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Approximate theory of acoustic waveguide of metamaterials

Published online by Cambridge University Press:  12 April 2011

CHIANG C. MEI  and
YING-HUNG LIU
CHIANG C. MEI*
Affiliation:
Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139-4307, USA
YING-HUNG LIU
Affiliation:
Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139-4307, USA
*
†Email address for correspondence: ccmei@mit.edu
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Abstract

We theoretically examine the propagation of sound in a waveguide bounded by a metamaterial formed by an array of small Helmholtz resonators. The field equation is shown to be similar to that governing sound in a bubbly liquid. The effects of dissipation on the wave dispersion are examined. In particular, it is shown that the energy in a monochromatic wave train is not transported by the real part of the complex group velocity unless dissipation is absent. We further derived the envelope equation and show that in a one-dimensional waveguide, energy is transported forward despite the backward motion of the envelope peak.

JFM classification

Acoustics: Acoustics

Information

Type
Papers
Information
Journal of Fluid Mechanics , Volume 678 , 10 July 2011 , pp. 203 - 220
Copyright
Copyright © Cambridge University Press 2011

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References

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