  A periodic assembly of acoustically-rigid blocks (termed 'grating'), situated
between two half spaces occupied by fluid-like media, lends itself to a
rigorous theoretical analysis of its response to an acoustic homogeneous plane
wave. This theory gives rise to two sets of linear equations, the first for the
amplitudes of the waves in the space between successive blocks, and the second
for the amplitudes of the waves in the two half spaces. The first set is solved
numerically to furnish reference solutions. The second set is submitted to
low-frequency approximation procedure whereby the pressure fields are found to
be those for a configuration in which the grating becomes a homogeneous layer
of the same thickness as the height of the blocks in the grating. A simple
formula is derived for the constitutive properties of this layer in terms of
those of the fluid-like medium in between the blocks. The homogeneous layer
model scattering amplitude transfer functions and spectral reflectance,
transmittance and absorptance reproduce quite well the corresponding rigorous
numerical functions of the grating over a non-negligible range of low
frequencies. Due to its simplicity, the homogeneous layer model enables
theoretical predictions of many of the key features of the acoustic response of
the grating.
