Resonant frequency shifts induced by a large spherical object in an air-filled acoustic cavity

Abstract

Acoustic resonances are modified when objects are introduced into a chamber. The magnitude of these changes depends on the object position, size, and shape, as well as on its acoustic properties. Here, an experimental study concerning the resonant frequency shifts induced by a solid spherical object in a quasi-one-dimensional air-filled acoustic cavity is reported. It is shown that Leung's theory does not account quantitatively for the observations. A novel and simple approach is proposed, based on the wave equation in a cavity of variable cross section. The results fit more accurately the measured frequency shifts.

The Use of Helmholtz Resonance for Measuring the Volume of Liquids and Solids

“…The larger they are the more efficiently they reflect the incident sound pressure waves. Studies conducted by Barmatz et al [ 15 ], Leung et al [ 16 ] and Cordero and Mujica [ 17 ] used rigid spheres in a ½ wave resonant cavity and found scattering to affect the resonant frequency. However, the Helmholtz resonator frequency is related to the chamber volume not a standing wave within the chamber.…”

Analysis of the resonance frequency shift in cylindrical cavities containing a sphere and its prediction based on the Boltzmann-Ehrenfest principle

“…The resonance frequency shift of a plane-wave mode in a rectangular cavity induced by a spherical solid, with a diameter comparable to the length of the square cross section of the cavity, has been investigated by Cordero and Mujica [9]. Their numerical calculations are in good agreement with experimental results for small spheres compared with the wavelength.…”

A resonance shift prediction based on the Boltzmann–Ehrenfest principle for cylindrical cavities with a rigid sphere

“…8 are consistent with the observations of Cordero and Mujica. 16 They used a sphere 6.35 mm in diameter within a square-section cavity, 6.8 mm in side and 100.0 mm long. It was reported that the differences between measurements of the resonance frequency shift and theoretical results given by Leung's equation were larger at the positions of the velocity antinodes of a pure plane-wave mode than when the sphere was placed at the pressure antinodes.…”

“…16 In this case, the main consideration was the change, due to the presence of the obstacle, of the cross-section area of the region occupied by the acoustic wave. Their theoretical calculations, obtained from a transcendental equation in terms of the confluent Heun function, are in good agreement with experimental results for small spheres compared with the wavelength.…”