develop a robust methodology for measuring the acoustic extinction cross section under realistic conditions, including non-ideal anechoic environments. The approach is applied experimentally to a Helmholtz resonator in an imperfect anechoic environment with standing-wave resonances. The retrieved extinction cross section exhibits a single pronounced resonance near 2000 Hz. The resonance position, peak magnitude, and spectral lineshape are consistent with full-wave numerical simulations. The results demonstrate that, when combined with appropriate data processing, the optical theorem provides a simple and reliable tool for characterizing acoustic resonators, opening new opportunities for quantitative analysis of acoustic scattering and absorption phenomena.