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This paper presents an analytical approach of the propagation of an acousticwave through a normally distributed disordered lattice made up of Helmholtzresonators connected to a cylindrical duct. This approach allows to determineanalytically the exact transmission coefficient of a weakly disordered lattice.Analytical results are compared to a well-known numerical method based on amatrix product. Furthermore, this approach gives an analytical expression ofthe localization length apart from the Bragg stopband which depends only on thestandard deviation of the normal distribution disorder. This expression permitsto study on one hand the localization length as a function of both disorderstrength and frequency, and on the other hand, the propagation characteristicson the edges of two sorts of stopbands (Bragg and Helmholtz stopbands). Lastly,the value of the localization length inside the Helmholtz stopband is comparedto the localization length in the Bragg stopband.

Analytical study of the propagation of acoustic waves in a 1D weakly disordered lattice