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The Transfer Matrix Method in Acoustics

Modelling One-Dimensional Acoustic Systems, Phononic Crystals and Acoustic Metamaterials

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Acoustic Waves in Periodic Structures, Metamaterials, and Porous Media

Part of the book series: Topics in Applied Physics ((TAP,volume 143))

Abstract

The transfer matrix method is a simple but powerful analytical tool used to model acoustic wave propagation in a wide range of one-dimensional problems. In this chapter, we present the method and summarize the most common building blocks encountered in one-dimensional acoustic systems. These include layers of fluids and porous media, ducts and waveguides of different geometries where thermoviscous losses can be accounted for, locally reacting elements such as Helmholtz or quarter-wavelength resonators, viscoelastic plates and membranes, micro-perforated panels or vibrating walls. Several examples are provided, including a multi-layered porous structure for room acoustics, the transmission problem of a double-leaf wall for building acoustics, and the analysis of the dispersion relations of acoustic waves in periodic media and metamaterials using locally resonant elements. Various one-dimensional wave-motion phenomena can be studied using the generalized framework provided by the transfer matrix method such as reflection, transmission, absorption, attenuation and dispersion, as illustrated in the examples.

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Notes

  1. 1.

    Note that \(Z = Z_\mathrm {eff}\), i.e., \({p}/{v_x}=\rho _\mathrm {eff}c_\mathrm {eff}\), only stands for plane waves travelling in an infinite medium.

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Acknowledgements

The authors would like to thank Julien Leng for his useful comments. N.J. acknowledges financial support from Spanish Ministry through grant “Juan de la Cierva - Incorporación” program (IJC2018-037897-I). We acknowledge support from the Metaudible (ANR-ANR-13-BS09-003) and Metaroom (ANR-18-CE08-0021) projects.

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Jiménez, N., Groby, JP., Romero-García, V. (2021). The Transfer Matrix Method in Acoustics. In: Jiménez, N., Umnova, O., Groby, JP. (eds) Acoustic Waves in Periodic Structures, Metamaterials, and Porous Media. Topics in Applied Physics, vol 143. Springer, Cham. https://doi.org/10.1007/978-3-030-84300-7_4

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