The Acoustic Resonance of Rectangular and Cylindrical Cavities

Abstract

An investigation is conducted on the acoustic resonance that develops in rectangular and cylindrical cavities with rigid walls. An analytical model for the small amplitude acoustic perturbations inside an enclosure with rigid walls is developed from classical linerized acoustics. The method is first applied to a rectangular geometry and the normalized mode shapes and frequencies of the first six standing wave modes are given. The results are used to diagnose whether coupling is likely to occur between the first two Rossiter modes and the acoustic standing waves, which may lead to a reinforcement of the flow instability. At the selected test conditions, the method indicates that the second Rossiter mode can couple with the first longitudinal acoustic mode. The acoustic resonant mode predictions for a cylindrical cavity of length to depth ratios 0.71 and 2.5, tested at nearincompressible speeds, suggest that the acoustic resonant modes and the main fluid dynamic instability in the enclosure are sufficiently apart in frequency not to strongly interact with one another. The parametrized analytical solutions developed in this study enable the aero-acoustic engineer to diagnose whether coupling between a given fluid dynamic instability and acoustic resonance is likely to affect a rectangular or cylindrical cavity component.

Synergetic Resonance Matching of a Microphone and a Photoacoustic Cell

“…In addition, the diameter of the main cavity was a major factor to determine the resonance characteristics whereas the height of the main cavity had little impact; thus, we investigated the radial and azimuthal mode of resonance in the main cavity. Solving the eigenmode and eigenfrequency of the Helmholtz wave equation in a simple one-end open cylindrical cavity [25] gives the resonance frequency of radial and azimuthal modes of the following form: $f(l,m)=\frac{c}{\pi }\frac{\alpha (l,m)}{D},$ where c is the speed of sound, α(l,m) is a cylindrical cavity natural circular wavenumber, D is the diameter of the cylindrical cavity, and l and m are the mode number of radial and azimuthal resonance, respectively. The first five modes of radial and azimuthal resonance frequencies (no longitudinal mode, i.e., n = 0) are in the order of α (1,0), α (1,1), α (1,2), α (2,0), and α (1,3), which are 1.2556, 2.4048, 3.5180, 4.0793, and 5.5201.…”

“…The solution of the Helmholtz equation at an acoustic resonance frequency in the radial mode results in an acoustic pressure distribution according to the following simplified relation, where the first order Bessel function is J m , the radial coordinate r , and the angular coordinate θ [25]: $p_{l,m}false(r,\theta false)\propto J_{m}false(r{\alpha }_{l,m}/Rfalse)\cos false(m\theta -{\varphi }_{m}false).$…”

Deterministic Model of Acoustic Wave Propagation in a Cavity

“…2, whereṽr is the radial velocity. Atr = 0, the acoustic particle velocity must have a finite value [6].…”

“…A deterministic model, using duct modal propagation, is useful for evaluating how different cavity geometries affect the propagation of acoustic pressure waves to the bottom of the cavity. Previous work in this area has primarily focused on predicting cavity modes [6]. This insight will be leveraged to determine how parameters such as lining material and cavity shape reduce the amount of hydrodynamic energy from the boundary layer that the microphone measures.…”

Calculation of the offset amplitudes in the Helmholtz resonators’ throat part at the resonance frequencies

“…При експериментальних дослідженнях було виявлено ряд додаткових резонансів. Як було зазначено у [3], насправді, варіанти розрахунку додаткових резонансних частот існують [4], але є досить громіздкими, оперують великим числом змінних [5].…”