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

Abstract

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.