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We analyze the Helmholtz equation in a complex domain. A sound absorbing structure at a part of the boundary is modelled by a periodic geometry with periodicity $\varepsilon>0$. A resonator volume of thickness $\varepsilon$ is connected…

Analysis of PDEs · Mathematics 2020-06-05 Patrizia Donato , Agnes Lamacz , Ben Schweizer

Rim and back geometry determine much of the behavior of sound inside the pot, whose effect on total, produced sound is subtle but discernible. The theory of sound inside a cylinder is reviewed and demonstrated. And previous work on the…

Popular Physics · Physics 2016-08-17 David Politzer

The question of whether there exists an approximation procedure to compute the resonances of any Helmholtz resonator, regardless of its particular shape, is addressed. A positive answer is given, and it is shown that all that one has to…

Spectral Theory · Mathematics 2021-03-04 Jonathan Ben-Artzi , Marco Marletta , Frank Rösler

In this paper, we consider an open tube of diameter $\epsilon>0$, on the side of which a small hole of size $\epsilon^2$ is pierced. The resonances of this tube correspond to the eigenvalues of the Laplacian operator with homogeneous…

Analysis of PDEs · Mathematics 2011-06-17 Romain Joly

Optical field fluctuations in self-defocusing media can be described in terms of sound waves in a 2D photon-fluid. It is shown that, while the background fluid couples with the usual flat metric, sound-like waves experience an effective…

General Relativity and Quantum Cosmology · Physics 2008-12-03 Francesco Marino

Confining sound is of significant importance for the manipulation and routing acoustic waves. We propose a Helmholtz resonator (HR) based subwavelength sound channel formed at the interface of two metamaterials, for this purpose. The…

Applied Physics · Physics 2021-03-31 Yun Zhou , Prabhakar R. Bandaru , Daniel F. Sievenpiper

An analysis is developed linking the form of the sound field from a circular source to the radial structure of the source, without recourse to far-field or other approximations. It is found that the information radiated into the field is…

Mathematical Physics · Physics 2015-05-20 Michael Carley

We investigate the acoustic properties of meta-materials that are inspired by sound-absorbing structures. We show that it is possible to construct meta-materials with frequency-dependent effective properties, with large and/or negative…

Analysis of PDEs · Mathematics 2016-03-18 Agnes Lamacz , Ben Schweizer

Understanding how sound propagates through different media is fundamental to both science and technology. While sound plays a critical role in natural navigation and underlies a wide range of applications - from medical ultrasound to sonar…

Physics Education · Physics 2025-07-30 Helio Takai , Tom Tomaszewski , Jeremy Tomaszewski , Joe Sundermier

We investigate the sound propagation in an air-filled tube periodically loaded with Helmholtz resonators. By tuning the Helmholtz with the Bragg resonance, we study the efficiency of slow sound propagation in the presence of the intrinsic…

Materials Science · Physics 2015-06-18 G. Theocharis , O. Richoux , V. Romero-García , V. Tournat

In this work we have developed a technique for the measurement of the resonance curve of Helmholtz resonators as a function of filling with beads and sands of different sizes, and water as the reference. Our measurements allowed us to…

Classical Physics · Physics 2023-07-06 M. V. Indenbom , S. P. Pogossian

Acoustic black holes represent a special class of metastructures allowing efficient absorption based on the slow sound principle. The decrease of the wave speed is associated with the spatial variation of acoustic impedance, while the…

Over the last few decades, both heat and broadband sound reduction have become increasingly significant as a result of concerns about the environment and noise pollution. In order to address this challenge, we provide a finite element…

In this work we discuss the problem of identifying sound sources from pressure measurements with a Bayesian approach. The acoustics are modelled by the Helmholtz equation and the goal is to get information about the number, strength and…

Numerical Analysis · Mathematics 2019-01-16 Sebastian Engel , Dominik Hafemeyer , Christian Münch , Daniel Schaden

A soundproof window or wall which is transparent to airflow is presented. The design is based on two wave theories of diffraction and acoustic metamaterials. It consists of a three-dimensional array of strong diffraction-type resonators…

Materials Science · Physics 2013-07-02 Sang-Hoon Kim , Seong-Hyun Lee

The 3d volume inside a spherical black hole can be defined by extending an intrinsic flat-spacetime characterization of the volume inside a 2-sphere. For a collapsed object, the volume grows with time since the collapse, reaching a simple…

General Relativity and Quantum Cosmology · Physics 2015-03-25 Marios Christodoulou , Carlo Rovelli

A microscopic description of Hawking radiation in sonic black holes has been recently presented (Giovanazzi S 2005 Phys. Rev. Lett. 94 061302). This exactly solvable model is formulated in terms of one-dimensional scattering of a Fermi gas.…

Other Condensed Matter · Physics 2009-11-11 S. Giovanazzi

Analogue black holes, which can mimic the kinetic aspects of real black holes, have been proposed for many years. The growth of the radial momentum of test particles toward the acoustic horizon is calculated for acoustic black holes in flat…

High Energy Physics - Theory · Physics 2022-04-29 QingBing Wang , Xian-Hui Ge

Sound propagation within certain non-relativistic condensed matter models obeys a relativistic wave equation despite such systems admitting entirely non-relativistic descriptions. A natural question that arises upon consideration of this…

Classical Physics · Physics 2021-10-18 Scott L. Todd , Nicolas C. Menicucci

Resonance is an ubiquitous phenomenon present in many systems. In particular, air resonance in cavities was studied by Hermann von Helmholtz in the 1850s. Originally used as acoustic filters, Helmholtz resonators are rigid-wall cavities…

Physics Education · Physics 2018-12-05 Martín Monteiro , Cecilia Stari , Cecilia Cabeza , Arturo C. Marti
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