Related papers: Computing the Sound of the Sea in a Seashell
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…
The volume of air that goes in and out of a musical instrument's sound hole is related to the sound hole's contribution to the volume of the sound. Helmholtz's result for the simplest case of steady flow through an elliptical hole is…
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…
We present a multiscale approach for identifying features in ocean beds by solving inverse problems in high frequency seafloor acoustics. The setting is based on Sound Navigation And Ranging (SONAR) imaging used in scientific, commercial,…
The study of the resonances of the Helmholtz resonator has been broadly described in previous works. Here, for a simple tube-shaped two dimensional resonator, we can perform a careful analysis of the transition zone where oscillations start…
A boundary integral formulation for the solution of the Helmholtz equation is developed in which all traditional singular behaviour in the boundary integrals is removed analytically. The numerical precision of this approach is illustrated…
Following the ideas of von Helmholtz and Plomp-Levelt, an algorithm for calculating the total dissonance of complex sounds, free from logical inconsistencies and useful for comparing different chords, is proposed. The method is tested by…
This study develops a ray technique for determining the resonance frequencies of triangular membranes. The technique is demonstrated for homogenous rectangular and triangular membranes with fixed boundaries. Where possible, the results are…
The human cochlea is a remarkable device, able to discern extremely small amplitude sound pressure waves, and discriminate between very close frequencies. Simulation of the cochlea is computationally challenging due to its complex geometry,…
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…
An averaging method for getting uniformly valid asymptotic approximations of the solution of hyperbolic systems of equations is presented. The averaged system of equations disintegrates into independent equations for non-resonance systems.…
We investigate a numerical method for studying resonances in quantum mechanics. We prove rigorously that this method yields accurate approximations to resonance energies and widths for shape resonances in the semiclassical limit.
A fully implementable filtered polynomial approximation on spherical shells is considered. The method proposed is a quadrature-based version of a filtered polynomial approximation. The radial direction and the angular direction of the…
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…
In this paper, we develop a numerical method for the computation of (quasi-)resonances in spherical symmetric, heterogeneous Helmholtz problems with piecewise smooth refractive index. Our focus lies in resonances very close to the real…
Under a geometric assumption on the region near the end of its neck, we prove an optimal exponential lower bound on the widths of resonances for a general two-dimensional Helmholtz resonator. An extension of the result to the n-dimensional…
We consider the problem of approximating a function using Herglotz wave functions, which are a superposition of plane waves. When the discrepancy is measured in a ball, we show that the problem can essentially be solved by considering the…
From ancient to modern times, acoustic structures have been used to control the propagation of acoustic waves. However, the design of the acoustic structures has remained widely a time-consuming and computational resource-consuming…
We present a novel neural network architecture for the efficient prediction of sound fields in two and three dimensions. The network is designed to automatically satisfy the Helmholtz equation, ensuring that the outputs are physically…
The solution of the Helmholtz equation in optical semiclassic approximation is associated with the calculation of ray paths and matrices of variations. The transformation rules for elements of matrices on the boundaries of the waveguide are…