### Abstract

The transmission of acoustic waves through a sequence of alternating layers with random thicknesses but otherwise fixed characteristics is studied by means of the transfer-matrix formalism of one-dimensional disordered chains. The law limNln(TN/N)-() of the exponential decay of the transmission coefficient TN as a function of the number (2N) of layers is determined in a weak- (strong-) disorder regime for an arbitrary (uniform) distribution of layer thicknesses. The localization constant () has a particularly simple form at extreme low and high frequencies. Namely (0)=const×2 with a slope given in terms of physical characteristics of the layers and ()=const defined by a transmission coefficient of a single interface. The predictions are tested by Monte Carlo simulations of a simple model with characteristics of certain rocks. For all frequencies beyond the weak-strong disorder turnover region discrepancies between theoretical and numerical results are merely a few percent.

Original language | English (US) |
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Pages (from-to) | 3358-3363 |

Number of pages | 6 |

Journal | Physical Review A |

Volume | 31 |

Issue number | 5 |

DOIs | |

State | Published - Jan 1 1985 |

Externally published | Yes |

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

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## Cite this

*Physical Review A*,

*31*(5), 3358-3363. https://doi.org/10.1103/PhysRevA.31.3358