  This paper presents an analytical approach of the propagation of an acoustic
wave through a normally distributed disordered lattice made up of Helmholtz
resonators connected to a cylindrical duct. This approach allows to determine
analytically the exact transmission coefficient of a weakly disordered lattice.
Analytical results are compared to a well-known numerical method based on a
matrix product. Furthermore, this approach gives an analytical expression of
the localization length apart from the Bragg stopband which depends only on the
standard deviation of the normal distribution disorder. This expression permits
to study on one hand the localization length as a function of both disorder
strength and frequency, and on the other hand, the propagation characteristics
on the edges of two sorts of stopbands (Bragg and Helmholtz stopbands). Lastly,
the value of the localization length inside the Helmholtz stopband is compared
to the localization length in the Bragg stopband.
