Abstract
Acoustic bandgaps are ranges of frequencies in a medium at which sound cannot propagate. The classical model often used in solid-state physics is that of a 1D chain of masses and springs, the analysis of which can predict the speed of sound in a material, its dispersive nature, and any forbidden sound frequencies. We use a lumped parameter model for the acoustic inertance and compliance of pipes and cavities to create 1D monatomic, diatomic, and triatomic chains that demonstrate these acoustic bandgaps experimentally. The ease of 3D-printing these devices means that this method can be used to explore bandgap engineering in acoustic systems for low-frequency applications and used as a simple platform for creating acoustic analogs of the solid-state physical problem. Furthermore, it allows us to explore novel polyatomic behavior (e.g., tetratomic and pentatomic) and could ultimately find use as filters for experiments requiring miniaturized acoustic isolation.
Highlights
An acoustic bandgap in a material is defined as a band of frequencies at which a sound wave cannot propagate—instead, the wavenumber of the wave solution is imaginary—and rather than propagating, acoustic excitations decay
The classical model often used in solid-state physics is that of a 1D chain of masses and springs, the analysis of which can predict the speed of sound in a material, its dispersive nature, and any forbidden sound frequencies
Bandgaps can be created in bespoke materials to create the so-called acoustic metamaterials1,2 that constitute an exciting area of research in which the material structure, rather than material properties, shapes the behavior of sound propagation
Summary
An acoustic bandgap in a material is defined as a band of frequencies at which a sound wave cannot propagate—instead, the wavenumber of the wave solution is imaginary—and rather than propagating, acoustic excitations decay. It is well known that in this model, for long wavelengths, the speed of sound is constant and non-dispersive, and as the wavelength decreases toward the scale of an individual mass-spring system, the speed of sound (or ∂ω/∂k) decreases to zero These models are solved using an ansatz that solutions are of the form u(t, x) = Aei(k+iδ)x−iωt, from which both the propagating wavenumber k and an evanescent decay wavenumber δ can be derived to create dispersion curves. Our objective is to explore acoustic analogs of these systems that have dispersive features at practical relevant audible frequencies rather than the terahertz frequencies found in solid-state physics models. We do this for a variety of reasons—pedagogical and investigative. We conclude with an experimental demonstration of three devices that reproduce the bandgap properties of modeled systems with practical audible acoustic frequencies
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