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<p>Helmholtz resonance provides a well-established acoustic basis for determining volume via the resonance-frequency–volume relationship. However, frequency-tracking methods are typically too slow for dynamic measurements. We present an alternative physical model, the sound-pressure quality-factor (SPQF) model, which estimates volume in real time from cavity sound-pressure amplitude, avoiding frequency hunting. The model follows from the equations governing the driven, underdamped vibration of the port-air mass. The resonator is excited at its empty-cavity natural frequency with a single-tone drive; inserting a sample reduces the steady-state pressure amplitude, from which displaced volume is inferred. We validate the method with liquid and solid samples in 1-, 2-, and 3-L cavities and in a mechanically adjustable chamber under dynamic conditions. The approach achieved millilitre-level accuracy for solids and relative expanded uncertainty <i>U</i>, <i>k</i> = <i>2</i> &lt; 0.1% of cavity capacity in static tests, and it tracked liquid discharge at ~ 15–20&#xa0;Hz. On the mechanically variable resonator, SPQF tracked piston-driven volume changes for speeds up to 75&#xa0;mm·s⁻<sup>1</sup>, delivering ~ 20 measurements in 1.5&#xa0;s.</p> Graphical Abstract

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Real-Time Cavity Volumetry via Helmholtz Resonance Using Pressure Amplitude: Proof of Concept

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月29日

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  • Mohammad Amin Barzegar,
  • Clive E. Davies,
  • Miles C. E. Grafton

摘要

Helmholtz resonance provides a well-established acoustic basis for determining volume via the resonance-frequency–volume relationship. However, frequency-tracking methods are typically too slow for dynamic measurements. We present an alternative physical model, the sound-pressure quality-factor (SPQF) model, which estimates volume in real time from cavity sound-pressure amplitude, avoiding frequency hunting. The model follows from the equations governing the driven, underdamped vibration of the port-air mass. The resonator is excited at its empty-cavity natural frequency with a single-tone drive; inserting a sample reduces the steady-state pressure amplitude, from which displaced volume is inferred. We validate the method with liquid and solid samples in 1-, 2-, and 3-L cavities and in a mechanically adjustable chamber under dynamic conditions. The approach achieved millilitre-level accuracy for solids and relative expanded uncertainty U, k = 2 < 0.1% of cavity capacity in static tests, and it tracked liquid discharge at ~ 15–20 Hz. On the mechanically variable resonator, SPQF tracked piston-driven volume changes for speeds up to 75 mm·s⁻1, delivering ~ 20 measurements in 1.5 s.

Graphical Abstract